tag:blogger.com,1999:blog-91699229115993010792024-03-17T10:42:43.635-07:00Eddie's Math and Calculator BlogA blog is that is all about mathematics and calculators, two of my passions in life. Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comBlogger1615125tag:blogger.com,1999:blog-9169922911599301079.post-23037335093524670052024-03-17T00:00:00.000-07:002024-03-17T00:00:00.352-07:00 Casio fx-9750GIII and fx-CG 50: Playing Games with the Probability Simulation Mode<p><span style="font-family: arial; font-size: medium;"><b>Casio fx-9750GIII and fx-CG 50: Playing Games with the Probability
Simulation Mode</b></span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgekHSSXeL7u-jYjotjdtDYkyO_Yc93ekjOsCrN4EcTP_z1sFAVPy__6bT1SxZVh37VSGyTLG-8Lj4fjHV3NCdrj1FL2ByBTexOlLse3u_F15knwUxSMX-b7Q2fogGIi-DJsW6mPjt_Wy1OBeRAubcVEDP-SiIrfFWYO9416UNPNtOY5cj9mUBlB1J0QY4/s853/fx-cg%2050%20probability%20app%20front.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="303" data-original-width="853" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgekHSSXeL7u-jYjotjdtDYkyO_Yc93ekjOsCrN4EcTP_z1sFAVPy__6bT1SxZVh37VSGyTLG-8Lj4fjHV3NCdrj1FL2ByBTexOlLse3u_F15knwUxSMX-b7Q2fogGIi-DJsW6mPjt_Wy1OBeRAubcVEDP-SiIrfFWYO9416UNPNtOY5cj9mUBlB1J0QY4/w640-h228/fx-cg%2050%20probability%20app%20front.jpg" width="640" /></a></div><br /><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
Probability Simulation add-in has six types of probability
simulations:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Coin Toss</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Dice Roll</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Spinner</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Marble Grab</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Card Draw</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Random Numbers</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
add-in application is available for the following calculators:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Casio fx-9750GIII and fx-9860GIII (and Graph 75/85/95 series, Graph
35+ E II)</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Casio fx-CG 10/20 and fx-CG 50 (and Graph 90+E)</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Casio fx-9860G
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">I
believe on the fx-9750GIII and fx-9860GIII, the Probability
Simulation Add-In is available out of the box. For others, the
add-in can be downloaded through Casio’s Worldwide Education
Website: <a href="https://edu.casio.com/download/index.php">https://edu.casio.com/download/index.php</a>.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Let’s
look at three ways we can use the Probability Simulation add-in in
games of chance. This is a great app when you don’t have a pair of
dice, playing cards, or a bag of marbles around.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">In
the Set Up menu, there is an option for seed from 1 to 99999.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><i>Screen shots are from the fx-CG 50.</i></span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Interaction
with Other Modes</span></b></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
Data can be stored into global lists 1-26. Lists in these Casio
calculators contain only numerical information. Numerical codes are
used for card suits and face cards.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">*
There are no commands from the Add-In that can be used in
programming. The simulation is mean to be a stand-alone app.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Drawing
a Poker Hand</span></b></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXOUgTEqSSrfHER4DqDHYSnoNWtHjFvDKrJzCNfk14sMlmM2Sv1uzTh58lqRP-HuU64SFTbfjPoy73NZE_2xju1Pf2yMZx9TFl8kE1mo8t2d5q2TIS8MUmBTWiWgSF4vqeB-7A1efPWSgPzkDjBB7pkYKrdnpzNbiKAB2OgdohKjKSamyLJNHK2scASjk/s1259/drawing%20a%20poker%20hand%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="497" data-original-width="1259" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXOUgTEqSSrfHER4DqDHYSnoNWtHjFvDKrJzCNfk14sMlmM2Sv1uzTh58lqRP-HuU64SFTbfjPoy73NZE_2xju1Pf2yMZx9TFl8kE1mo8t2d5q2TIS8MUmBTWiWgSF4vqeB-7A1efPWSgPzkDjBB7pkYKrdnpzNbiKAB2OgdohKjKSamyLJNHK2scASjk/w640-h252/drawing%20a%20poker%20hand%201.jpg" width="640" /></a></div><br /><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE4IfzKnoiO-0HY-GUeEt3NH13JIbrAS0VvErnwrydAw4TmDXD2EQogB4xtN7-vncMqa2wx4ie2iQPOoKyUOm36kgjicUXw5mrWSdLUfkVfV_cgQLDYYP1g5bjOgfzIFpJ_b-pt32Ofonay-jqSp8EQjQ5hVkiI5HApUgBQndpsMa6D2AsVREBliY1_pA/s1261/drawing%20a%20poker%20hand%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="509" data-original-width="1261" height="258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE4IfzKnoiO-0HY-GUeEt3NH13JIbrAS0VvErnwrydAw4TmDXD2EQogB4xtN7-vncMqa2wx4ie2iQPOoKyUOm36kgjicUXw5mrWSdLUfkVfV_cgQLDYYP1g5bjOgfzIFpJ_b-pt32Ofonay-jqSp8EQjQ5hVkiI5HApUgBQndpsMa6D2AsVREBliY1_pA/w640-h258/drawing%20a%20poker%20hand%202.jpg" width="640" /></a></div><br /><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: large;">From
the main screen, press F5 for Card Draw. To simulate poker, go into
set up by pressing [SHIFT] {SET UP}. We can set either a 52 playing
card deck, which is the standard deck without Jokers, or a reduced
deck of 32 cards (sevens through Aces only). We don’t want
Replacement, so turn that off. Press [ EXIT ] to go back to the
simulation.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">To
draw a single card, press [ F1 ]. To draw multiple cards, press [ F2
] for { +n }. At the prompt, press [AC/ON] and enter the number of
cards.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">We
will have to memorize the cards or note the down on paper or another
writing device.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">To
save the cards drawn, select [ F3 ] (STORE). There are three lists:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Draw:
Draw number</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Value:
Card value. 1 = Ace, 11 = Jack, 12 = Queen, 13 = King</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Suit:
1 = Heart, 2 = Club, 3 = Spade, 4 = Diamond</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Lists
can be allocated to the global list variables List 1 to List 26.
Press [ F6 ] { EXE } to store the cards. Storing results works
similarly in other applications.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Rolling
Dice in Adventure Games</span></b></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;"><br /></span></b></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXKUktrhhwSSTwWr9WQgkJOseUCBjskdH28tI0CKmt3YthEOQxQkdRXOGN5ZoTiFkmLv7h5EfScD3MmXt8gBkRFBO2Rdhk242lCD8TSK6mh3Opry_wcgvEfNPTtQ87g78QcYsFVuD-7kq4ebG7r0d16qSCclOI_um3POncMHIJvmHP4Pd9di_CrmKRYEU/s1261/drawing%20a%20poker%20hand%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="509" data-original-width="1261" height="258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXKUktrhhwSSTwWr9WQgkJOseUCBjskdH28tI0CKmt3YthEOQxQkdRXOGN5ZoTiFkmLv7h5EfScD3MmXt8gBkRFBO2Rdhk242lCD8TSK6mh3Opry_wcgvEfNPTtQ87g78QcYsFVuD-7kq4ebG7r0d16qSCclOI_um3POncMHIJvmHP4Pd9di_CrmKRYEU/w640-h258/drawing%20a%20poker%20hand%202.jpg" width="640" /></a></div><br /><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">In
adventure and fantasy games such as Dungeon and Dragons, sometimes
dice beyond the standard six-sided die is needed. The Dice Roll (F2
from the Main Menu) has dice that are four-sided, six-sided,
eight-sided, twelve-sided, and twenty-sided. Up to three dice can be
thrown at once.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">A
Simple Lottery</span></b></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgozF5avBRHjADRRwwnJMypLyPN7NQglnLER6cYRxEA-UBXaJsqJv7GklZzE5ixszMlsBdnjoEzs4tXITKIoF8xnY49UO2lUJlJRXs87pqr3OV91bKz6SHt82W2cD5Dc9CiZGyJs1W9F50yIZhyphenhyphenIWmG65hAj6GCwqPCyscHi9vToekI_n6oTjJz4aJ96xY/s1257/a%20simple%20lottery.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="491" data-original-width="1257" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgozF5avBRHjADRRwwnJMypLyPN7NQglnLER6cYRxEA-UBXaJsqJv7GklZzE5ixszMlsBdnjoEzs4tXITKIoF8xnY49UO2lUJlJRXs87pqr3OV91bKz6SHt82W2cD5Dc9CiZGyJs1W9F50yIZhyphenhyphenIWmG65hAj6GCwqPCyscHi9vToekI_n6oTjJz4aJ96xY/w640-h250/a%20simple%20lottery.jpg" width="640" /></a></div><br /><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Random
integers from 0 to 99 can be drawn with the Random Numbers. Again,
the set up menu is the key. For the lottery, turn the Repeat option
off. Above are four draws from a simple lottery from 63 numbers.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">This
has been a look at Casio’s Probability Simulation Add-In. Until
next time,</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Eddie</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><br />
</p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-81940941809151909222024-03-16T00:00:00.000-07:002024-03-16T00:00:00.242-07:00DM42 and DM41X: Timing Programs<p><b><span style="font-family: arial; font-size: medium;">DM42 and DM41X: Timing Programs</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">How
Long Does it Take?</span></b></p>
<p class="western" style="line-height: 150%;"><span style="font-family: arial; font-size: medium;">There is a convenient way of timing programs on the Swiss Micros DM42
and DM41X. This is accomplished by the TIME function. The TIME
function returns the time, initially shown in HH:MM:SS format. HH
represents hours, MM represents minutes, and SS represents seconds.
The time is stored internally in HH.MMSS format.
</span></p><p class="western" style="line-height: 150%;"><span style="font-family: arial;"><span style="font-size: medium;">We will also use the
HMS- function. The HMS- subtracts two time values in HH.MMSS format.</span></span></p><p class="western" style="line-height: 115%; margin-bottom: 0in;">
</p><p class="western" style="line-height: 150%;"><span style="font-family: arial;"><span style="font-size: medium;">A</span></span><span style="font-family: arial; font-size: large;">
format that time the performance of an algorithm:</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">TIME
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">STO
## (store in any variable desired)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">...</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">[main
code here]</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">…</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">TIME</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">RCL
## (recall time stored in the beginning)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">HMS-</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">“TIME=”
(shows the time using a message, optional)
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">ARCL
ST X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">AVIEW
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">RTN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The elapsed time is in HH.MMSS format.</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">One
word of caution, I would not use this method if you plan to run the
test and midnight (12:00 AM or 0:00 hours) comes in between
execution.
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Example
Code</span></b></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Here
is an example program that measure long a loop takes. In the
example, the loop requires to display the x and y values for the
function:</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">y =
2/5 × ln((x + 1)^2 ÷ 5) for x = 0 to 25.</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><u><span style="font-family: arial; font-size: medium;">Swiss
Micros DM41X Code</span></u></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">01
LBL ^T TIMETST</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">02
0.025</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">03
STO 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">04
TIME
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">05
STO 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">06
LBL 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">07
RCL 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">08
INT</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">09
^T X=</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">10
ARCL X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">11
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">12
PSE</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">13
XEQ 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">14
^T Y=</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">15
ARCL X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">16
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">17
PSE</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">18
ISG 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">19
GTO 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">20
TIME</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">21
RCL 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">22
HMS-</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">23
^T TIME=</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">24
ARCL X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">25
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">26
RTN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">27
LBL 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">28
1</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">29
+</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">30
X↑2</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">31
5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">32
/</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">33
LN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">34
2</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">35
*</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">36
5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">37
/</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">38
RTN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><u><span style="font-family: arial; font-size: medium;">Swiss
Micros DM42 Code</span></u></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">00
{75-byte Prgm}</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">01
LBL “TIMETST”</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">02
0.025</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">03
STO 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">04
TIME
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">05
STO 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">06
LBL 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">07
RCL 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">08
IP</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">09
“X=”</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">10
ARCL ST X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">11
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">12
PSE</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">13
XEQ 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">14
“Y=”</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">15
ARCL ST X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">16
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">17
PSE</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">18
ISG 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">19
GTO 00</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">20
TIME</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">21
RCL 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">22
HMS-</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">23
“TIME=”</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">24
ARCL ST X</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">25
AVIEW</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">26
RTN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">27
LBL 01</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">28
1</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">29
+</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">30
X↑2</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">31
5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">32
÷</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">33
LN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">34
2</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">35
×</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">36
5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">37
÷</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">38
RTN</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
results that I have:</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">DM41X
(SN 00843): 0.0049 (49 seconds)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">DM42
(SN 03911): 0.0053 (53 seconds)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">For
reference, here are the values (rounded to 4 digits):</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<table cellpadding="0" cellspacing="0" style="width: 100%;">
<colgroup><col width="128*"></col>
<col width="128*"></col>
</colgroup><tbody><tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western">
<b><span style="font-family: arial; font-size: medium;">X</span></b></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western">
<b><span style="font-family: arial; font-size: medium;">Y</span></b></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
-0.6438</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
-0.0893</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
2</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0.2351</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
3</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0.4653</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
4</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0.6438</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
5</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0.7896</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
6</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
0.9130</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
7</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.0198</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
8</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.1140</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
9</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.1983</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
10</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.2745</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
11</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.3442</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
12</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.4082</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
13</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.4675</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
14</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.5227</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
15</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.5743</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
16</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.6228</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
17</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.6685</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
18</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.7118</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
19</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.7528</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
20</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.7918</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
21</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.8291</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
22</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.8646</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
23</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.8987</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
24</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.9313</span></p>
</td>
</tr>
<tr valign="top">
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
25</span></p>
</td>
<td style="border: none; padding: 0in;" width="50%"><p align="center" class="western"><span style="font-family: arial; font-size: medium;">
1.9627</span></p>
</td>
</tr>
</tbody></table>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">I
hope you find this helpful. Take care and until next time,</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Eddie</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"></p><p class="western" style="line-height: 150%; margin-bottom: 0in;">
<span style="font-family: arial; font-size: medium;"><span style="color: black;">All original content copyright, © 2011-2024.
Edward Shore. Unauthorized use and/or unauthorized distribution for
commercial purposes without express and written permission from the
author is strictly prohibited. This blog entry may be distributed
for noncommercial purposes, provided that full credit is given to the
author. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><br />
</p><br /><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-33254471333828747862024-03-14T00:00:00.000-07:002024-03-14T00:00:00.130-07:00Spotlight: Casio fx-6500G<p><span style="font-family: arial; font-size: medium;"> </span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;">
<span style="color: black; font-family: arial; font-size: medium;"><b>Spotlight: Casio fx-6500G</b></span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">For
my birthday, I present a review of the Casio fx-6500G.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Of-EpnZqKk8Fs4sTx3jv6V-r4qbzh6_09dh0sWcuF0EfUJ1JrwSSvFqWd7StP0njJEXGCjlFv4e8qfbY2oSXJt3oHLOSRVsG87P5qa8nH6-eDquo2XQu8soVC1PeTSN-5sMvTzjHpWduMFL_TmTe-YDu1UQ0gjvf1RldH52tPsrfe1x4FrxP6w4a4Fs/s4624/my%2047th%20birthday%20screen.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0Of-EpnZqKk8Fs4sTx3jv6V-r4qbzh6_09dh0sWcuF0EfUJ1JrwSSvFqWd7StP0njJEXGCjlFv4e8qfbY2oSXJt3oHLOSRVsG87P5qa8nH6-eDquo2XQu8soVC1PeTSN-5sMvTzjHpWduMFL_TmTe-YDu1UQ0gjvf1RldH52tPsrfe1x4FrxP6w4a4Fs/w480-h640/my%2047th%20birthday%20screen.jpg" width="480" /></a></div><br /><span style="font-family: arial; font-size: medium;"><br />
</span><p></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;"><b>Quick
Facts</b></span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Model:
fx-6500G</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Company:
Casio</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Timeline:
1986 – 1988</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Type:
Graphing Scientific Calculators</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Power:
3 x CR2032</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Programming
Memory: 486 steps at default</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Number
of Memory Registers: 26 at default</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Screen
Size: 96 x 32 pixels</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Graph
Types: Function, Scatter plot, Histogram, Linear Regression Plot,
Point Plot</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">Linear
Regression </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Base
Operations and Logic Functions</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Hyperbolic
Functions</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p><p class="western" style="line-height: 150%; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEb7-RR97bOtAd2Dv_Eh5CqW84fmdZhyphenhyphenzwXOpo1CbMhgnyV8csBPAwNzLhHibrSvl2uhzQU6MWONnqM2ksuQrwkUH5TqKL_nMbnj6QiEB8mmGRHQCWHrgEkCCDwPwjFW99c1rCPudWPdB_VJQnAf_wQJmw9C8tZarpoZXlgo3oZWBP4iJ2OZr3pacZ5kw/s4624/maximum%20memory.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEb7-RR97bOtAd2Dv_Eh5CqW84fmdZhyphenhyphenzwXOpo1CbMhgnyV8csBPAwNzLhHibrSvl2uhzQU6MWONnqM2ksuQrwkUH5TqKL_nMbnj6QiEB8mmGRHQCWHrgEkCCDwPwjFW99c1rCPudWPdB_VJQnAf_wQJmw9C8tZarpoZXlgo3oZWBP4iJ2OZr3pacZ5kw/w480-h640/maximum%20memory.jpg" width="480" /></a></div><br /><span style="font-family: arial; font-size: medium;"><br /></span><p></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;"><b>Screen
Sizes and Memory of Casio’s Early Calculators</b></span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<table cellpadding="4" cellspacing="0" style="width: 665px;">
<colgroup><col width="213"></col>
<col width="214"></col>
<col width="213"></col>
</colgroup><tbody><tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">fx-7000G (1985)</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="214"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">422 bytes, up to 78 registers</span></p>
</td>
<td style="border: 1px solid #000000; padding: 0.04in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">96 x 64 pixels</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">fx-6500G (1986)</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="214"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">486 bytes, up to 86 registers</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">96 x 32 pixels</span></p>
</td>
</tr>
<tr valign="top">
<td height="21" style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">fx-7500G (1988)</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="214"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">4006 bytes, up to 526 registers</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">96 x 64 pixels</span></p>
</td>
</tr>
<tr valign="top">
<td height="20" style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">fx-6300G (1991)</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="214"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">400 bytes, up to 76 registers</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="213"><p class="western">
<span style="color: black; font-family: arial; font-size: medium;">40 x 23 pixels</span></p>
</td>
</tr>
</tbody></table>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">(measures
from rskey.org, Casio fx-6300G manual, Casio fx-7500G manual) </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-VgtfzzzLdS_PQ67aBGCKET6zjbrZqwsutAEI7jgv6Y9RUOAq_vozz1A-bydlmrXD5zU7qxpBy5X4bDB67Ovd658aqNOHRXnZu4hk6-dPy3ZV4DchwLuLUI3wAeVdPPnqwENrFV0G9VMePOtDeH1ZebGWibjIETlkVsuGaa7VEXDGq0pvi9d9WBTYobc/s4624/graph%20of%20sine%20and%20cosine.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-VgtfzzzLdS_PQ67aBGCKET6zjbrZqwsutAEI7jgv6Y9RUOAq_vozz1A-bydlmrXD5zU7qxpBy5X4bDB67Ovd658aqNOHRXnZu4hk6-dPy3ZV4DchwLuLUI3wAeVdPPnqwENrFV0G9VMePOtDeH1ZebGWibjIETlkVsuGaa7VEXDGq0pvi9d9WBTYobc/w480-h640/graph%20of%20sine%20and%20cosine.jpg" width="480" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLJMtylDLgxuYBYwyTDdxbqXiVsIRgTS8dBjjw-X4kftHU498RPbIRZU2ik7OGWJI2Qu3AG1yeS8Bt-5vYi1JgFxBZlQz4RvF2QruybrjNBaPGFo39CnkGCyDfffBhuoGnC4W5WN_H_iI74CFYTfsVL4TLLtwGR3n4bO9URZQEZ-9uc7i3tyCxBEQuLOU/s4624/in%20base%20mode.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLJMtylDLgxuYBYwyTDdxbqXiVsIRgTS8dBjjw-X4kftHU498RPbIRZU2ik7OGWJI2Qu3AG1yeS8Bt-5vYi1JgFxBZlQz4RvF2QruybrjNBaPGFo39CnkGCyDfffBhuoGnC4W5WN_H_iI74CFYTfsVL4TLLtwGR3n4bO9URZQEZ-9uc7i3tyCxBEQuLOU/w480-h640/in%20base%20mode.jpg" width="480" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijLDJJ-mw1lBxKG4xP2zQYwd2wR_Y_VarpCuOYesDkxWldRFmjSYM3bAjIv53m5hZCoaTKU_dUQ6mJTXsDZ1uDoo7FbsWkIg1-oWgoxE1sr-F9MyVPlShkPKMYpDuNejkxPx91VqPlMltWlZKOcW9Gr1AdYJ8eCVkdgwp0u4iOhvXzFUmHN5rWc0gNvEw/s4624/polar%20to%20rec%20conversion.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijLDJJ-mw1lBxKG4xP2zQYwd2wR_Y_VarpCuOYesDkxWldRFmjSYM3bAjIv53m5hZCoaTKU_dUQ6mJTXsDZ1uDoo7FbsWkIg1-oWgoxE1sr-F9MyVPlShkPKMYpDuNejkxPx91VqPlMltWlZKOcW9Gr1AdYJ8eCVkdgwp0u4iOhvXzFUmHN5rWc0gNvEw/w480-h640/polar%20to%20rec%20conversion.jpg" width="480" /></a></div><br /><span style="font-family: arial; font-size: medium;"><br />
</span><p></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Other
Features</span></b></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Like
the other early Casio graphing calculators, including the fx-7000G,
fx-7500G, and later the fx-6300G, the fx-6500G has the a similar
structure.
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
screen of the fx-6500G is just as wide of the screens of the fx-7000G
and fx-7500G, but half of the height. The screen of the fx-6500G is
still bigger than the fx-6300G and graphs take the entire screen,
which I appreciate.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">There
are four statistical modes:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">SD1:
single-variable statistics analysis mode</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">SD2:
single-variable statistics graphics mode for Histograms, data lines,
and normal curves</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">LR1:
linear regression analysis mode, with the regression equation y = A
+ Bx</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">LR2:
linear regression graphics mode for scatter plots and linear
regression trend lines</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">The
defragment mode ( [ MODE ] [ . ] {Defm}) can allow an additional 60
registers at the expense of programming steps. Each new </span><span style="color: black;">register
costs 8 programming steps. Array registers are accessed in the
format A[#], where A is the letter of memory and # is the number of
registers away from the variable. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">For
example:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">A[0]
accesses A</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">A[1]
accessed B</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">A[2]
accesses C</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">A[25]
accesses Z</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">A[26]
accessed the first expanded memory, the same as Z[1]</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">#
can be a negative integer. Array-type memories allow for indirect
registers. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">The
programming command set is relatively simple, and most of it has
remained throughout the entire Casio graphing and programming
calculator set:</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">There
are 10 program slots: P0 through P9. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">:
separates program lines from each other. The carriage return by
pressing [ EXE ] also terminates the line. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">◢
is the run/stop symbol. Any quoted text or numeric value is shown
as the calculator stops. Press [ EXE ] to continue. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">⇒
is the jump command and is used for quick If-Then-Else structures.
The syntax is: </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">condition
⇒ do if the condition is true : (or ◢) jump to here if the
condition is false.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Goto
and Lbl: goto and label. There are ten labels available in each
for each program: Lbl 0 through Lbl 9.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Prog:
Prog executes another program as a subroutine. An implied “return”
is automatically executed at the end of program.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Isz:
Increment and skip. Adds 1 to a variable and skips the next
command if the new value is 0.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Isz
variable : do if var=var+1≠0 is true : (or ◢) skip to here if
the var=var+1=0</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Dsz:
Decrement and skip. Subtracts 1 from a variable’s value and skips
the next command if the new value is 0. If find Dsz particularly
useful in simple For-Next loops.</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Dsz
variable : do if var=var-1≠0 is true : (or ◢) skip to here if
the var=var-1=0</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><b><span style="color: black; font-family: arial; font-size: medium;">Final
Thoughts</span></b></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">The
calculator looks nice and clean. The fx-6500G offers all of the
features of the fx-7000G and fx-7500G (and fx-6300G less the
fractions) in a scientific calculator size. I like the fact the
graphs do fill the entire screen. Programs and calculation modes
have up to four lines. The fx-6500G is the way to handle a
smaller-sized graphing calculator, which makes it a very sought,
harder to find, calculator. </span>
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Eddie</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 150%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author. </span>
</p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-39329987199852177732024-03-10T00:00:00.000-08:002024-03-10T00:00:00.134-08:00Fun with the TI-81 (March 2024 Edition)<p></p><p class="western"><b><span style="font-family: arial; font-size: medium;">
Fun with the TI-81 (March 2024 Edition)</span></b></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br /></span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLXuWUcSPeAgzt-c0cfOMbrurQ02NP7X09OjQmQdzqKYkAz1-wtNkXsX8-XhrQLW6SrQZPjI72AHWmCE0SzzFvHghXl97ocrK8dk7ccD0kr3akEatKt5z6qMphEYQ9xidRx-xHtBKekXYTezfrFaxlHpxVWlBGDEn42uLIbtgj2YINUB4l5Vw0zW02F_w/s2206/TI-81%20Splash%20Screen.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial; font-size: medium;"><img border="0" data-original-height="1459" data-original-width="2206" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLXuWUcSPeAgzt-c0cfOMbrurQ02NP7X09OjQmQdzqKYkAz1-wtNkXsX8-XhrQLW6SrQZPjI72AHWmCE0SzzFvHghXl97ocrK8dk7ccD0kr3akEatKt5z6qMphEYQ9xidRx-xHtBKekXYTezfrFaxlHpxVWlBGDEn42uLIbtgj2YINUB4l5Vw0zW02F_w/w640-h424/TI-81%20Splash%20Screen.jpg" width="640" /></span></a></div><span style="font-family: arial; font-size: medium;"><br /></span><p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><b><span style="font-family: arial; font-size: medium;">TI-81 SCATTER</span></b></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1rnnbdx984EbIkjlbzyJNSFATdhaH4JP6c5d427XLJp4qC9aEvmYujnW3Nsx5qahCvEYpuELbtAmBhIzXx4BYJmfdAMKDZp8uNUZ66bT2RjIvyF1OLHdJn_HZxLxi48Z7k5rNczZW4y8R6niB7iKSOmd2SqwVGPDkEXLEPzBiQYb3jGNWjEEcvGF2Pzo/s2204/TI-81%20XY%20Graph.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1567" data-original-width="2204" height="456" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1rnnbdx984EbIkjlbzyJNSFATdhaH4JP6c5d427XLJp4qC9aEvmYujnW3Nsx5qahCvEYpuELbtAmBhIzXx4BYJmfdAMKDZp8uNUZ66bT2RjIvyF1OLHdJn_HZxLxi48Z7k5rNczZW4y8R6niB7iKSOmd2SqwVGPDkEXLEPzBiQYb3jGNWjEEcvGF2Pzo/w640-h456/TI-81%20XY%20Graph.jpg" width="640" /></a></div><br /><p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Produces a scatter plot.
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Size: 52 bytes</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Code:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">If Dim{x}=0</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “NO DATA”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">If Dim{x}=0</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Stop</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">ClrDraw</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">1→I</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Lbl 0</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">PT-On({x}(I),{y}(I))</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">IS>(I,Dim{x})</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Goto 0</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">DispGraph</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Note: Dim{x} returns the number of data points in
the statistics list {x}.
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Keystrokes: [ VARS ], DIM, 7: Dim{x}</span></p>
<p class="western"><br /></p><p class="western"><span style="font-family: arial; font-size: medium;">
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><b>TI-81 ANGLES</b></span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Given three pints, the internal and external angle
are calculated.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxnM5tO9vpQpWourYbVn7KYLAVvfP5QoZF8uB4uBdnK8YIGXxad5gzVacURDp-I8KGL-xde406NSE7sJjylxH5iAxCmTq7UOWA80inKenfXOQCsIGjJ9aLMKH3PV0Xoe4WuqGsb1ZFk60NZ5aQMLTws3qQQ-6X9JN-BZpbBkCEgjIQpzg0A3tm8eB6ggk/s442/external%20and%20internal%20angles.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="412" data-original-width="442" height="596" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxnM5tO9vpQpWourYbVn7KYLAVvfP5QoZF8uB4uBdnK8YIGXxad5gzVacURDp-I8KGL-xde406NSE7sJjylxH5iAxCmTq7UOWA80inKenfXOQCsIGjJ9aLMKH3PV0Xoe4WuqGsb1ZFk60NZ5aQMLTws3qQQ-6X9JN-BZpbBkCEgjIQpzg0A3tm8eB6ggk/w640-h596/external%20and%20internal%20angles.jpg" width="640" /></a></div><br /><p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Size: 196 bytes</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Code:</span></p>
<p class="western"><span style="font-size: large;"><span style="font-family: courier;">Deg</span></span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “SIDE PT (S,T)”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input S</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input T</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “CORNER (M,N)”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input M</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input N</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “SIDE PT (U,V)”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input U</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input V</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">(S-M)*(U-M)+(T-N)*(V-N)→D</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">√((S-M)^2+(T-N)^2)→A</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">√((U-M)^2+(V-M)^2)→B</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">cos^-1 (D/(A*B))→I</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">360-I→E</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “INTERNAL ANGLE”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp I</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “EXTERNAL ANGLE”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp E</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Example:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">(S,T) = (-4,-6)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">(M,N) = (1,1)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">(U,V) = (3,5)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">INTERNAL ANGLE: 171.0273734</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">EXTERNAL ANGLE: 188.9726266</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Source:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Cook, John D. “Ramanujan approximation for
circumference of ellipse” John D. Cook Consulting. May 5, 2015.
</span><a href="https://www.johndcook.com/blog/2013/05/05/ramanujan-circumference-ellipse/" style="font-family: arial; font-size: large;">https://www.johndcook.com/blog/2013/05/05/ramanujan-circumference-ellipse/</a><span style="font-family: arial; font-size: large;">
Accessed January 24, 2024</span></p>
<p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><b>TI-81 ELLIPSE</b></span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Given the length of the semi-axis, the program
draws the ellipse, calculates the area, and approximates the
circumference using Ramanujan formula.</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Size: 195 bytes</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Code:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Param</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Rad</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “SEMI X-AXIS”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input A</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “SEMI Y-AXIS”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input B</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">(A-B)/(A+B)→L</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">π*(A+B)*(1+(3*L^2)/(10+√(4-3*L^2))→P</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">π*A*B→R</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “APPROX. CIR=”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp P</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “AREA=”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp R</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Pause</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">All-Off</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">“A*cos T”→X_1T</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">“B*sin T”→Y_1T</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">X1T-On</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">-A-1→Xmin</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">A+1→Xmax</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">-B-1→Ymin</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">B+1→Ymax</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">0→Tmin</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">2π→Tmax</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">π/24→Tstep</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">DispGraph</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Notes:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">All-Off turns all the graphing equations off from
graphing.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">[ 2<sup>nd</sup> ] {Y-VARS}, OFF, 1: All-Off</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">XT1 and YT1 are the equation variables x1(t) and
y1(t):</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">[ 2<sup>nd</sup> ] {Y-VARS}, Y, 5: X_1T and 6:
Y_1T, respectively</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Example:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">SEMI X-AXIS? 2</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">SEMI Y-AXIS? 3</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Results:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">APPROX. CIRC= 15.86543959</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">AREA= 18.84955592</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil8alZ5Uju0BXfEZgSHKEg7GgguOTIqO9gahi9uzp9KFg81YHtcvYS8XMlDUhetehnHXEq40New3HnVS185T356lKt4zn85X-suDEe-tUGNHEU7EqEZr2gosfulI7oNRj98EJk_ZZ1MFF038SdPGaDLec9EE7ikcRiPZAlF7DpVG5PQSgaPdfgNVWG6PA/s2578/TI-81%20Ellipse.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2063" data-original-width="2578" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil8alZ5Uju0BXfEZgSHKEg7GgguOTIqO9gahi9uzp9KFg81YHtcvYS8XMlDUhetehnHXEq40New3HnVS185T356lKt4zn85X-suDEe-tUGNHEU7EqEZr2gosfulI7oNRj98EJk_ZZ1MFF038SdPGaDLec9EE7ikcRiPZAlF7DpVG5PQSgaPdfgNVWG6PA/w640-h512/TI-81%20Ellipse.jpg" width="640" /></a></div><br /><p class="western"><br /></p>
<p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><b>TI-81 RELATIVE</b></span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Calculate the consequences of reality when it
comes to a length and mass of an object traveling near the speed of
light, c = 299,792,458 m/s.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Size: 141 bytes</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Code:</span></p>
<p class="western"><span style="font-size: large;"><span style="font-family: courier;">299792458→C</span></span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “C=”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp C</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “M/S”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Pause</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “°/. OF C”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input P</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">P*C/100→U</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">√(1-(U/C)^2)→V</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “LENGTH”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input L</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “OBS LENGTH=”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">L*V→K</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp K</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Pause</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “MASS”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Input M</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp “OBS. MASS=”</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">M/V→N</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">Disp N</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Enter the percentage of the speed of light (70%,
80%, 90%, etc.). Three characters are used to create the percent
sign (%) (°, / , . )</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Example:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">92.5% of the speed of light</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">length: 40.8 m</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">mass: 6,700 kg</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Results:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">observed length = 15.50265784 m</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">observed mass = 17,633.10542 kg</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Source:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Jackson, Mark D. <u>The QuickStudy for Physics</u>
BarCharts Publishing Inc. Boca Raton, Florida. 2007. ISBN 13:
9781423202677. pp. 114-115</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Eddie</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024.
Edward Shore. Unauthorized use and/or unauthorized distribution for
commercial purposes without express and written permission from the
author is strictly prohibited. This blog entry may be distributed
for noncommercial purposes, provided that full credit is given to the
author.
</span></p><br /><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-25750332994798630252024-03-09T00:00:00.000-08:002024-03-09T00:00:00.140-08:00Casio FX-702P, Swiss Micros DM42, HP 27S: Design of Coil Spring<p></p><p class="western" style="line-height: 115%; margin-bottom: 0in;">
<b><span style="color: black; font-family: arial;">Casio FX-702P, Swiss Micros DM42, HP 27S:
Design of Coil Spring</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><span style="color: black;">Today’s
blog calculates the load of a coil spring. </span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial;">Variables
Used</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<table cellpadding="4" cellspacing="0" style="width: 100%;">
<colgroup><col width="85*"></col>
<col width="85*"></col>
<col width="85*"></col>
</colgroup><tbody><tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="33%"><p class="western"><span style="font-family: arial;">
P</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="33%"><p class="western"><span style="font-family: arial;">
LOAD</span></p>
</td>
<td style="border: 1px solid #000000; padding: 0.04in;" width="33%"><p class="western"><span style="font-family: arial;">
Load (kg)</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
G</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
SHEAR</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Shear Modulus (kg/mm^2)</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
A</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
WDIA, W.DIA</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Diameter of the wire (mm)</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Y</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
DEFL</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Deflection (mm)</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
N, NA</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
#COIL</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Number of Coils</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
D</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
CDIA, C.DIA</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Diameter of the coil (mm)</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
K = (G×A^4)÷(8×N×D)</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western">
<span style="font-family: arial;"><br />
</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Spring Constant (kg/mm) <br />
(FX-702P only)</span></p>
</td>
</tr>
</tbody></table>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;"><b>Casio
FX-702P Code</b></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="font-weight: normal; line-height: 115%;"><span style="font-family: arial;"><span style="color: black;">The
original BASIC programs are listed here (Casio, pg. </span><span style="color: black;">72</span><span style="color: black;">,
Program Library FX-702P, see sources):</span></span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
5 FOR L=1 TO 5</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
10 INP “K,P:1,A:2,D:3,NA:4”,I</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
20 FOR J=1 TO 4</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
30 IF I=J THEN 100</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
40 NEXT J</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
50 GOTO 10</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;">
<span style="font-family: courier;"><br />
</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
100 INP “G=”,G</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
110 G=G/8</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
120 IF I=2 THEN 150</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
130 INP “A=”,A:A=A↑4</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
140 IF I=3 THEN 170</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
150 INP “D=”,D:D=D↑3</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
160 IF I=4 THEN 180</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
170 INP “NA”=,N</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
180 INP “Y=”,Y</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
190 IF I=1;K=G*A/N/D:P=K*Y:PRT “K=”;K,”P=”;P:GOTO 240</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
200 INP “P=”,P</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
210 IF I=2;A=(P*D*N/G/Y)↑(1/4):PRT “A=”;A:GOTO 240</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
220 IF I=3;D=(A*G*Y/N/P)↑(1/3):PRT “D=”;D:GOTO 240</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
230 N=G*A*Y/D/R:PRT “NA=”;N</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
240 NEXT L</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: courier;">
250 END</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;">
<span style="font-family: arial;"><br />
</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">
INP: input</span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">
PRT: print</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial;">Swiss
Micros DM42 Solver Code: SPRING</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">Also
for HP 42S, Free42, Plus42.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black;"><br /><span style="font-family: courier;">
00
{ 103-Byte Prgm }<br />
01▸LBL "SPRING"<br />
02 MVAR
"LOAD"<br />
03 MVAR "SHEAR"<br />
04 MVAR
"W.DIA"<br />
05 MVAR "C.DIA"<br />
06 MVAR
"#COIL"<br />
07 MVAR "DEFL"<br />
08 RCL
"SHEAR"<br />
09 RCL "W.DIA"<br />
10 4<br />
11
Y↑X<br />
12 ×<br />
13 RCL× "DEFL"<br />
14 8<br />
15
RCL× "#COIL"<br />
16 RCL "C.DIA"<br />
17 3<br />
18
Y↑X<br />
19 ×<br />
20 ÷<br />
21 +/-<br />
22 RCL+ "LOAD"<br />
23
RTN<br />
24 .END.</span><br />
</span><br />
</p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Run
SPRING through the SOLVER.</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p><p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br /></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="color: black; font-family: arial;">HP
27S Equation: SPRING</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><span style="color: black;">Spaces
added for readability. </span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: courier;">SPRING:
SHEAR × WDIA^4 × DEFL ÷ (8 ×#COIL × CDIA^3)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="color: black; font-family: arial;">Example:
Copper Spring Coil</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Shear:
G = 4558.131472 kg/mm^2</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Coil
Diameter: D = 10 mm</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Wire
Diameter: A = 0.7 mm</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Deflection:
Y = 5 mm</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Number
of Coils: N = 4</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Result:
Load: P: 0.17100 kg</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><span style="color: black;">Calculate
the wire diameter if the load is 0.25 kg. </span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Result:
Wire Diameter: A: 0.79672 mm</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">What
if instead we have 8 coils? Wire diameter resets to 0.7 mm.</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><span style="color: black;">Result:
Load: P: 0.08550 kg </span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial;">Table
of Shear Modulus Values</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">These
are the shear modulus of various mediums. The higher the shear
modulus is, the more rigid the solid is. If the solid’s modulus
is smaller, it is easier to deform or change its shape. For
liquids, the modulus is zero. The table below has two units, GPa
(gigapascal) and kg/mm^2. The conversion rate is approximately 1 GPa
= 101.9716212978 kg/mm^2.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">The
values in are from the “What is the Shear Modulus?” article by
Dr. Helmenstine (see the Sources section) in GPa.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<table cellpadding="4" cellspacing="0" style="width: 100%;">
<colgroup><col width="85*"></col>
<col width="85*"></col>
<col width="85*"></col>
</colgroup><tbody><tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="33%"><p class="western">
<span style="font-family: arial;"><span style="color: blue;"><b>Shear Modulus </b></span>
</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: 1px solid #000000; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0.04in;" width="33%"><p class="western">
<span style="color: blue; font-family: arial;"><b>GPa</b></span></p>
</td>
<td style="border: 1px solid #000000; padding: 0.04in;" width="33%"><p class="western">
<span style="color: blue; font-family: arial;"><b>kg/mm^2</b></span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Rubber</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
0.0006</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
0.06118297278</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Plywood</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
0.62</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
63.2224052</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Nylon</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
4.1</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
418.0836473</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Lead</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
13.1</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
1335.828239</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Aluminum</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
25.5</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
2600.276343</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Brass</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
40</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
4078.864852</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Copper</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
44.7</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
4558.131472</span></p>
</td>
</tr>
<tr valign="top">
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
Titanium</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
41.1</span></p>
</td>
<td style="border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; border-top: none; padding-bottom: 0.04in; padding-left: 0.04in; padding-right: 0.04in; padding-top: 0in;" width="33%"><p class="western"><span style="font-family: arial;">
4191.033635</span></p>
</td>
</tr>
</tbody></table>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;"><b>Source</b>:</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%;"><span style="font-family: arial;"><span style="color: black;">Casio.
</span><span style="color: black;"><u>Program Library: FX-702P</u></span><span style="color: black;">
pp. 71-72 (English)</span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;">Helmenstine,
Anne Marie, Ph.D. "What Is the Shear Modulus?" ThoughtCo,
Feb. 17, 2021, <a href="http://thoughtco.com/shear-modulus-4176406">thoughtco.com/shear-modulus-4176406</a>.
Retrieved January 21, 2024.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">TranslatorsCafe.com
“</span><span style="font-family: arial;">Convert gigapascal [GPa] to kilogram-force/millimeter²
[kgf/mm²]”</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><a href="https://www.translatorscafe.com/unit-converter/en-US/pressure/5-28/gigapascal-kilogram-force/millimeter%C2%B2/">https://www.translatorscafe.com/unit-converter/en-US/pressure/5-28/gigapascal-kilogram-force/millimeter%C2%B2/</a>
Retrieved January 21, 2024
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial;">Eddie</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial;"><span style="color: black;">All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author. </span>
</span></p><br /><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-51004569747150844142024-03-03T00:00:00.000-08:002024-03-03T00:00:00.138-08:00Casio FX-702P and Swiss Micros DM42: Spearman’s Coefficient of Rank Correlation<p></p><p class="western" style="margin-bottom: 0in;"></p><p class="western"><span style="font-family: arial; font-size: medium;"><b>
Casio FX-702P and Swiss Micros DM42: Spearman’s Coefficient of
Rank Correlation
</b></span></p>
<p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><b>Introduction: Correlation of Rankings Between Two
Events</b></span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><span style="font-weight: normal;">The Spearman’s
coefficient rank correlation tests the relationship between two
variables according to the rank of the two variables. Ranks are
assumed to be positive integers; 1 for 1</span><sup><span style="font-weight: normal;">st</span></sup><span style="font-weight: normal;">,
2 for 2</span><sup><span style="font-weight: normal;">nd</span></sup><span style="font-weight: normal;">,
3 for 3</span><sup><span style="font-weight: normal;">rd</span></sup><span style="font-weight: normal;">,
etc. The Spearman’s correlation is said to be non-parametric,
eliminating the requirement that the data is normally distributed.</span></span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">The correlation has a range between -1 and +1.
Two variables have a strong statistical relationship if the
correlation is close to -1 or +1. Conversely, these variables have
no relationship if the correlation is equal to 0.
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Let the variables A and B be the two variables.
Again, A and B are ranks.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Assuming that there are no ties in ranking in
either A or B, the correlation is calculated as:</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">r = 1 - ( 6 × C)^2 ) ÷ (n^3 – n)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">where:
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">C = Σ( (A_i – B_i)^2, k = 1 to n)
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">n = number of ranks</span></p>
<p class="western"><br /></p><p class="western"><b style="font-family: arial; font-size: large;">Casio FX-702P Code</b></p>
<p class="western"><span style="font-family: arial; font-size: large;">This is a port of the Spearman’s Coefficient of
Rank Correlation program set from Casio for the fx-702P. The original
BASIC programs are listed here (Casio, pg. 89, Program Library
FX-702P, see sources):</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">P0 (rank input):
</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">10 C=0:N=1</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">20 PRT “A”;N;:INP A</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">30 PRT “B”;N;:INP B</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">40 C=C+(A-B)↑2</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">50 N=N+1:GOTO 20</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">P1 (calculate the correlation):
</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">10 N=N-1</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">20 R=1-6*C/(N↑3-N)</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">30 PRT “R=”;R</span></p>
<p class="western"><span style="font-family: courier; font-size: medium;">40 END</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Note: PRT and INP are shortcut commands for PRINT
and INPUT, respectively. The three letter shortcuts are allowed
(and encouraged) on the fx-702P.
</span></p>
<p class="western"><span style="font-family: arial; font-size: large;"><br /></span></p><p class="western"><span style="font-family: arial; font-size: large;"><b>Swiss Micros DM 42 Code: SPEAR</b></span></p>
<p class="western"><br /></p><p class="western"><span style="font-size: medium;"><span style="font-family: courier;">
00 {
119-Byte Prgm }<br />
01▸LBL "SPEAR"<br />
02 "SPEARMAN
CORR"<br />
03 AVIEW<br />
04 PSE<br />
05 0<br />
06 STO 03<br />
07
1<br />
08 STO 04<br />
09 "ENTER RANK #S"<br />
10 AVIEW<br />
11
PSE<br />
12▸LBL 00<br />
13 "DONE? XEQ 01"<br />
14
AVIEW<br />
15 PSE<br />
16 "A"<br />
17 ARCL 04<br />
18
├"?"<br />
19 PROMPT<br />
20 "B"<br />
21 ARCL
04<br />
22 ├"?"<br />
23 PROMPT<br />
24 -<br />
25 X↑2<br />
26
STO+ 03<br />
27 1<br />
28 STO+ 04<br />
29 GTO 00<br />
30▸LBL 01<br />
31
1<br />
32 STO- 04<br />
33 RCL 04<br />
34 3<br />
35 Y↑X<br />
36 RCL-
04<br />
37 1/X<br />
38 RCL× 03<br />
39 6<br />
40 ×<br />
41 +/-<br />
42
1<br />
43 +<br />
44 STO 05<br />
45 "R="<br />
46 ARCL 05<br />
47
AVIEW<br />
48 .END.</span><br />
<br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Note: ├ is the append string character, call it
up by pressing [ (shift) ] { ALPHA } [ ENTER ].</span></p>
<p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><u>Instructions</u></span></p>
<p class="western"><span style="font-family: arial; font-size: large;">1. Sort event A and B to their relative rankings.
We are not analyzing data point by their values, but their
rankings.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">2. Press [ XEQ ] {SPEAR}</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">3. For each rank of event A, type the rank and
press [ R/S ]. For each rank of event B, type the rank and press [
R/S ]. There are prompts to guide rank entry.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">4. When done, execute label 01 by pressing [ XEQ
] 01.</span></p>
<p class="western"><br /></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><u>Example</u></span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Two algorithms A and B are analyzed. The time
between run time with algorithms A and B are:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">A: 48 seconds, B: 63 seconds</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 50 seconds, B: 64 seconds</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 53 seconds, B: 61 seconds</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 55 seconds, B: 66 seconds</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 57 seconds, B: 69 seconds</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Ranking the times relative to algorithm A are:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">A: 48 seconds (rank 1), B: 63 seconds (rank 2)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 50 seconds (rank 2), B: 64 seconds (rank 3)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 53 seconds (rank 3), B: 61 seconds (rank 1)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 55 seconds (rank 4), B: 66 seconds (rank 4)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A: 57 seconds (rank 5), B: 69 seconds (rank 5)</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Calculate the Spearman correlation:</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">XEQ SPEAR</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A1? 1 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">B1? 2 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A2? 2 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">B2? 3 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A3? 3 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">B3? 1 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A4? 4 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">B4? 4 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">A5? 5 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">B5? 5 R/S</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">XEQ 01</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">Result: R = 0.7000</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">The Spearman correlation is 0.7.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><b>Sources</b></span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><span style="color: black;">“Spearman’s rank
correlation coefficient” </span>DATAtab Team (2024). DATAtab:
Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL:
<a href="https://datatab.net/" target="_blank">https://datatab.net </a> Retrieved
January 17, 2024.</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">“Spearman’s rank <span style="color: black;">correlation</span>
coefficient” Wikipedia.
<a href="https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient" target="_blank">https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient</a>
Edited January 17, 2024. Retrieved January 17, 2024.
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Casio. <u>Program Library: FX-702P</u> pg. 89
(English)</span></p>
<p class="western"><span style="font-family: arial; font-size: large;">(The Casio Ledudu web page, <a href="https://casio.ledudu.com/pockets.asp?lg=eng&type=53" target="_blank">https://casio.ledudu.com/pockets.asp?lg=eng&type=53</a>, </span><span style="font-family: arial; font-size: large;">has the library in French).</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">Eddie</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;"><br />
<br />
</span></p>
<p class="western"><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024.
Edward Shore. Unauthorized use and/or unauthorized distribution for
commercial purposes without express and written permission from the
author is strictly prohibited. This blog entry may be distributed
for noncommercial purposes, provided that full credit is given to the
author.
</span></p><br /><p></p><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-71498137583929344252024-03-02T00:00:00.000-08:002024-03-02T00:00:00.128-08:00Spotlight: Casio fx-95 US Equation<p></p><p class="western" style="line-height: 115%; margin-bottom: 0in;">
<b><span style="font-family: arial; font-size: medium;">Spotlight: Casio fx-95 US Equation</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Welcome
to another retro review.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span lang="en-US"><b>Quick
Facts</b></span></span></p>
<p class="western" style="font-weight: normal; line-height: 115%; margin-bottom: 0in;">
<span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Model:
</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">fx-95US
Equation</span></span></span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Company:
</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">Casio</span></span></span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Timeline:
</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">unknown,
I’m guessing the 1980s</span></span></span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Type:
</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">Scientific
Calculator </span></span></span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Number
of Digits: </span></span></span><span><span lang="en-US"><span style="font-weight: normal;">10</span></span></span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">Power:
</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">2</span></span></span><span><span lang="en-US"><span style="font-weight: normal;">
AA batteries </span></span></span><span><span lang="en-US"><span style="font-weight: normal;">(per
manual)</span></span></span></span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span><span lang="en-US"><span style="font-weight: normal;">There
are also two variations of the fx-95US Equation: </span></span></span>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">fx-95
Equation</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">fx-500</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
fx-95 US Equation and fx-95 Equation have a flip hard case, while the
fx-500 does not. For the purposes of replacing the battery, I would
have preferred the fx-500 case. The fx-500 requires two LR44
batteries.</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIzUXiEIZ3bCFBsH1R1Zn5DDRiK85k7exnqcXRK7RPRzcIXbXTesWeEycCEFr2OMO5cMmH3dYyZoba6NXuANM7l8jX-GM9IlyhTI_3uMTnW3SngJIHQ9SJ1uH7gfeaSzUPDP_KWnVLbnexkQuUq2gaOWp0uaQwIlhekCbbrATKw-JQi0ac5KCIlRU02DM/s4624/fx-95%20US%20Equation%20full.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIzUXiEIZ3bCFBsH1R1Zn5DDRiK85k7exnqcXRK7RPRzcIXbXTesWeEycCEFr2OMO5cMmH3dYyZoba6NXuANM7l8jX-GM9IlyhTI_3uMTnW3SngJIHQ9SJ1uH7gfeaSzUPDP_KWnVLbnexkQuUq2gaOWp0uaQwIlhekCbbrATKw-JQi0ac5KCIlRU02DM/w480-h640/fx-95%20US%20Equation%20full.jpg" width="480" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoIbM3AylBQOPyYlqqgCnX1Qua9GHsZKNdXGboiVBY0JbXM4luG9C-TmdzSVDZpJFF8wXJC7YWR8-9_T1a1b9lX4oicE0iJUhTdBcw1eXd8WjdcuOZNbjSCn6HCIiMUC25gL9GACrN0RNhlR-AQFcZF5xohEaLgT8xthyPtjF4pQIu86kSyDM6Wnj-CLg/s4624/fx-95%20US%20Equation%20close%20up.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3468" data-original-width="4624" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoIbM3AylBQOPyYlqqgCnX1Qua9GHsZKNdXGboiVBY0JbXM4luG9C-TmdzSVDZpJFF8wXJC7YWR8-9_T1a1b9lX4oicE0iJUhTdBcw1eXd8WjdcuOZNbjSCn6HCIiMUC25gL9GACrN0RNhlR-AQFcZF5xohEaLgT8xthyPtjF4pQIu86kSyDM6Wnj-CLg/w640-h480/fx-95%20US%20Equation%20close%20up.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC4nripCI8L67FjFht0Bx6UzsiNfEGZUMfVpgL0HwGb85AixynRs-UwiJi19YEH31JRIN_n9Bvzfne4ow2EFLo8ySM6dk9Z3Fvn9ciQmC3DqHylD8-CLTFPmjBb7m3ampj5pKUjP-0qaMbIYKr_bMA07BPeKxcnMWmp6ndMIgd4ofaRd0vEXFlsTYXwbc/s4624/fx-95%20US%20Equation%20back%20cover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC4nripCI8L67FjFht0Bx6UzsiNfEGZUMfVpgL0HwGb85AixynRs-UwiJi19YEH31JRIN_n9Bvzfne4ow2EFLo8ySM6dk9Z3Fvn9ciQmC3DqHylD8-CLTFPmjBb7m3ampj5pKUjP-0qaMbIYKr_bMA07BPeKxcnMWmp6ndMIgd4ofaRd0vEXFlsTYXwbc/w480-h640/fx-95%20US%20Equation%20back%20cover.jpg" width="480" /></a></div><br /><p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Three
Equation Modes</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
fx-95 US Equation (and fx-500) is a basic, 10-digit scientific
calculator with fractions. You have basic set of functions,
including trigonometry, hyperbolic functions, random numbers, powers,
roots, logarithms, and basic one-variable statistics.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
main attraction is the three equation modes:</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">MODE
1: QUAD (quadratic equation – real numbers only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">MODE
2: SIMUL-2 (2 x 2 linear system)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">MODE
3: SIMUL-3 (3 x 3 linear system)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Entering
coefficients and viewing answers happen by pressing the [ M+ ] key.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
fx-95 US does not allow for complex number solutions.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Examples:</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">x^2
+ 5 × x + 6 = 0</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Solutions:
X 1: -2; X 2: -3</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">x^2
+ 16 × x + 64 = 0</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Solutions:
x: -8 (repeated root)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">-x^2
+ 3 × x – 9 = 0</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Solutions:
1: - E - (complex roots)
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">-2x
+ 3y = 5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">x +
17y = 48</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">a1:
-2, b1: 3, c1: 5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">a2:
1, b2: 17, c2: 48</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Solutions:
X: 1.59459, Y: 2.72973</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">-x +
z = 5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">-2x
– y – z = -3</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">3x +
y – 2z = 1</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">a1:
-1, b1: 0, c1: 1, d1: 5</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">a2:
-2, b2: -1, c2: -1, d2: -3</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">a3:
3, b3: 1, c3: -2, d3: 1</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Solutions:
X: -6 ½, Y: 17 ½, Z: -1 ½
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Check
the left side as it will display the variable you are working with.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">fx-95
US Equation vs. fx-260 Solar (II)</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidd0sJh2R_1neIQ_H7GE3mucvN4Vzl0DBiKcY7r3t2eYTqbGFET79Pg6T2sKBoJlQTBBXiF7M9RklDk4hwHUd8y6MDHuYJ5-Mh8XutboYDEKc3TDGLJUFGiYyIQS0xV397ghlGv-ZJZOVJdF7MMZvIgXe-oAMzolV_4MKgrCTIXNpHRCHgBjUcSdEeriM/s4624/fx-95%20US%20Equation%20vs%20fx-260%20Solar%20II.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidd0sJh2R_1neIQ_H7GE3mucvN4Vzl0DBiKcY7r3t2eYTqbGFET79Pg6T2sKBoJlQTBBXiF7M9RklDk4hwHUd8y6MDHuYJ5-Mh8XutboYDEKc3TDGLJUFGiYyIQS0xV397ghlGv-ZJZOVJdF7MMZvIgXe-oAMzolV_4MKgrCTIXNpHRCHgBjUcSdEeriM/w480-h640/fx-95%20US%20Equation%20vs%20fx-260%20Solar%20II.jpg" width="480" /></a></div><br /><p class="western" style="line-height: 115%; margin-bottom: 0in;"><br /></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><u><span style="font-family: arial; font-size: medium;">Comparison
of Modes</span></u></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
. (decimal point): SD</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
0: COMP</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
1: QUAD (fx-95 US Equation only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
2: SIMUL-2 (fx-95 US Equation only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
3: SIMUL-3 (fx-95 US Equation only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
4: DEG (SHIFT MODE 4 to convert to degrees, fx-260 Solar only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
5: RAD (SHIFT MODE 5 to convert to radians, fx-260 Solar only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
6: GRA (SHIFT MODE 6 to convert to grads, fx-260 Solar only)</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
7: FIX</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
8: SCI</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Mode
9: NORM</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
fx-260 adds the following functions: x^3, nCr, nPr.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
availability of the Casio fx-95US EQUATION is fairly good.
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Source</span></b></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Casio
Computer Co, Ltd. <u>fx-95, fx-500 Manual</u>. Manual available
on manualslib.com.
<a href="https://www.manualslib.com/manual/358116/Casio-Fx-500.html#manual">https://www.manualslib.com/manual/358116/Casio-Fx-500.html#manual</a>
Retrieved January 20, 2024</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Casio
Ledudu. “CASIO fx-95US EQUATION”
<a href="https://casio.ledudu.com/pockets.asp?type=1239&lg=eng">https://casio.ledudu.com/pockets.asp?type=1239&lg=eng</a>
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="color: black; font-family: arial; font-size: medium;">Eddie</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="line-height: 115%; margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><span style="color: black;">All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author. </span>
</span></p><br /><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-66754239417171982532024-02-25T06:18:00.000-08:002024-02-25T06:18:00.124-08:00Casio Graphing Calculators: Equation Variables<p></p><p align="left" class="western" style="margin-bottom: 0in;">
<span style="font-family: arial; font-size: medium;"><b>Casio Graphing Calculators: Equation Variables </b>
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Introduction</span></b></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAdm_lSsDZWcSYmUWo5vaggdkfa_CJa0jMI25qPaPqPcta9pF7DPvJLNztqHB7QHgy2bPEpQViYegtlx4Hzubg7vC8DMJfLBuu2MQvn0gK53otc2hsgNCkgAnWVvr6PsxT7FzYYnn9yZPjQ52s-SIgeos3Kd8J8krVq5akWDPldSEfljTUlAkPOXQmYTg/s857/selecting%20equation%20mode.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="281" data-original-width="857" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAdm_lSsDZWcSYmUWo5vaggdkfa_CJa0jMI25qPaPqPcta9pF7DPvJLNztqHB7QHgy2bPEpQViYegtlx4Hzubg7vC8DMJfLBuu2MQvn0gK53otc2hsgNCkgAnWVvr6PsxT7FzYYnn9yZPjQ52s-SIgeos3Kd8J8krVq5akWDPldSEfljTUlAkPOXQmYTg/w640-h210/selecting%20equation%20mode.jpg" width="640" /></a></div><br /><p align="left" class="western" style="margin-bottom: 0in;"><br /></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Most
modern Casio graphing calculators have an Equation solver mode that
solves linear systems (Simultaneous), polynomials (Polynomial), and
general equations.
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">To find
run Equation mode, press [ MENU ] { A }*.
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">(*Equation
mode is currently option A (fx-9750GIII, fx-CG 50, fx-CG 10/20,
fx-9860 Slim))</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Simultaneous
Equations: SimRes and SimCoef</span></b></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaoG14v1ykJ0hIY3g_kjvCwl2bHNPkbRDzwHEG2VaUz8oWcJ89VXYEU2glx6BRarUwX2mSnDkLumbXE95jLDoeuQJH6VgtNYJklh7SLvWfj9z3oLSK0bSVGuWXa6tsdPbWVIPNRLTLLfAjwso8_LQYSJYuzqd27WFj26OCLVMyXAVmgD6wTPJIYnhZ1Ro/s1281/simultaneous%20equation%20mode.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="513" data-original-width="1281" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaoG14v1ykJ0hIY3g_kjvCwl2bHNPkbRDzwHEG2VaUz8oWcJ89VXYEU2glx6BRarUwX2mSnDkLumbXE95jLDoeuQJH6VgtNYJklh7SLvWfj9z3oLSK0bSVGuWXa6tsdPbWVIPNRLTLLfAjwso8_LQYSJYuzqd27WFj26OCLVMyXAVmgD6wTPJIYnhZ1Ro/w640-h256/simultaneous%20equation%20mode.jpg" width="640" /></a></div><br /><p align="left" class="western" style="margin-bottom: 0in;"><br /></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
simultaneous equation mode solves linear systems up to 6 x 6. The
coefficients of the equations are stored in the variable <span style="font-weight: normal;">Sim
Coef (labeled SimCoef in VARS-EQUATION menu)</span> while the results
are stored in the variable Sim Result (labeled SimRes).
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><b>Polynomials:
PlyRes and PlyCoef</b>
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhRWSL8Udvy2C-owQCAvt2IowqyDrgGdRMyTRO7gKw_DOPLVVxAT94iFomt35RJ0hnT5E0JyxyXDX3xE5ZkixwPor1Esmsr21UGJ4674-FZoVrvpmzFvqdv7x_JFoLtTBdmrqX9NzCKFLkuFAihIslZiudNIS1TXOuF2SpfO26vDDZwOSqqK5Rr3iN-Jo/s1301/polynomial%20equation%20mode.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="529" data-original-width="1301" height="260" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhRWSL8Udvy2C-owQCAvt2IowqyDrgGdRMyTRO7gKw_DOPLVVxAT94iFomt35RJ0hnT5E0JyxyXDX3xE5ZkixwPor1Esmsr21UGJ4674-FZoVrvpmzFvqdv7x_JFoLtTBdmrqX9NzCKFLkuFAihIslZiudNIS1TXOuF2SpfO26vDDZwOSqqK5Rr3iN-Jo/w640-h260/polynomial%20equation%20mode.jpg" width="640" /></a></div><br /><p align="left" class="western" style="margin-bottom: 0in;"><br /></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The
polynomial equation mode solves polynomials with real coefficients up
to degree 6 (3 in early graphing models). The coefficients of the
polynomial are stored in the variable Poly Coef (labeled PolyCoef in
the VARS-EQUATION menu) while the results are stored in the variable
Poly Result (labeled PolyRes).</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><b><span style="font-family: arial; font-size: medium;">Accessing
Equation Variables Outside of Equation Mode</span></b></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEiwLiErqnFbhv1b3vQs3hWufySQ9qVLNvNYz_9IiLStjiTFmVChjT65UOw-6eR8lyboZYI8fnO5Bl2BlSgXCMOpmHpm2nlU0Ba8bVPfgbWElNUAT5Kl32grQCiWCdEuM03RvJZ7HGCYgDD7UprIn28jHc7QkW5Ljmtjk6bGU241afQAjQbYGC41OXGp4/s939/operations%20with%20equation%20variables.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="645" data-original-width="939" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEiwLiErqnFbhv1b3vQs3hWufySQ9qVLNvNYz_9IiLStjiTFmVChjT65UOw-6eR8lyboZYI8fnO5Bl2BlSgXCMOpmHpm2nlU0Ba8bVPfgbWElNUAT5Kl32grQCiWCdEuM03RvJZ7HGCYgDD7UprIn28jHc7QkW5Ljmtjk6bGU241afQAjQbYGC41OXGp4/w640-h440/operations%20with%20equation%20variables.jpg" width="640" /></a></div><br /><p align="left" class="western" style="margin-bottom: 0in;"><br /></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The four
equation variables can be recalled by pressing [ VARS ], [ F6 ] { >
}, [ EQUA ] { F3 }.
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">F1:
SimRes (S·Rlt on older models)</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">F2:
SimCoef (S·Cof on older models)</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">F3:
PlyRes (P·Rlt on older models)</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">F4:
PlyCof (P·Cof on older models)</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">The four
variables are read-only matrices. We can not store values or
information to read-only variables.
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">If we want
to extract specific values from the equations variables, we must
store them into a Matrix variable (A – Z, θ). For example, to
retrieve the number from the 1<sup>st</sup> row and column of Sim
Coef:</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">Sim
Coef → Mat A</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">Mat
A[1,1]</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">We can
execute operations on equation variables. An interesting check is to
run the simultaneous solver of the variable by typing:</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: courier; font-size: medium;">Rref
Sim Coef</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">and
reading the last column.</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;">Until next
time,</span></p>
<p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;">
<span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;">
<span style="color: black; font-family: arial; font-size: medium;">Eddie</span></p>
<p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;">
<span style="font-family: arial; font-size: medium;"><br />
</span></p>
<p class="western" style="margin-bottom: 0in;"><span style="font-family: arial; font-size: medium;"> All original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author.
</span></p><p></p><p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;">
</p><p class="western" style="margin-bottom: 0in;"><br />
</p><p>
</p><p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;"><br /></p>
<p align="left" class="western" style="line-height: 100%; margin-bottom: 0in;"><br /></p><p></p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-43865673120896178012024-02-24T00:00:00.000-08:002024-02-24T00:00:00.151-08:00Swiss Micros DM42 and HP 42S: Moon Landing Simulator from the HP 33-E Applications Book<p><b><span style="font-family: Arial, sans-serif;"><span style="font-size: 12pt;"><span lang="en-US">Swiss
Micros DM42 and HP 42S: </span></span></span><span style="font-family: Arial, sans-serif;"><span style="font-size: 12pt;"><span lang="en-US">Moon
Landing Simulator </span></span></span><span style="font-family: Arial, sans-serif;"><span style="font-size: 12pt;"><span lang="en-US">from
the HP 33-E Applications Book</span></span></span></b></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><b><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Landing
the Rocket</span></span></span></b></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">The
goal is to provide enough fuel to get the rocket to land on the moon
safely. The use of fuel pushes the rocket away from the surface and
slow down the descent. Don’t crash or use too much fuel to escape
into space. </span></span></span>
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Variables:</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">X:
Position</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">V:
Velocity</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">F:
Fuel</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">G:
Gravity</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">B:
Amount of Fuel to burn</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Initial
Values (from the HP-33E Applications):</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">X
= 500</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">V
= -50</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">F
= 120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">G
= 5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">I
wasn't sure about the win condition (X = 0, V = 0?). </span></span></span>
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">I
show the position, velocity, and fuel after each successful turn.
Enter the amount of units to burn at the burn prompt. </span></span></span>
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Download
here:
</span></span></span><a href="https://drive.google.com/file/d/1YsYzIMxALuRx_MHSSzGFFEQJdrN656DS/view?usp=sharing"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">https://drive.google.com/file/d/1YsYzIMxALuRx_MHSSzGFFEQJdrN656DS/view?usp=sharing</span></span></span></a></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><b>DM42
and HP 42S Code: MOON</b></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">00
{ 184-Byte Prgm }</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">01▸LBL
"MOON"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">02
500</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">03
STO "X"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">04
-50</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">05
STO "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">06
120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">07
STO "F"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">08
5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">09
STO "G"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">10▸LBL
01</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">11
"POS:"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">12
ARCL "X"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">13
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">14
STOP</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">15
"VEL:"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">16
ARCL "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">17
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">18
STOP</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">19
"FUEL:"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">20
ARCL "F"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">21
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">22
STOP</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">23
RCL "X"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">24
X=0?</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">25
GTO 07</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">26▸LBL
02</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">27
"BURN?"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">28
PROMPT</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">29
STO "B"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">30
RCL "F"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">31
X<Y?</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">32
GTO 05</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">33▸LBL
03</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">34
RCL "B"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">35
STO- "F"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">36
RCL- "G"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">37
STO "A"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">38
RCL "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">39
RCL+ "X"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">40
RCL "A"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">41
2</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">42
÷</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">43
+</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">44
STO "X"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">45
X≥0?</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">46
GTO 04</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">47
GTO 06</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">48▸LBL
04</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">49
RCL "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">50
RCL+ "A"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">51
STO "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">52
GTO 01</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">53▸LBL
05</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">54
2</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">55
RCL× "G"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">56
RCL "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">57
X↑2</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">58
+</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">59
SQRT</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">60
+/-</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">61
STO "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">62▸LBL
06</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">63
"VEL:"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">64
ARCL "V"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">65
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">66
"YOU LOSE"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">67
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">68
RTN</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">69▸LBL
07</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">70
"SUCCESS!"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">71
AVIEW</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Courier New, monospace;"><span style="font-size: small;"><span lang="en-US">72
.END.</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><b><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Example
Game</span></span></span></b></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">XEQ
"MOON"</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Initial
Turn</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
500</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-50</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
0</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
447.5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-55</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
0</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
390</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-60</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
0</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
327.5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-65</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
120</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
262.5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-65</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
115</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
0</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
195</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-70</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
115</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
125</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-70</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
115</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
10</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">POS:
57.5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">VEL:
-65</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">FUEL:
100</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">BURN?
12.5</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">"YOU
LOSE" -3.75</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">So
close. Good luck!</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><b><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Source</span></span></span></b></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US"><u>HP-33
Applications</u></span></span></span><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US"><span style="text-decoration: none;">.
Hewlett Packard. Corvallis, OR. February 1978</span></span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in;"><span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">Eddie</span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0in;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0in; orphans: 2; widows: 2;">
<span style="font-family: Arial, sans-serif;"><span style="font-size: small;"><span lang="en-US">All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the
author. </span></span></span>
</p>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-30840786534313543692024-02-18T00:00:00.000-08:002024-02-18T00:00:00.141-08:00 Casio fx-CG 50 CORDIC Simulation: Approximating Sine and Cosine of Angles<p><span style="font-family: arial; font-size: medium;"><b>Casio fx-CG 50 CORDIC Simulation: Approximating Sine and Cosine of Angles</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction - How Computers Calculate Mathematical Functions</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">First developed by Jack E. Volder, the Coordinate Rotation Digital Computer, better known as CORDIC, is an algorithm used to calculate many mathematical functions, including trigonometric functions, logarithms, exponentials, and hyperbolic functions. CORDIC is a fundamental algorithm, which variants of CORDIC are used in computers and calculators.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Today's focus will be a calculating sines and cosines of angles. The steps will be detailed in the next sections. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>CORDIC1: Series of Arctangents</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Let Θ be the angle. The first step is to build Θ as additions and subtractions of terms of arctan(1 ÷ (2^n)), starting at n = 0 and stopping at the required accuracy. Let A be the approximation. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Θ = 45° requires only one term:</span></p><p><span style="font-family: arial; font-size: medium;">A = 45° = arctan 1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Θ ≈ 71.56505118°</span></p><p><span style="font-family: arial; font-size: medium;"> A = 71.56505118° = arctan 1 + arctan 1/2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Θ ≈ 32.47119229°</span></p><p><span style="font-family: arial; font-size: medium;">A = 32.47119229° = arctan 1 - arctan 1/2 + arctan 1/4</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A series to recreate Θ = 30° takes 32 terms of ±arctan (1 ÷ 2^n) from n = 0 to n = 31. (8 decimal places) This is known as coordinate rotation.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program CORDIC1 determines the number of terms need to created to obtain Θ. Accuracy in this code is set to 5 decimal places, but can be adjusted (see the line in blue). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b><u>Casio fx-CG 50 Program Code: CORDIC1</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Deg</span></p><p><span style="font-family: courier; font-size: medium;">"ANGLE"?->Θ</span></p><p><span style="font-family: courier; font-size: large;">0->I</span></p><p><span style="font-family: courier; font-size: large;">0->A</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 0</span></p><p><span style="font-family: courier; font-size: medium;">tan^-1 (2^(-I))->T</span></p><p><span style="font-family: courier; font-size: medium;">If A<Θ</span></p><p><span style="font-family: courier; font-size: medium;">Then </span></p><p><span style="font-family: courier; font-size: medium;">A+T->A</span></p><p><span style="font-family: courier; font-size: medium;">Else </span></p><p><span style="font-family: courier; font-size: medium;">A-T->A</span></p><p><span style="font-family: courier; font-size: medium;">IfEnd</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">I+1->I</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;">Abs (A-Θ)>1×10^-5=>Goto 0</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">ClrText</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 1,3,"Θ: "</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 5,3,Θ</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 1,4,"A: "</span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 5,4,A</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Green Locate 1,7,I</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Notes:</span></p><p><span style="font-family: arial; font-size: medium;">-> is the store arrow →</span></p><p><span style="font-family: arial; font-size: medium;"></span></p><p><span style="font-family: arial; font-size: medium;">=> is the jump command ⇒</span></p><div><br /></div><p><span style="font-family: arial; font-size: medium;">For reference:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">arctan 1 = 45°</span></p><p><span style="font-family: arial; font-size: medium;">arctan 1/2 ≈ 26.56505118°</span></p><p><span style="font-family: arial; font-size: medium;">arctan 1/4 ≈ 14.03624347°</span></p><p><span style="font-family: arial; font-size: medium;">arctan 1/8 ≈ 7.125016349°</span></p><p><span style="font-family: arial; font-size: medium;">arctan 1/16 ≈ 3.576334375°</span></p><p><span style="font-family: arial; font-size: medium;">arctan 1/32 ≈ 1.789910608°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>CORDIC2: Calculating Sine and Cosine</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Imagine the coordinate (cos Θ, sin Θ) on a unit circle. A unit circle is a circle with radius of length 1 and center located at the origin (0,0). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Set the initial angle at 0°. Then x = cos 0° = 1 and y = sin 0° = 0. The initial vector is set to be [ [ cos 0° ] [ sin 0° ] ] = [ [ 1 ] [ 0 ] ].</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Approximate Θ in terms of arctangent (1 ÷ (2^n)), starting at n = 0. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>Direction of Rotation</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Set σ as the direction of rotation. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A rotation is positive if we add arctan(1 ÷ (2^n)) to A. For a positive rotation, set σ_i = +1. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A rotation is negative if we subtract arctan(1 ÷ (2^n)) to A. For a negative rotation, set σ_i = -1. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"> Θ ≈ 32.47119229°</span></p><p><span style="font-family: arial; font-size: medium;">A = 32.47119229° = arctan 1 - arctan 1/2 + arctan 1/4</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Then: σ_0 = 1 (positive rotation), σ_1 = -1 (negative rotation), σ_2 = 1 (positive rotation). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u><b>Multiplying Factor</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The number of iterations is also used to determine the required multiplication factor:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">n = Π( 1 ÷ √(1 + 2^(-2 × I)), I = 0 to I = terms needed - 1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For the example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"> Θ ≈ 32.47119229°</span></p><p><span style="font-family: arial; font-size: medium;">Needed 3 iterations, i_0 to i_2. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Then:</span></p><p><span style="font-family: arial; font-size: medium;">n = 1 ÷ √(1 + 2^(-2 × 0)) × 1 ÷ √(1 + 2^(-2 × 1)) × 1 ÷ √(1 + 2^(-2 × 2))</span></p><p><span style="font-family: arial; font-size: medium;">= 4 × √170 ÷ 85</span></p><p><span style="font-family: arial; font-size: medium;">≈ 0.6135719911</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u><b>Calculating the Next Iteration</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The next iteration for x and y are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x_i+1 = x_i - 2^(-i) × σ_i × y_i</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y_i+1 = 2^(-i) × σ_i × x_i + y_i</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">When A is sufficiently near or equal to Θ, the cosine and sine are approximated as:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">cos(A) ≈ n × x_final</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">sin(A) ≈ n × y_final</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For the example:</span></p><p><span style="font-family: arial; font-size: medium;"> Θ ≈ 32.47119229°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The approximated angle, in this case, happens to be exact angle, A = Θ. And,</span></p><p><span style="font-family: arial; font-size: medium;">cos(A) ≈ 0.8436614877 </span></p><p><span style="font-family: arial; font-size: medium;">sin(A) ≈ 0.5368754922</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For more details, please check out resources in the Sources section. I particularly like Oxford's <i>A Very Short Introduction</i> series. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b><u>Casio fx-CG 50 Program Code: CORDIC2</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This algorithm is adopted from the Python example (see Wikipedia article). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Deg</span></p><p><span style="font-family: courier; font-size: medium;">"ANGLE"?->Θ</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">0->I</span></p><p><span style="font-family: courier; font-size: medium;">0->A</span></p><p><span style="font-family: courier; font-size: medium;">1->X</span></p><p><span style="font-family: courier; font-size: medium;">0->Y</span></p><p><span style="font-family: courier; font-size: medium;">1->N</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 0</span></p><p><span style="font-family: courier; font-size: medium;">tan^-1 (2^(-I))->T</span></p><p><span style="font-family: courier; font-size: medium;">If A<Θ</span></p><p><span style="font-family: courier; font-size: medium;">Then </span></p><p><span style="font-family: courier; font-size: medium;">A+T->A</span></p><p><span style="font-family: courier; font-size: medium;">1->S</span></p><p><span style="font-family: courier; font-size: medium;">Else </span></p><p><span style="font-family: courier; font-size: medium;">A-T->A</span></p><p><span style="font-family: courier; font-size: medium;">-1->S</span></p><p><span style="font-family: courier; font-size: medium;">IfEnd</span></p><p><span style="font-family: courier; font-size: medium;">N÷√(1+2^(-2*I))->N</span></p><p><span style="font-family: courier; font-size: medium;">X-S*2^(-I)*Y->P</span></p><p><span style="font-family: courier; font-size: medium;">Y+X*S*2^(-I)->Q</span></p><p><span style="font-family: courier; font-size: medium;">P->X</span></p><p><span style="font-family: courier; font-size: medium;">Q->Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">I+1->I</span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;">Abs (A-Θ)>1×10^-5=>Goto 0</span></p><p><span style="font-family: courier; font-size: medium;">X*N->X</span></p><p><span style="font-family: courier; font-size: medium;">Y*N->Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">ClrText</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 1,3,"Θ: "</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 5,3,Θ</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 1,4,"A: "</span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 5,4,A</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 1,5,"cos :"</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 7,5,X</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 1,6,"sin :"</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 7,6,Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Green Locate 1,7,I</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>CORDIC3: Doing it without a Arctangent function</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><span style="font-family: arial;">In reality, most of the time the arctangent function also has to be approximated. There are many ways to approximate, which varying accuracy. </span><span style="font-family: arial;">I used the fx-CG50's statistics mode to come up with a regression equation with the following lists:</span></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x_list = sequence of 1÷(2^i) from i = 0 to i = 39 </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y_list = sequence of arctan(1÷(2^i)) from i = 0 to i = 39</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Of the regression models the fx-CG50 offers, the best regression model is quartic regression (4th-order polynomial):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y ≈ 9.43597784 × x^4 - 22.116232 × x^3 + 0.40116676 × x^2 + 57.2790727 × x + 1.4558 × 10^-5</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Remember that I am working with degree angle measurement. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGJ0f3UrYCHaA2oVKfWJNsjZ3d31gPux2mYNgie1yLUdbhscSfrv44-bNPiuh5jevjQVW7lRqvR0W1rha0iWayZsI7pXj8M_J1yzq4S1LeV5u1urkP7TBqFn3TR51uo7kD2lxrAUb79BuW5vUbhc3XRN42YEkLI49yVLfQJz2Wumn8_XXHNCdlmGRjCoA/s857/Casio%20fx-CG%2050%20-%20CORDIC%20Quartic%20Stat%20Fit%20(to%20put%20before%20CORDIC3).jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="733" data-original-width="857" height="548" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGJ0f3UrYCHaA2oVKfWJNsjZ3d31gPux2mYNgie1yLUdbhscSfrv44-bNPiuh5jevjQVW7lRqvR0W1rha0iWayZsI7pXj8M_J1yzq4S1LeV5u1urkP7TBqFn3TR51uo7kD2lxrAUb79BuW5vUbhc3XRN42YEkLI49yVLfQJz2Wumn8_XXHNCdlmGRjCoA/w640-h548/Casio%20fx-CG%2050%20-%20CORDIC%20Quartic%20Stat%20Fit%20(to%20put%20before%20CORDIC3).jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><u><b>Casio fx-CG 50 Program Code: CORDIC3</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Deg</span></p><p><span style="font-family: courier; font-size: medium;">"ANGLE"?->Θ</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">0->I</span></p><p><span style="font-family: courier; font-size: medium;">0->A</span></p><p><span style="font-family: courier; font-size: medium;">1->X</span></p><p><span style="font-family: courier; font-size: medium;">0->Y</span></p><p><span style="font-family: courier; font-size: medium;">1->N</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 0</span></p><p><span style="font-family: courier; font-size: medium;">2^(-I)->K</span></p><p><span style="font-family: courier; font-size: medium;">9.43597784917955K^(4)-22.1162323028173K^(3)+</span></p><p><span style="font-family: courier; font-size: medium;">0.401166766193516K^2+57.2790727477367K+</span></p><p><span style="font-family: courier; font-size: medium;">1.45584715586876×10^-5->T</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">If A<Θ</span></p><p><span style="font-family: courier; font-size: medium;">Then </span></p><p><span style="font-family: courier; font-size: medium;">A+T->A</span></p><p><span style="font-family: courier; font-size: medium;">1->S</span></p><p><span style="font-family: courier; font-size: medium;">Else </span></p><p><span style="font-family: courier; font-size: medium;">A-T->A</span></p><p><span style="font-family: courier; font-size: medium;">-1->S</span></p><p><span style="font-family: courier; font-size: medium;">IfEnd</span></p><p><span style="font-family: courier; font-size: medium;">N÷√(1+2^(-2*I))->N</span></p><p><span style="font-family: courier; font-size: medium;">X-S*2^(-I)*Y->P</span></p><p><span style="font-family: courier; font-size: medium;">Y+X*S*2^(-I)->Q</span></p><p><span style="font-family: courier; font-size: medium;">P->X</span></p><p><span style="font-family: courier; font-size: medium;">Q->Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">I+1->I</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: courier; font-size: medium;">Abs (A-Θ)>1×10^-5=>Goto 0</span></p><p><span style="font-family: courier; font-size: medium;">X*N->X</span></p><p><span style="font-family: courier; font-size: medium;">Y*N->Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">ClrText</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 1,3,"Θ: "</span></p><p><span style="font-family: courier; font-size: medium;">Blue Locate 5,3,Θ</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 1,4,"A: "</span></p><p><span style="font-family: courier; font-size: medium;">Red Locate 5,4,A</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 1,5,"cos :"</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 7,5,X</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 1,6,"sin :"</span></p><p><span style="font-family: courier; font-size: medium;">Black Locate 7,6,Y</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Green Locate 1,7,I</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For the example:</span></p><p><span style="font-family: arial; font-size: medium;"> Θ ≈ 32.47119229°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Approximating Θ within 8 decimal places (10^-5) yields these results:</span></p><p><span style="font-family: arial; font-size: medium;">A: <span style="color: red;">32.4711</span>8598</span></p><p><span style="font-family: arial; font-size: medium;">cos A: <span style="color: red;">0.84366</span>83456</span></p><p><span style="font-family: arial; font-size: medium;">sin A: <span style="color: red;">0.5368</span>647154</span></p><p><span style="font-family: arial; font-size: medium;">24 terms used</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Sources</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"CORDIC" Wikipedia. Last Edited January 11, 2024. Accessed January 12, 2024. <a href="https://en.wikipedia.org/wiki/CORDIC" target="_blank">https://en.wikipedia.org/wiki/CORDIC</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Brummelen, Glen Van. <u>Trigonometry: A Very Short Introduction</u> Oxford University Press: Oxford, United Kingdom. 2020. ISBN 978-0-19-881431-3</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-86156492055714445172024-02-17T00:00:00.000-08:002024-02-17T00:00:00.146-08:00TI-30Xa Algorithms: Annuity Factors<p><span style="font-family: arial; font-size: medium;"><b>TI-30Xa Algorithms: Annuity Factors</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Even when a calculator isn't (technically) programmable, algorithms can be applied to scientific and financial calculations.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The calculations take numerical arguments that are stored in the TI-30Xa's three memory slots: M1, M2, and M3. Store amounts into the memory registers by the [ STO ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Careful: For the solar versions of the TI-30Xa, do not press the [ON/AC] button as doing so clears the memory registers.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Today's list of routines deals with annuity factors.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>SPFV: Future Value of a Single Present Value Factor</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SPFV = (1 + i%)^n</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">FV = PV × SPFV</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u><b>SPPV: Present Value of a Single Future Value Factor</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SPPV = (1 + i%)^(-n)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">PV = FV × SPPV</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u><b>USFV: Future Value of a Payment Stream Factor</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">USFV = ((1 + i%)^n - 1) ÷ i%</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">FV = PMT × USFV</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>USPV: Present Value of a Payment Stream Factor</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">USPV = (1 - (1 + i%)^(-n)) ÷ i%</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">PV = PMT × USPV</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where:</span></p><p><span style="font-family: arial; font-size: medium;">PV = present value</span></p><p><span style="font-family: arial; font-size: medium;">PMT = payment</span></p><p><span style="font-family: arial; font-size: medium;">FV = future value</span></p><p><span style="font-family: arial; font-size: medium;">n = number of periods</span></p><p><span style="font-family: arial; font-size: medium;">i% = periodic interest rate</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For monthly payments per year:</span></p><p><span style="font-family: arial; font-size: medium;">n = number of years × 12</span></p><p><span style="font-family: arial; font-size: medium;">i% = annual interest rate ÷ 12</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For quarterly payments per year: </span></p><p><span style="font-family: arial; font-size: medium;">n = number of years × 4</span></p><p><span style="font-family: arial; font-size: medium;">i% = annual interest rate ÷ 4</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For the routines, n is stored in memory register 1 and i% is stored in memory register 2. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">n [ STO ] 1 </span></p><p><span style="font-family: arial; font-size: medium;">i% [ STO ] 2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SPFV: Future Value of a Single Present Value Factor</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"> [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SPPV: Present Value of a Single Future Value Factor</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"> [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ ± ] [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">USFV: Future Value of a Payment Stream Factor</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ ( ] [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ - ] 1 [ ) ] </span></p><p><span style="font-family: arial; font-size: medium;">[ ÷ ] [ RCL ] 2 [ 2nd ] { % } [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">USPV: Present Value of a Payment Stream Factor</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ ( ] 1 [ - ] [ ( ] 1 [ + ] [ RCL ] 2 [ 2nd ] { % } [ ) ] [ y^x ] [ RCL ] 1 [ ± ] [ ) ]</span></p><p><span style="font-family: arial; font-size: medium;">[ ÷ ] [ RCL ] 2 [ 2nd ] { % } [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Let n = 60, i% = 5 </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">60 [ STO ] 1</span></p><p><span style="font-family: arial; font-size: medium;">5 [ STO ] 2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SPFV: 18.67918589</span></p><p><span style="font-family: arial; font-size: medium;">SPPV: 0.053535524</span></p><p><span style="font-family: arial; font-size: medium;">USFV: 353.5837179</span></p><p><span style="font-family: arial; font-size: medium;">USPV: 18.92928953</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-80559627359846570302024-02-11T00:00:00.000-08:002024-02-11T00:00:00.126-08:00Spotlight: Casio CFX-9850GB Plus <p><span style="font-family: arial;"><b>Spotlight: <span style="color: #2b00fe;">Casio </span><span style="color: #38761d;">CFX-9850GB </span><span style="color: #ffa400;">Plus </span></b></span></p><p><span style="font-family: arial;">(Retro Review)</span></p><p><span style="font-family: arial;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfHFoA821x5G3l9m-Bkz_5MDn5nOt6rsOaMY-yaiYXHmOZOkTxLZHRAQzOYE4uIctYgvwM6nurtMZSCctaFjK1wDGZdhoyUrFsaqFnyMfrOTSB_lNQpXziu_aIUM1-tJfLszpmGQEOwY7kggugmUUm8N7L96zkmkaRsJvyZVw_NKZTpgkpYMeIXMRXWrI/s4624/cfx-9850gb%20plus%20full%20screen.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfHFoA821x5G3l9m-Bkz_5MDn5nOt6rsOaMY-yaiYXHmOZOkTxLZHRAQzOYE4uIctYgvwM6nurtMZSCctaFjK1wDGZdhoyUrFsaqFnyMfrOTSB_lNQpXziu_aIUM1-tJfLszpmGQEOwY7kggugmUUm8N7L96zkmkaRsJvyZVw_NKZTpgkpYMeIXMRXWrI/w480-h640/cfx-9850gb%20plus%20full%20screen.jpg" width="480" /></a></div><br /><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ6QwYs7Zz-D7whHE-PiTzKW7mZ3EA_J_0S7cYKzmQHxRXsyySxoQzcTvc3Y1ovnZho5yWeGtn9cni4mqsM3hcWmSe5RRMjkHpAqcLRDpulRyHm9rGC0PjlOlW7MHpBtwgxtkyra3KhxghnDzH5ivjSEb6P1kRvG00JhstxHajVC_L5fU3oCOaojd-Wx0/s4624/contrast%20screen.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3468" data-original-width="4624" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ6QwYs7Zz-D7whHE-PiTzKW7mZ3EA_J_0S7cYKzmQHxRXsyySxoQzcTvc3Y1ovnZho5yWeGtn9cni4mqsM3hcWmSe5RRMjkHpAqcLRDpulRyHm9rGC0PjlOlW7MHpBtwgxtkyra3KhxghnDzH5ivjSEb6P1kRvG00JhstxHajVC_L5fU3oCOaojd-Wx0/w640-h480/contrast%20screen.jpg" width="640" /></a></div><br /><span style="font-family: arial;"><br /></span><p></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Quick Facts</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Model: CFX-9850GB Plus</span></p><p><span style="font-family: arial;">Company: Casio</span></p><p><span style="font-family: arial;">Timeline: late 1990s (circa 1997) to 2008</span></p><p><span style="font-family: arial;">Type: Graphing, Algebraic, floating decimal with fractions</span></p><p><span style="font-family: arial;">Number of Digits: 10</span></p><p><span style="font-family: arial;">Power: 4 AAA batteries plus CR 2032 backup</span></p><p><span style="font-family: arial;">Colors: <span style="color: #ffa400;">orange</span>, <span style="color: #2b00fe;">blue</span>, <span style="color: #38761d;">green</span></span></p><p><span style="font-family: arial;">Screen Size: 128 x 64 pixels</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">There are two versions of the CFX-9850GB Plus: </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">* First edition (1997 - 2002): Black case, black slide cover, about 32,000 bytes of memory. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">* Second edition (2002 - 2008): White case, green cover, about 64,000 bytes of memory.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I have the first edition. Even though this calculator is no longer in production, the CFX-9850G series is still available through online sites such as eBay and thrift stores. I purchased mine on eBay from Petchiart Shop. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Graphing in Color</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The CFX-9850G series is the first series of calculators to include a multicolored display. Graphs, tables, statistical plots, and sequences can be displayed in up to three colors: blue, green, and orange. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">How were the colors accomplished? Colors are determined by the contrast of the pixels. Pixels with the lightest contrast are displayed as <span style="color: #ffa400;">orange</span>. Pixels with a medium contrast are displayed as <span style="color: #2b00fe;">blue</span>. Pixels with the darkest contrast are displayed as <span style="color: #38761d;">green</span>. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Text and regular calculations are shown in blue. We can change the color of the text to green or orange through [OPTN], [F6] (>), [F1] (COLR). Blue text is the default. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Calculator Modes</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">1 Run: Main Calculator</span></p><p><span style="font-family: arial;">2 Statistics: Statistics. Regressions include linear, med-med, quadratic, cubic, quartic, logarithmic, exponential, power, sinusoidal, and logistic.</span></p><p><span style="font-family: arial;">3 Matrices: Matrix editing and manipulation mode</span></p><p><span style="font-family: arial;">4 Lists: List editing and manipulation mode. Up to six lists can be stored (List 1 - List 6)</span></p><p><span style="font-family: arial;">5 Graphing: Functions with and without shading (Y(X)), Polar (r(Θ)), Parametric (X(T), Y(T)), Horizontal Lines (x=c) </span></p><p><span style="font-family: arial;">6 Dynamic Graphing: Leave one variable to change during graphing</span></p><p><span style="font-family: arial;">7 Tables</span></p><p><span style="font-family: arial;">8 Recursion: graphing recursion sequences</span></p><p><span style="font-family: arial;">9 Conics: graphing conics using templates</span></p><p><span style="font-family: arial;">A Equation: Simultaneous linear systems to the order of 6 equations, quadratic polynomials, cubic polynomials, general solver</span></p><p><span style="font-family: arial;">B Program: Programs can be write-protected with a password if desired. </span></p><p><span style="font-family: arial;">C TVM: Finance including simple interest, compound interest, amortization, cost/sell/margin, date addition, days between dates</span></p><p><span style="font-family: arial;">D Link</span></p><p><span style="font-family: arial;">E Contrast menu</span></p><p><span style="font-family: arial;">F Memory Manager</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Also included through the [OPTN] key:</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Complex numbers: arithmetic, parts (real, imaginary, absolute value, argument/angle), conjugate</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Hyperbolic functions</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Probability functions</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Numeric function including fractional and integer parts, rounding function (internally round the number to fix settings).</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Angle: Angle units including decimal degrees/degree-minute-second conversions</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Logic: AND, OR, NOT. The calculator has integer modes (decimal, octal, hexadecimal, binary). </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Function Memory: store up to 6 functions for recall. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">ESYM: engineering suffixes (mega, micro, etc)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The calculator is run in LineIO format (linear). There is no textbook mode or an exact function when it comes to terms of pi (π) or square roots (√).</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Peripherals</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">To transfer files between the calculator and a computer, the CFX-9850GB Plus uses an FA-123 connection cable. If this calculator is not purchased new or like new, the cable will have to be a separate purchase, which may not be an easy find. I believe the FA-123 is a USB cable. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">There is a SB-62 cable which connects the calculator to a class of Casio label printers, such as the Casio KL-2000 Printer. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Built-In Library</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">What separates the CFX-9850GB PLUS (and the CFX-9950GB PLUS) from the rest of the series is the inclusion of a built in software library which can be loaded into the calculator's memory at any time. All of the library's programs are write-protected and require a password to edit. I don't know the password, sorry.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">The software library includes programs that used the EA-100 data analyzer, differential equations, drawing Mandelbrot sets, geometry, amortization, complex number powers and roots, double and triple integrals, and slope filed graphs. (not an all-inclusive list).</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I want to try them all.</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><b>Comparison of the Color Calculators (vs. fx-CG 50)</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I want to close out this spotlight by comparing the CFX-9850 PLUS with its LCD contrast pixels versus the current Casio fx-CG 50, a full-color graphing calculator. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">In the following pictures, the fx-CG50 is on the left, the CFX-9850GB PLUS is on the right. </span></p><p><span style="font-family: arial;"><br /></span></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJTZN8Ew1D6EM8BAAetPDidtGAYJv18F4xVyQx5hNbKuDsFHlHGRbZhZCEty1TZGJa7FmoHtzsX71qqyu39Y9z0DzlsUGWIJ7Dv8zY2YGlBmBAkd1IuK3wrePw4pr_CGnJvuGIrkmIDt3oAPowpfPz-dOByk90BGY_c6sa9wSVOdmFbSswBJVFw3f46PE/s4551/compare%20pic%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1623" data-original-width="4551" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJTZN8Ew1D6EM8BAAetPDidtGAYJv18F4xVyQx5hNbKuDsFHlHGRbZhZCEty1TZGJa7FmoHtzsX71qqyu39Y9z0DzlsUGWIJ7Dv8zY2YGlBmBAkd1IuK3wrePw4pr_CGnJvuGIrkmIDt3oAPowpfPz-dOByk90BGY_c6sa9wSVOdmFbSswBJVFw3f46PE/w640-h228/compare%20pic%201.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVDh_-w1gmmjiW90CU_k9Rr0B6NpdR3xhUUUsukelTlQbZLsSp4naAVWAhH73HyDBHDPgNE9W4HRXHuHRuerdkjqCF_MfifFokmq0sx97A7q0U-jq5WG-f8yaLdPhJ9F7bfSIWNhDklhgQFfvAJOSvyOt8ZJhKUv_cMoZISd0Cw8FBKBbdLncZnKY8neI/s4273/compare%20pic%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1648" data-original-width="4273" height="246" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVDh_-w1gmmjiW90CU_k9Rr0B6NpdR3xhUUUsukelTlQbZLsSp4naAVWAhH73HyDBHDPgNE9W4HRXHuHRuerdkjqCF_MfifFokmq0sx97A7q0U-jq5WG-f8yaLdPhJ9F7bfSIWNhDklhgQFfvAJOSvyOt8ZJhKUv_cMoZISd0Cw8FBKBbdLncZnKY8neI/w640-h246/compare%20pic%202.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB53aooMUePVDMv7DwXPv9DOBgkvGQmq4hApVVi8m5pRUb8LCoL3ZLBPvJsEMObY0bMzPGA20bfxHeIkSiYqsqcjv-rJKxjTbwTJJxJIC75uj_WHjwu5Yk5N3EKpHO9nRgmNHBXo73q93dYqv3hkpJvw-rFg6NUKbapHj7xZf5w-esVsjQ_c1kWIvsr7g/s4206/compare%20pic%203.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1488" data-original-width="4206" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB53aooMUePVDMv7DwXPv9DOBgkvGQmq4hApVVi8m5pRUb8LCoL3ZLBPvJsEMObY0bMzPGA20bfxHeIkSiYqsqcjv-rJKxjTbwTJJxJIC75uj_WHjwu5Yk5N3EKpHO9nRgmNHBXo73q93dYqv3hkpJvw-rFg6NUKbapHj7xZf5w-esVsjQ_c1kWIvsr7g/w640-h226/compare%20pic%203.jpg" width="640" /></a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgB53aooMUePVDMv7DwXPv9DOBgkvGQmq4hApVVi8m5pRUb8LCoL3ZLBPvJsEMObY0bMzPGA20bfxHeIkSiYqsqcjv-rJKxjTbwTJJxJIC75uj_WHjwu5Yk5N3EKpHO9nRgmNHBXo73q93dYqv3hkpJvw-rFg6NUKbapHj7xZf5w-esVsjQ_c1kWIvsr7g/s4206/compare%20pic%203.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNpToYUo1LDrxlkHCJ9y_ujBDNgKv7EZKEyiFRZvTJu7E5nsj7iT5RvGxi9GNHE4wPVAia1vdYzLRl2325FiAN7mB0V5Erl_eZSPn19B4coDls-k7M8eOOSyRrvbQ6Kj5ZBMdI3laDfFOdrk_LCAhSmYUhC7-MtPSfhZ-Ou1pQS2fzr6RZ8a8AnjIVpWY/s3397/compare%20pic%204.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1156" data-original-width="3397" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNpToYUo1LDrxlkHCJ9y_ujBDNgKv7EZKEyiFRZvTJu7E5nsj7iT5RvGxi9GNHE4wPVAia1vdYzLRl2325FiAN7mB0V5Erl_eZSPn19B4coDls-k7M8eOOSyRrvbQ6Kj5ZBMdI3laDfFOdrk_LCAhSmYUhC7-MtPSfhZ-Ou1pQS2fzr6RZ8a8AnjIVpWY/w640-h218/compare%20pic%204.jpg" width="640" /></a></div></div><br /><span style="font-family: arial;"><br /></span><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><p><span style="font-family: arial;"><b>Sources</b></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">"CFX-9850G PLUS" Casio Ledudu. 2022. Accessed January 9, 2024. <a href="https://casio.ledudu.com/pockets.asp?type=280&lg=eng" target="_blank">https://casio.ledudu.com/pockets.asp?type=280&lg=eng</a></span></p><p><span style="font-family: arial;">(this link includes the main manual)</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">"Casio 9850 series" Wikipedia. Last Edited May 14, 2023. Accessed December 30, 2023. <a href="https://en.wikipedia.org/wiki/Casio_9850_series" target="_blank">https://en.wikipedia.org/wiki/Casio_9850_series</a></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Casio. Casio CFX9850GB Plus Software Library. <a href="https://support.casio.com/en/manual/manualfile.php?cid=004013009" target="_blank">https://support.casio.com/en/manual/manualfile.php?cid=004013009</a></span></p><p><span style="font-family: arial;">Accessed December 30, 2023. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Vis, Peter. "Casio Serial Cable Compatibility" The Quantum Archive. Accessed January 9, 2024. <a href="https://www.petervis.com/electronics%20guides/Casio%20Serial%20Cables/Casio%20Serial%20Cable%20Compatibility.html" target="_blank">https://www.petervis.com/electronics%20guides/Casio%20Serial%20Cables/Casio%20Serial%20Cable%20Compatibility.html</a></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">I am always impressed with Casio graphing calculators. Often, they give the most functions and capability for the least money. Money well spent. </span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">Eddie</span></p><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-34911145949742806972024-02-10T00:00:00.000-08:002024-02-10T00:00:00.128-08:00 Spotlight: Aristo Multilog Nr. 970 Slide Rule<p><span style="font-family: arial; font-size: medium;"><b>Spotlight: Aristo Multilog Nr. 970 Slide Rule</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Release Year: 1954</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Santa Barbara and Carpentaria, California, are two of my favorite places to visit. While on vacation in December 2023 in Santa Barbara, I bought a Aristo Nr. Slide Rule at Antique Alley. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhmsVawwLB7O1obQKKzyxBo3Zc6yWW-NVx8q-bIvb5B3lwM0SB2Cub-xKm_VVGc6wyy0O70kj_oQViQhyphenhypheng5zlgeq9WgiCv8ljKgtmwXFlxVni3aqm-Q_HKCjgPRlnkr3lReD-m2dBfwkUDr2_wdNNQglnnq0h0C8GYiys8aYHvOKjDNlVP7enaokT5zw0/s4624/pic%20-%20Aristo%20Nr%20970%20general.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1760" data-original-width="4624" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhmsVawwLB7O1obQKKzyxBo3Zc6yWW-NVx8q-bIvb5B3lwM0SB2Cub-xKm_VVGc6wyy0O70kj_oQViQhyphenhypheng5zlgeq9WgiCv8ljKgtmwXFlxVni3aqm-Q_HKCjgPRlnkr3lReD-m2dBfwkUDr2_wdNNQglnnq0h0C8GYiys8aYHvOKjDNlVP7enaokT5zw0/w640-h244/pic%20-%20Aristo%20Nr%20970%20general.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW_trxNijBcaUUjlL81HeaQsiWwdcjmKD9xEVacEw4o8p3CL7wq3UitFzMFJt6SvXXtWj91zqKmelLW8uuhe9ItDOmXiJ0ldeQF64lKZgFpZFlLzTjmEdupYdAGPV2bk19NZ9vHujRkg1-Z3CR8vDFe3kbZJJQML391xh4q2ohTyMSWKfpXzcv_qvbCoE/s4473/pic%20-%20Aristo%20Nr%20970.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1073" data-original-width="4473" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW_trxNijBcaUUjlL81HeaQsiWwdcjmKD9xEVacEw4o8p3CL7wq3UitFzMFJt6SvXXtWj91zqKmelLW8uuhe9ItDOmXiJ0ldeQF64lKZgFpZFlLzTjmEdupYdAGPV2bk19NZ9vHujRkg1-Z3CR8vDFe3kbZJJQML391xh4q2ohTyMSWKfpXzcv_qvbCoE/w640-h154/pic%20-%20Aristo%20Nr%20970.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Not only did the slide rule have a nice, hard case, the slide rule is large. The slide rule also has a functional description of each scale. I also like the slide rule uses two colors, black and <span style="color: #b45f06;">brown</span>, to distinguish the scales from each other. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw8dpBsRbJ-6sNB_GiVS4AKBxjuUYNfLH53ADS98TBUso3PpCwK8NX8KGI18MRDAi17CD7Q0dgpZ35m4nVJNxvwJhMR1ZwvxNzBzhyQv1Lc8pJV6K4HHzZDtB-M4yAY23UMV8YsX9XOx17q1dIHij3wOVoImlwxAMzQQqGQqFIwyzVM7a-nn-1qO5cMOY/s5545/pic%20-%20Aristo%20Nr%20Side%201.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3025" data-original-width="5545" height="350" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw8dpBsRbJ-6sNB_GiVS4AKBxjuUYNfLH53ADS98TBUso3PpCwK8NX8KGI18MRDAi17CD7Q0dgpZ35m4nVJNxvwJhMR1ZwvxNzBzhyQv1Lc8pJV6K4HHzZDtB-M4yAY23UMV8YsX9XOx17q1dIHij3wOVoImlwxAMzQQqGQqFIwyzVM7a-nn-1qO5cMOY/w640-h350/pic%20-%20Aristo%20Nr%20Side%201.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Side 1:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">LL00: e^(-0.001X)</span></p><p><span style="font-family: arial; font-size: medium;">K: X^3 (K = D^3)</span></p><p><span style="font-family: arial; font-size: medium;">A: X^2 (A = D^2)</span></p><p><span style="font-family: arial; font-size: medium;">CF: πX </span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">CIF: 1/(πX)</span></p><p><span style="font-family: arial; font-size: medium;">L: lg X (log X)</span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">CI: 1/X</span></p><p><span style="font-family: arial; font-size: medium;">C: X</span></p><p><span style="font-family: arial; font-size: medium;">D: X</span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">DI: 1/X</span></p><p><span style="font-family: arial; font-size: medium;">LL0: e^(0.001X)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjblbta3ueHbtHg_TN5RnTt3cfqNfZpUb9AHxyxuUNj93yDD-fCJoXsMaW05UHAn4wLqxdU7b2d4pprvlhLeta3EzgeV-pbStkZZp4y4d9WOBd6hc79boPuJEGocaPT160JyVaNqWF3rv0r8qA2KbFGAGV1yKA2QY1Op89rOTD-sejL69Drk5wrjUWhVJs/s5393/pic%20-%20Aristo%20Nr%20Side%202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2977" data-original-width="5393" height="354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjblbta3ueHbtHg_TN5RnTt3cfqNfZpUb9AHxyxuUNj93yDD-fCJoXsMaW05UHAn4wLqxdU7b2d4pprvlhLeta3EzgeV-pbStkZZp4y4d9WOBd6hc79boPuJEGocaPT160JyVaNqWF3rv0r8qA2KbFGAGV1yKA2QY1Op89rOTD-sejL69Drk5wrjUWhVJs/w640-h354/pic%20-%20Aristo%20Nr%20Side%202.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;">Side 2:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">LL01: e^(-0.01X)</span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">LL02: e^(-0.1X)</span></p><p><span style="color: #b45f06; font-family: arial; font-size: medium;">LL03: e^(-X)</span></p><p><span style="font-family: arial; font-size: medium;">DF: πX</span></p><p><span style="font-family: arial; font-size: medium;">B: X^2</span></p><p><span style="font-family: arial; font-size: medium;">T: ∡tg (tan X, X is in degrees, tan D° = T)</span></p><p><span style="font-family: arial; font-size: medium;">ST: ∡arc (tan X, sin X)</span></p><p><span style="font-family: arial; font-size: medium;">S: ∡sin (arcsin X, sin D° = T) </span></p><p><span style="font-family: arial; font-size: medium;">C: X</span></p><p><span style="font-family: arial; font-size: medium;">D: X </span></p><p><span style="font-family: arial; font-size: medium;">LL3: e^X (LL3 = e^D)</span></p><p><span style="font-family: arial; font-size: medium;">LL2: e^(0.1X)</span></p><p><span style="font-family: arial; font-size: medium;">LL1: e^(0.01X)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">As a bonus, the slide rule came with a reference card. One one side is the Dietzgen Slide Rule Conversion Tables (U.S. and SI units, 1950), and other side is a table of common areas, surface areas, volumes, and trigonometric properties of the right triangle. I don't know if this was standard addition when the Aristo Multilog Nr. 970 was sold. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This may be my favorite slide rule: not only the scales are large (and as a result easier on the eyes to read), but the fact that there are function descriptions on the scales is a big plus. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-55543397629414051032024-02-04T00:00:00.000-08:002024-02-04T00:00:00.132-08:00 Some RPN Routines: Including Maximum and Minimum of Two Numbers<p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>Some RPN Routines: Including Maximum and Minimum of Two Numbers</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Here are some RPN routines that hopefully you find helpful. I am assuming that the values are stored in memory registers before calculation and a general four-level stack is used (HP 11C, 12C, 15C, 42S, 32S, 32SII, DM41X, DM32, DM42, DM15, WP34, etc.). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>(a + b + c) × (a + b - c)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Assume that: </span></p><p><span style="font-family: arial; font-size: medium;">Memory register 1 = a</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 2 = b</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 3 = c</span></p><p><span style="font-family: arial; font-size: medium;">(Your memory registers may have different names or labels)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic is allowed:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">RCL+ 2</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">LST x</span></p><p><span style="font-family: courier; font-size: medium;">RCL- 3</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">(LST x = LAST x)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic isn't available:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">LST x</span></p><p><span style="font-family: courier; font-size: medium;">RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">-</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example: a= 10, b = 2, c = 7. Result: 95</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b> (s + a) × (s + b) × (s + c)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Assume that: </span></p><p><span style="font-family: arial; font-size: medium;">Memory register 1 = a</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 2 = b</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 3 = c</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 4 = s</span></p><p><span style="font-family: arial; font-size: medium;">(Your memory registers may have different names or labels)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic is allowed:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">RCL+ 1</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL+ 2</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL+ 3</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic isn't available:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">+</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example: a = 4, b = 8, c = 2, s = 3. Result: 385</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b> (s - a) × (s - b) × (s - c)</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Assume that: </span></p><p><span style="font-family: arial; font-size: medium;">Memory register 1 = a</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 2 = b</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 3 = c</span></p><p><span style="font-family: arial; font-size: medium;">Memory register 4 = s</span></p><p><span style="font-family: arial; font-size: medium;">(Your memory registers may have different names or labels)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic is allowed:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">RCL- 1</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL- 2</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL- 3</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If recall arithmetic isn't available:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">RCL 4</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">ENTER</span></p><p><span style="font-family: courier; font-size: medium;">RCL 1</span></p><p><span style="font-family: courier; font-size: medium;">-</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL 2</span></p><p><span style="font-family: courier; font-size: medium;">-</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">RCL 3</span></p><p><span style="font-family: courier; font-size: medium;">-</span></p><p><span style="font-family: courier; font-size: medium;">×</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example: a = 8, b = 10, c = 3, s = 24. Result: 4,704</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Maximum and Minimum of the X and Y Stacks</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In a program, we can arrange the stack to show the maximum and minimum between two numbers as follows:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #783f04; font-family: arial; font-size: medium;"><u>Maximum on the X Stack, Minimum on the Y Stack:</u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">...</span></p><p><span style="font-family: courier; font-size: medium;">x≤y </span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If the value of x is less than or equal to y, swap the stack values. Otherwise, leave the stack as is.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #783f04; font-family: arial; font-size: medium;"><u>Minimum on the X Stack, Maximum on the X Stack:</u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">HP 12C, HP 11C, HP 10C, and the HP 41C/DM41 family, due to the lack of the x≥y command:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">... </span></p><p><span style="font-family: courier; font-size: medium;">x≤y</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Same routine as the maximum routine, except an extra swap command is placed.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All others:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">... </span></p><p><span style="font-family: courier; font-size: medium;">x≥y</span></p><p><span style="font-family: courier; font-size: medium;">x<>y</span></p><p><span style="font-family: courier; font-size: medium;">...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x≥y is TEST 9 on the HP 15C. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If the value of x is greater than or equal to y, swap the stack values. Otherwise, leave the stack as is.</span></p><p><span style="font-family: arial; font-size: medium;"></span></p><p><span style="font-family: arial; font-size: medium;">Of course, if your calculator has the maximum (MAX) and minimum (MIN) functions, by all means, use them. </span></p><div><br /></div><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-37697972245760227712024-02-03T00:00:00.000-08:002024-02-03T00:00:00.128-08:00Swiss Micros DM42 and TI-84 Plus: Sum of an Infinite Geometric Series<p><span style="font-family: arial; font-size: medium;"><b>Swiss Micros DM42 and TI-84 Plus: Sum of an Infinite Geometric Series</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">An infinite geometric series has the form:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">a + a × r + a × r^2 + a × r^3 + ...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">= a × (1 + r + r^2 + r^3 + ....)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If |r| < 1, the series converges and a sum exists. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">∞</span></p><p><span style="font-family: arial; font-size: medium;">Σ a × r^n = a ÷ (1 - r)</span></p><p><span style="font-family: arial; font-size: medium;">n=0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">∞</span></p><p><span style="font-family: arial; font-size: medium;">Σ a × r^(n-1) = a ÷ (1 - r)</span></p><p><span style="font-family: arial; font-size: medium;">n=1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">However if |r| ≥ 1, the series diverges and does not have as sum.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #351c75; font-family: arial; font-size: medium;"><b><u>DM42 Program: GSUM</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculators: DM42, HP 42S, Free42, Plus42</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">00 { 36-Byte Prgm }</span></p><p><span style="font-family: courier; font-size: medium;">01 LBL "GSUM"</span></p><p><span style="font-family: courier; font-size: medium;">02 ENTER</span></p><p><span style="font-family: courier; font-size: medium;">03 ABS</span></p><p><span style="font-family: courier; font-size: medium;">04 1</span></p><p><span style="font-family: courier; font-size: medium;">05 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">06 X>Y?</span></p><p><span style="font-family: courier; font-size: medium;">07 GTO 00</span></p><p><span style="font-family: courier; font-size: medium;">08 R↓</span></p><p><span style="font-family: courier; font-size: medium;">09 R↓</span></p><p><span style="font-family: courier; font-size: medium;">10 1</span></p><p><span style="font-family: courier; font-size: medium;">11 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">12 -</span></p><p><span style="font-family: courier; font-size: medium;">13 ÷</span></p><p><span style="font-family: courier; font-size: medium;">14 RTN</span></p><p><span style="font-family: courier; font-size: medium;">15 LBL 00</span></p><p><span style="font-family: courier; font-size: medium;">16 CLX</span></p><p><span style="font-family: courier; font-size: medium;">17 "DIVERGES"</span></p><p><span style="font-family: courier; font-size: medium;">18 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">19 .END.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In the case the series diverges, the X stack is cleared (displays 0). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #351c75; font-family: arial; font-size: medium;"><b><u>TI-84 Plus Program: GSUM</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculators: TI-84 Plus, TI-84 Plus CE (Python), TI-83 Premium CE (Python)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Disp "Σ(A*R^N,0,INF)","Σ(A*R^(N-1),1,I)"</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A,R</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Disp "A=",A,"R=",R</span></p><p><span style="font-family: courier; font-size: medium;">If abs(R)<1</span></p><p><span style="font-family: courier; font-size: medium;">Then</span></p><p><span style="font-family: courier; font-size: medium;">A/(1-R)→S</span></p><p><span style="font-family: courier; font-size: medium;">Disp "SUM=",S</span></p><p><span style="font-family: courier; font-size: medium;">Else</span></p><p><span style="font-family: courier; font-size: medium;">Disp "DIVERGES"</span></p><p><span style="font-family: courier; font-size: medium;">End</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Examples</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = 2.5</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: 0.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = 3.75</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: -2.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -2.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = diverges</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: 2.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = 2.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = diverges</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-40665993441679440932024-01-28T00:00:00.000-08:002024-01-28T00:00:00.132-08:00Swiss Micros DM42 and TI-84 Plus: Sum of an Infinite Geometric Series<p><span style="font-family: arial; font-size: medium;"><b>Swiss Micros DM42 and TI-84 Plus: Sum of an Infinite Geometric Series</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">An infinite geometric series has the form:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">a + a × r + a × r^2 + a × r^3 + ...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">= a × (1 + r + r^2 + r^3 + ....)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If |r| < 1, the series converges and a sum exists. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">∞</span></p><p><span style="font-family: arial; font-size: medium;">Σ a × r^n = a ÷ (1 - r)</span></p><p><span style="font-family: arial; font-size: medium;">n=0</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">∞</span></p><p><span style="font-family: arial; font-size: medium;">Σ a × r^(n-1) = a ÷ (1 - r)</span></p><p><span style="font-family: arial; font-size: medium;">n=1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">However if |r| ≥ 1, the series diverges and does not have as sum.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>DM42 Program: GSUM</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculators: DM42, HP 42S, Free42, Plus42</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">00 { 36-Byte Prgm }</span></p><p><span style="font-family: courier; font-size: medium;">01▸LBL "GSUM"</span></p><p><span style="font-family: courier; font-size: medium;">02 ENTER</span></p><p><span style="font-family: courier; font-size: medium;">03 ABS</span></p><p><span style="font-family: courier; font-size: medium;">04 1</span></p><p><span style="font-family: courier; font-size: medium;">05 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">06 X>Y?</span></p><p><span style="font-family: courier; font-size: medium;">07 GTO 00</span></p><p><span style="font-family: courier; font-size: medium;">08 R↓</span></p><p><span style="font-family: courier; font-size: medium;">09 R↓</span></p><p><span style="font-family: courier; font-size: medium;">10 1</span></p><p><span style="font-family: courier; font-size: medium;">11 X<>Y</span></p><p><span style="font-family: courier; font-size: medium;">12 -</span></p><p><span style="font-family: courier; font-size: medium;">13 ÷</span></p><p><span style="font-family: courier; font-size: medium;">14 RTN</span></p><p><span style="font-family: courier; font-size: medium;">15▸LBL 00</span></p><p><span style="font-family: courier; font-size: medium;">16 CLX</span></p><p><span style="font-family: courier; font-size: medium;">17 "DIVERGES"</span></p><p><span style="font-family: courier; font-size: medium;">18 AVIEW</span></p><p><span style="font-family: courier; font-size: medium;">19 .END.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In the case the series diverges, the X stack is cleared (displays 0). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>TI-84 Plus Program: GSUM</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculators: TI-84 Plus, TI-84 Plus CE (Python), TI-83 Premium CE (Python)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Disp "Σ(A*R^N,0,INF)","Σ(A*R^(N-1),1,I)"</span></p><p><span style="font-family: courier; font-size: medium;">Prompt A,R</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Disp "A=",A,"R=",R</span></p><p><span style="font-family: courier; font-size: medium;">If abs(R)<1</span></p><p><span style="font-family: courier; font-size: medium;">Then</span></p><p><span style="font-family: courier; font-size: medium;">A/(1-R)→S</span></p><p><span style="font-family: courier; font-size: medium;">Disp "SUM=",S</span></p><p><span style="font-family: courier; font-size: medium;">Else</span></p><p><span style="font-family: courier; font-size: medium;">Disp "DIVERGES"</span></p><p><span style="font-family: courier; font-size: medium;">End</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = 2.5</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: 0.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -0.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = 3.75</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: -2.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = -2.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = diverges</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A: 3, R: 2.2</span></p><p><span style="font-family: arial; font-size: medium;">Stack: Y = 3, X = 2.2</span></p><p><span style="font-family: arial; font-size: medium;">Result = diverges</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-30339836075462711782024-01-27T00:00:00.000-08:002024-01-27T00:00:00.131-08:00HP Prime - Restart and Some CAS Command Comparisons<div><span style="font-family: arial; font-size: medium;"><b>HP Prime - Restart and Some CAS Command Comparisons</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-size: medium;"><b><span style="font-family: courier;">restart </span><span style="font-family: arial;">- A Rescue in CAS Mode</span></b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">I learned about this command in a recent HPCC virtual meeting about the command restart. One of the participants had trouble storing equations in variables. After changing settings and trying other formats, the restart command was introduced and it solved the problem. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">What the restart command does is purge all the variables in CAS variables and reset all CAS settings. The restart command can be typed or found in the Catalog.</span></div><div><span style="font-family: arial; font-size: medium;">The command does not require arguments.</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">When the restart command, the screen will show:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">============== restarted ==============</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Pressing enter will show a list of the CAS variables in a list. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><b><br /></b></span></div><div><span style="font-family: arial; font-size: medium;"><b>Some CAS Command Comparisons</b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>ifactor vs. ifactors</u></b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">ifactor </span><span style="font-family: arial; font-size: medium;">gives the prime factorization of integers.</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">ifactors </span><span style="font-family: arial; font-size: medium;">returns a list of prime factors with the associated multiplicity in a list in the format: </span></div><div><span style="font-family: arial; font-size: medium;">[ factor1, multiplicity1, factor2, multiplicity2, ... ]</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Examples:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">ifactor(480) returns 2^5 * 3 * 5</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">ifactors(480) returns [2, 5, 3, 1, 5, 1]</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">ifactor(507) returns 3 * 13^2</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">ifactors(507) returns [3, 1, 13, 2]</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>normal vs. regroup</u></b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Both the normal and regroup commands can be found in the catalog or can be typed. According to the help facility:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">normal </span><span style="font-family: arial; font-size: medium;">simplifies an expression to an irreducible form.</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">regroup </span><span style="font-family: arial; font-size: medium;">simplifies and collects terms in an expression, to match the Minimum simplification setting. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Examples:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">normal(a*(b+a-b^2)) returns a^2-a*b^2+a*b</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">regroup(a*(b+a-b^2)) returns a*(-b^2+a*b)</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">normal(x+5*x+6*(x^2-3*x)) returns 6*x^2-12*x</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">regroup(x+5*x+6*(x^2-3*x)) returns 6*(x^2-3*x)+6*x</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">normal(x^2*√2-(x^3-1)/(x+1)) returns ((√2-1)*x^3+2*√2*x^2+1)/(x+2)</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">regroup(x^2*√2-(x^3-1)/(x+1)) returns √2*x^2-(x^3-1)/(x+2)</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">normal((x+3)^5) returns x^5+15*x^4+90*x^3+270*x^2+405*x+243</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">regroup((x+3)^5) just returns (x+3)^5</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>iquo vs irem vs. iquorem</u></b></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">The three commands iquo, irem, and iquorem are commands in Euclidean Division.</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">iquo(x,y)</span><span style="font-family: arial; font-size: medium;"> returns the quotient of x/y</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">irem(x,y)</span><span style="font-family: arial; font-size: medium;"> returns the remainder of x/y</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: courier; font-size: medium;">iquorem(x,y)</span><span style="font-family: arial; font-size: medium;"> returns the quotient and remainder of x/y in a list.</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">The arguments x and y must be positive integers. </span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Examples:</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">iquo(258,19) returns 13</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">irem(258,19) returns 11</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">iquorem(258,19) returns [13, 11]</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">258 = 13 * 19 + 11</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">I really need to work with the CAS engine of the HP Prime more often,</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">Eddie</span></div><div><span style="font-family: arial; font-size: medium;"><br /></span></div><div><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></div><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-61135786831524776372024-01-21T00:00:00.000-08:002024-01-21T00:00:00.127-08:00Approximating Limits to Avoid Overflow <p><span style="font-family: arial; font-size: medium;"><b>Approximating Limits to Avoid Overflow</b></span></p><div><br /></div><p><span style="font-family: arial; font-size: medium;">For most 10-digit scientific calculators, the maximum that a number can be before an overflow error occurs is 9.999999999×10^99.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Maximum Number</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">What is the maximum number x can be before the calculator overflows? (For reference, I used a TI-84 Plus to calculate these numbers.)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Function: Maximum Number</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">e^(x^2): 15.17427129</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x!: 69 (most calculators only allow nonnegative integers for the factorial function)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3^x: 209.5903274</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">e^x: 230.2585093</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2^x: 332.1928095</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x^4: slightly less than 1E25 (1 × 10^25) (like 9.99999999999E24)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x^3: 2.15443469E33 (2.15443469 × 10^33)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x^2: slightly less than 1E50 (1 × 10^50) (like 9.99999999999E49)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x^(3/2): 4.641588833E66 (4.641588833 × 10^66) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Limits to Infinity</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Why is this important? This could be useful in applications, say approximating values of y(x) when x approaches infinity.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 1:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y = ln(x) / x^3</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To find the limit x can be, look at the function presented and select the "part" that has the lowest limit. In this case, that "part" is x^3. Approach to that limit.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(1E33): 7.59853081E-98</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(1.5E33): 2.26343032E-98</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(2E33): 9.58480691E-99</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(2.1E33): 8.28498493E-99</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">It would appear that ln(x)/x^3 approaches 0 as x approaches ∞.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The key is to select x values that will not cause the calculator to provide the overflow error.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 2: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y = e^x/x^2</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">e^x has a max x of 230.2585093, while x^2 has a max x of 9.99999999999E49. To prevent an overflow, we must choose x values approaching the lower max, in this case, 230.2585093.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(229.9): 1.321975623E95</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(230): 1.459738847E95</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(230.1): 1.611859E95</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(230.2): 1.779832347E95</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">It would appear that e^x/x^2 approaches ∞ as x approaches ∞.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example 3:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y = (x^3 - 1) / (x! * x^2)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Since the factorial is involved, the highest x can be is 69.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">But y(69) overflows in this case! Then we have to select lower x values until we can get answers. This can be a trial and error approach.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(68): overflow</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(67): 1.83706434E-93</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(66): 1.21246228E-91</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">y(65): 7.88100352E-90</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Looking at the results from y(65), y(66), and y(67), it appears that (x^3 - 1) / (x! * x^2) approaches 0 as x approaches ∞.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Remember that this isn't proof, but we can get an idea how a rational function will behave. We still need the tools such as the ratio, root, and other tests.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-2293767866802729762024-01-20T00:00:00.000-08:002024-01-20T00:00:00.139-08:00Retro Review: Panasonic CompuVoice JF-721U<p><span style="font-family: arial; font-size: medium;"><b>Retro Review: Panasonic CompuVoice JF-721U</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">My partner, Chris, gave me this calculator as a Christmas present. Thank you and love you, Chris!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglG5XeOHB9VCpb1FINet_G-8PFT4tM1mTggrDJitWAnP-zAt6MFJkfDR2ZvDFd2J4BQCDyzFVYSpL1AEaa1OM16jAx5PtcvQS8X1oju0Os5nTbKshA9GvjD0FBVRM_oHIH65fsu4-yq7NfMRGsmKf7_Fq4Io1gOwia8QZ6P0goLP2CpLsvKMktQ1T1b3Q/s4624/20231217_161558.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglG5XeOHB9VCpb1FINet_G-8PFT4tM1mTggrDJitWAnP-zAt6MFJkfDR2ZvDFd2J4BQCDyzFVYSpL1AEaa1OM16jAx5PtcvQS8X1oju0Os5nTbKshA9GvjD0FBVRM_oHIH65fsu4-yq7NfMRGsmKf7_Fq4Io1gOwia8QZ6P0goLP2CpLsvKMktQ1T1b3Q/w480-h640/20231217_161558.jpg" width="480" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGbMWIyDvOwz8IK-ToYuQH7VQmkTjiQcpqdJlI205MQENMUmUno5n8rIfwuNHfk7AEczMU5CqYvcmqRwmutorXVVTUiqAXcfhAGwfO_Ys9yuFH6fnt9x7kLHqOOlfy3JeN2FH5k64pOMwcS0G1cHteJeTKFrlCpGL4F2B7jn_nKsoqSCDJVsU8yxenQU/s4624/20231218_055836.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4624" data-original-width="3468" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGbMWIyDvOwz8IK-ToYuQH7VQmkTjiQcpqdJlI205MQENMUmUno5n8rIfwuNHfk7AEczMU5CqYvcmqRwmutorXVVTUiqAXcfhAGwfO_Ys9yuFH6fnt9x7kLHqOOlfy3JeN2FH5k64pOMwcS0G1cHteJeTKFrlCpGL4F2B7jn_nKsoqSCDJVsU8yxenQU/w480-h640/20231218_055836.jpg" width="480" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Quick Facts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Model: JF-721U</span></p><p><span style="font-family: arial; font-size: medium;">Company: Panasonic</span></p><p><span style="font-family: arial; font-size: medium;">Timeline: early to mid 1980s</span></p><p><span style="font-family: arial; font-size: medium;">Type: Four Function Calculator, Stopwatch, Timer, Clock, with Voice</span></p><p><span style="font-family: arial; font-size: medium;">Number of Digits: 8</span></p><p><span style="font-family: arial; font-size: medium;">Power: 3 AA batteries</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>An All-In One Calculator</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This is like a dream machine: a calculator, a clock, stopwatch, timer, and it talks, and it came with a beautiful brown leather power that shows the clock and a button labeled [ TIME ], when pressed the calculator reads the time. [ TIME ] is located on the upper left hand corner of the calculator next to its speaker. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Chris definitely did well!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The voice is a male machine voice, loud and clear. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Three Modes: LOCK, COMP-TIME-STOP WATCH, and SET</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The switch on the JF-721U selects the calculator's three modes: LOCK, COMP-TIME-STOP WATCH, and SET. Let's go through these modes one by one. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>LOCK Mode</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">LOCK mode is basically the calculator's sleep mode. The display shows the clock and the only key that operates is the [ TIME ] button. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>COMP-TIME-STOP WATCH Mode</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">On this mode, we can run the calculator, timer, and the stopwatch. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Timer: The timer can be set in hours (h) and minutes (m) only. To set the timer, press the [ SET ] button, enter the time desired in hh-mm format, and press [ S/S ]. The [ S/S ] acts as the start/stop button.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Stopwatch: The stopwatch is actived by pressing the [ SET ] and [ S/S ] keys in sequence to start the stopwatch. The stop the stopwatch again, press the [ S/S ] key and record the time. If the voice is turned on, the final time will be read. We can start and stop the stopwach as many times as we want. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To cancel the stopwatch without seeing the result, press the clear [ C ] button.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calculator: The JE-721U is a four-function calculator. The calculator is activated by the clear [ C ] button. There are three standard memory keys: memory plus [ M+ ], memory minus [ M- ], and memory recall-clear [ MRC ]. The number in the memory register is retained as long as there is battery power.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">One curious thing with the percent key, [ % ], is that the key only works with multiplication and division problems. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To add a percent: </span></p><p><span style="font-family: arial; font-size: medium;">Enter the number, press [ × ], enter the percent, press [ % ], press [ + ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To subtract a percent: </span></p><p><span style="font-family: arial; font-size: medium;">Enter the number, press [ × ], enter the percent, press [ % ], press [ - ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The calculator's change sign key is labeled [ (-) ]. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In this mode, the calculator's voice is toggled on and off by the [ VOICE ] key.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The hour [ HOUR ] key is also available. If the hour key is on, then the calculator will announce the hour.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b>SET Mode</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">We can set the clock and the alarm in SET mode. In this mode we can set the clock and an alarm.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To set the clock: press [ SET ], enter the hour and minute, and then the [ TM ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To set the alarm: press [ SET ], enter the hour and minute, and then the [ ALM ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In this mode, the decimal key, [ . ], switches between AM/PM. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If this calculator can handle military time (00:00 to 23:59), I don't know how to set it. Also, the calculator is a clock only, so for daylight savings time, the time must be manually set. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Final Thoughts</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I like this calculator. The voice is loud and clear and the time functions are really nice additions. I imagined the CompuVoice calculators set on the desks of professionals and were companions of travelers back in the 1980s. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-37112020378634299012024-01-14T00:00:00.000-08:002024-01-14T00:00:00.143-08:00Swiss Micros DM32: Remote XEQ: Calling Program from Other State Files<p><span style="font-family: arial; font-size: medium;"><b>Swiss Micros DM32: Remote XEQ: Calling Program from Other State Files</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: red; font-family: arial; font-size: medium;">Required Firmware: 2.07 or later</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The Swiss Micros DM32 is truly an enhanced HP 32SII, and some of the new features take this platform to the next level. One of the newest features is the ability to call programs from other state files, which Swiss Micros calls Remote XEQ. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">What is a state file? A state file is a calculator file that contains its set of programs, equations, variables, and settings. Since the DM32, like the HP 32SII, has only have one letter label names, state files are the way to expand and organize lots of programs and equations without having to re-program the calculator every time.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Calling programs from other state files allow the use of programs from other available state files. How do you know if a state file is available? Press the fourth key from the left on the top row of keys. There will be a list of available states loaded into calculator memory. If the state file that you need isn't listed, select Load (second key from the left on the row of blank keys in the Available States menu) and load the required state file. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">As of Firmware 2.07, we can only execute remote labels in programs, not from the home screen. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Using Remote XEQ in a Program</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">1. Make sure your source state file is available. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">2. In the program, press [ XEQ ] twice. ( [ XEQ ] [ XEQ ]) You will be taken to a screen of available state files.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">3. Select the source state file. In the Available States screen, use the plus [ + ] and minus [ - ] keys to scroll the cursor. Press [ ENTER ].</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">4. Insert the required label from the source file. All variables in the remote execution are considered local.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Communication Note: When you have a program that uses remote XEQ, be sure upload both the source and the current state files, and communicate that both files have to be available (active) to those you download your programs. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Example</b></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Jjx5MGvrVNYd-5KJixRDuJqOPcybyzfSKVrOhmz5m2otWczlcNmoLCATh7un3Bx5Z5m_Cbh08sl6eElHcTh-jj6K-asd0xC056xw_XoFVvmQSCNl2VF-iBlCASagydUMVwFEnhd-kCLcWM5qKWH9J4LS0I5KMu5voiGM0vGwDFZTNcao8-Tl4lVSI_4/s953/picture-DM32%20calling%20other%20states.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="619" data-original-width="953" height="416" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Jjx5MGvrVNYd-5KJixRDuJqOPcybyzfSKVrOhmz5m2otWczlcNmoLCATh7un3Bx5Z5m_Cbh08sl6eElHcTh-jj6K-asd0xC056xw_XoFVvmQSCNl2VF-iBlCASagydUMVwFEnhd-kCLcWM5qKWH9J4LS0I5KMu5voiGM0vGwDFZTNcao8-Tl4lVSI_4/w640-h416/picture-DM32%20calling%20other%20states.jpg" width="640" /></a></div><br /><p><span style="font-family: arial; font-size: large;">Let's assume the following states are available: demo.d32 and clean.d32. The demo file is the source file containing the following program:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">R01 LBL R</span></p><p><span style="font-family: courier; font-size: medium;">R02 1/x </span></p><p><span style="font-family: courier; font-size: medium;">R03 x<>y</span></p><p><span style="font-family: courier; font-size: medium;">R04 1/x </span></p><p><span style="font-family: courier; font-size: medium;">R05 +</span></p><p><span style="font-family: courier; font-size: medium;">R06 1/x </span></p><p><span style="font-family: courier; font-size: medium;">R07 RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This calculates 1/(1/x + 1/y). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In the clean file, we can call program R from demo by:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">A01 LBL A</span></p><p><span style="font-family: courier; font-size: medium;">A02 XEQ R:DE </span></p><p><span style="font-family: arial; font-size: medium;"> </span></p><p><span style="font-family: arial; font-size: medium;">(Press [ XEQ ] [ XEQ ], select demo from the list of available states, [ ENTER ] , R)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">A03 RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Now executing program A in the clean state will execute program R in the demo state.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In the demo state:</span></p><p><span style="font-family: arial; font-size: medium;">4 [ ENTER ] 9 [ XEQ ] R returns 2.7692 (FIX 4 mode is set)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">In the clean state:</span></p><p><span style="font-family: arial; font-size: medium;">4 [ ENTER ] 9 [ XEQ ] A returns 2.7692 (FIX 4 mode is set)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Source</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SwissMicros GmbH "DM32 User Manual" v3.46b 2016-2023</span></p><p><a href="https://technical.swissmicros.com/dm32/doc/dm32_user_manual.html" target="_blank"><span style="font-family: arial; font-size: medium;">https://technical.swissmicros.com/dm32/doc/dm32_user_manual.html</span></a><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I hope you find this new feature useful,</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-84561903703609986552024-01-13T00:00:00.000-08:002024-01-13T00:00:00.138-08:00TI-30Xa Algorithms: Probability<p><span style="font-family: arial; font-size: medium;"><b>TI-30Xa Algorithms: Probability</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Even when a calculator isn't (technically) programmable, algorithms can be applied to scientific and financial calculations.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The calculations take numerical arguments that are stored in the TI-30Xa's three memory slots: M1, M2, and M3. Store amounts into the memory registers by the [ STO ] key. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Careful: For the solar versions of the TI-30Xa, do not press the [ON/AC] button as doing so clears the memory registers.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The registers used:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M1 = n </span></p><p><span style="font-family: arial; font-size: medium;">M2 = k </span></p><p><span style="font-family: arial; font-size: medium;">M3 = p </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>Repeated Combinations</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">nHk = (n + k -1)Ck = (n + k - 1)! ÷ (k! × (n - 1)!)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M1: n = number of objects</span></p><p><span style="font-family: arial; font-size: medium;">M2: k = number of objects chosen in the population</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">nHk = number of combinations of picking k from n objects, assuming repeats are allowed</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Algorithm:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ ( ] [ RCL ] 1 [ + ] [ RCL ] 2 [ - ] 1 [ ) ] [ 2nd ] (nCr) [ RCL ] 2 [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M1: n = 50</span></p><p><span style="font-family: arial; font-size: medium;">M2: k = 5</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Result: 3,162,510</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>Binomial Probability Distribution</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Prob(k) = nCk × p^k × (1 - p)^(n - k) = n! ÷ (k! × (n - k)!) × p^k × (1 - p)^(n - k) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M1: n = number of trials</span></p><p><span style="font-family: arial; font-size: medium;">M2: k = number of successes</span></p><p><span style="font-family: arial; font-size: medium;">M3: p = probability of success (in decimal; i.e. enter 0.30 for 30%)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Prob = probability of k successes out of n trials with a success probability p</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Algorithm: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ RCL ] 1 [ 2nd ] (nCr) [ RCL ] 2 [ × ] [ RCL ] 3 [ y^x ] [ RCL ] 2 [ × ] [ ( ] 1 [ - ] [ RCL ] 3 [ ) ] [ y^x ] [ ( ] [ RCL ] 1 [ - ] [ RCL ] 2 [ ) ] [ = ] </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M1: n = 50</span></p><p><span style="font-family: arial; font-size: medium;">M2: k = 5</span></p><p><span style="font-family: arial; font-size: medium;">M3: p = 0.8</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Result: 2.442763967 × 10^-26</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u><b>Geometric Probability Distribution</b></u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Prob(k) = (1 - p)^(k - 1) × p</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M2: k = number of failures before the first success</span></p><p><span style="font-family: arial; font-size: medium;">M3: p = probability of success (in decimal) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Prob = probability of a event taking k trials before the first success</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Algorithm:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ ( ] 1 [ - ] [ RCL ] 3 [ ) ] [ y^x ] [ ( ] [ RCL ] 2 [ - ] 1 [ ) ] [ × ] [ RCL ] 3 [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">M2: k = 5</span></p><p><span style="font-family: arial; font-size: medium;">M3: p = 0.8</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Result: 0.00128</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><b><u>A Simple Pseudorandom Number Generator</u></b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The TI-30Xa does not have a random number function. To generate random numbers, a pseudorandom number generator algorithm must be used in the form of:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x_n+1 = f(x_n)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">where x_0 is the initial value, known as the seed value. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A simple </span><span style="font-family: arial; font-size: large;">pseudorandom</span><span style="font-family: arial; font-size: large;"> </span><span style="font-family: arial; font-size: medium;"> number generator to generate numbers between 0 and 1 is:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">x_n+1 = frac(997 × x_n + π)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Algorithm:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">With x_n in display:</span></p><p><span style="font-family: arial; font-size: medium;">[ × ] 997 [ + ] [ π ] [ = ] </span></p><p><span style="font-family: arial; font-size: medium;">[ - ] the integer part of the number in the display [ = ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Result: x_n+1. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There is no fraction part or integer part functions are not available on the TI-30Xa. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Example: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Starting seed: 0.7896 </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ × ] 997 [ + ] </span></p><p><span style="font-family: arial; font-size: medium;">[ π ] [ = ] Display: 799.3457927</span></p><p><span style="font-family: arial; font-size: medium;">[ - ] 799 [ = ] Display: 0.345792654</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ × ] 997 [ + ] </span></p><p><span style="font-family: arial; font-size: medium;">[ π ] [ = ] Display: 347.8968683</span></p><p><span style="font-family: arial; font-size: medium;">[ - ] 347 [ = ] Display: 0.896868283</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ × ] 997 [ + ] </span></p><p><span style="font-family: arial; font-size: medium;">[ π ] [ = ] Display: 897.3192706</span></p><p><span style="font-family: arial; font-size: medium;">[ - ] 897 [ = ] Display: 0.319270625</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ × ] 997 [ + ] </span></p><p><span style="font-family: arial; font-size: medium;">[ π ] [ = ] Display: 321.4544059</span></p><p><span style="font-family: arial; font-size: medium;">[ - ] 321 [ = ] Display: 0.454405908</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">and so on...</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The random numbers with the starting seed 0.7896 are:</span></p><p><span style="font-family: arial; font-size: medium;">0.345792654</span></p><p><span style="font-family: arial; font-size: medium;">0.896868283</span></p><p><span style="font-family: arial; font-size: medium;">0.319270625</span></p><p><span style="font-family: arial; font-size: medium;">0.454405908</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Take as many decimal points as you wish. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">If you enjoy this post, I will consider making a series using the TI-30Xa calculator (and similar simple scientific calculators). Until next time,</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-58232512169489474392024-01-07T00:00:00.000-08:002024-01-07T00:00:00.134-08:00Casio fx-9750GIII: Equatorial to Galactic Coordinates Conversions <p><span style="color: #800180; font-family: arial; font-size: medium;"><b>Casio fx-9750GIII: Equatorial to Galactic Coordinates Conversions </b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: arial; font-size: medium;"><u>Coordinate Systems</u></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There are several coordinate systems used by astronomers to determine the placement of celestial objects, such as stars, galaxies, planets, and black holes, in our night skies.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Two coordinate systems are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Equatorial System:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The equatorial system frames the University with the Earth's center as the center of the university. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Right Ascension (α): Customarily stated in hours, minutes, and seconds (H°M°S°). Each hour is equivalent to 15 degrees. The right ascension at 0 hours is aligned where the sun would be during the vernal equinox. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Declination (δ): Customarily stated in degrees, minutes, and seconds (D°M°S°). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic System:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The galactic system frames the University, aligning it with the Milky Way Galaxy. The center of the system is our Sun. The </span><span style="font-family: arial; font-size: large;">galactic </span><span style="font-family: arial; font-size: medium;">longitude at 0 degrees aligns with the center of our galaxy (Sagittarius A*).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic Longitude (l): Customarily stated in degrees, minutes, and seconds (D°M°S°). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic Latitude (b): Customarily stated in degrees, minutes, and seconds (D°M°S°). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program EQT2GLT converts equatorial coordinates (α, δ) to galactical coordinates (l, b). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b = arcsin( cos δ × cos 27.1284° × cos(α - 192.8595°) + cos δ × cos 27.1284° )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l = </span></p><p><span style="font-family: arial; font-size: medium;">arctan( ( sin δ - sin b × sin 27.1284° ) ÷ ( cos δ × sin(α -192.8595°) × cos 27.1284°) + 32.93117169°</span></p><p><span style="font-family: arial; font-size: medium;">= atan2((sin δ - sin b × sin 27.1284°), (cos δ × sin(α -192.8595°) × cos 27.1284°)) + 32.93117169°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b is in hours, from -90 to 90 degrees.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l is in degrees, from 0 to 360 degrees. Be sure to consider quadrants in your calculation. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The program GLT2EQT converts galactical coordinates (l, b) to equatorial coordinates (α, δ). </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">δ = arcsin( (cos b × cos 27.1284° × sin( l - 32.93117169° ) + sin b × sin 27.1284° )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α = arctan( ( cos b × cos( l - 32.93117169° ) ) ÷ ( sin b × cos 27.1284° - cos b × sin 27.1284° × sin( l - 32.93117169° ) ) + 192.8595°</span></p><p><span style="font-family: arial; font-size: medium;">= atan2((cos b × cos(l - 32.93117169°),(sin b × cos 27.1284° - cos b × sin 27.1284° × sin(l-32.93117169°)) + 192.8595°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">δ is in degrees, from -90 to 90 degrees. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α is in hours, from 0 to 24 hours. Be sure to consider quadrants in your calculation. Remember that 1 hour is equivalent to 15 degrees. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The equations are from Practical Astronomy With Your Calculator by Peter Duffett-Smith, with the constants updated for J2000.0.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">From the "Conversion of coordinates" page of Tobias Westmeier's webpage, the J2000.0 of the north pole are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α0 ≈ 192.8595° (12h 51m 26.28s)</span></p><p><span style="font-family: arial; font-size: medium;">δ0 ≈ 27.1284° (27°07'42.24")</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">(Sources: Duffett-Smith, Westmeier - refer to the Source section)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">For more details, please refer to the Equatorial to Galactic Coordinates: Updating the Constants posted on January 6, 2023. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div><span style="font-size: medium;"><div style="font-family: arial;"><b>Casio fx-9750GIII Program: EQT2GLT</b></div><div style="font-family: arial;"><br /></div><div><span style="font-family: courier;">a+bi</span></div><div><span style="font-family: courier;">Deg</span></div><div><span style="font-family: courier;">"EQUATORIAL -> GALACTIC"</span></div><div><span style="font-family: courier;">"J2000.0"</span></div><div><span style="font-family: courier;">"R.A. IN H°M°S°"</span></div><div><span style="font-family: courier;">?->A</span></div><div><span style="font-family: courier;">"DEC. IN D°M°S°"</span></div><div><span style="font-family: courier;">?->D</span></div><div><span style="font-family: courier;">15*A->A</span></div><div><span style="font-family: courier;">192.8595->R</span></div><div><span style="font-family: courier;">27.1284->E</span></div><div><span style="font-family: courier;">32.93117169->C</span></div><div><span style="font-family: courier;">sin^-1 (cos D*cos E*cos (A-R)+sin D*sin E)->B</span></div><div><span style="font-family: courier;">sin D-sin B*sin E->Y</span></div><div><span style="font-family: courier;">cos D*sin (A-R)*cos E->X</span></div><div><span style="font-family: courier;">Arg (X+Yi)->T</span></div><div><span style="font-family: courier;">Y<⇒T+360->T</span></div><div><span style="font-family: courier;">T+C->L</span></div><div><span style="font-family: courier;">ClrText</span></div><div><span style="font-family: courier;">"B="</span></div><div><span style="font-family: courier;">B ▶DMS◢</span></div><div><span style="font-family: courier;">"L="</span></div><div><span style="font-family: courier;">L ▶DMS</span></div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">Note: The calculator is set to the following modes: degrees, and rectangular complex mode. </div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">Example: </div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">The star Hamal in the constellation Aries (Alpha Arietis) is located approximately at:</div><div style="font-family: arial;">α = 2 hours, 7 minutes, 10 seconds</div><div style="font-family: arial;">δ = 23°27'44"</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">Enter hours-minutes-seconds and degrees-minutes-seconds by pressing [ OPTN ], [ F6 ] ( > ), [ F5 ] (ANGL), [ F4 ] (°''').</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">b: -36°12'22.12"</div><div style="font-family: arial;">L: 144°34'33.2"</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;"><br /></div><div style="font-family: arial;"><b>Casio fx-9750GIII Program: EQT2GLT</b></div><div style="font-family: arial;"><br /></div><div><span style="font-family: courier;">a+bi</span></div><div><span style="font-family: courier;">Deg</span></div><div><span style="font-family: courier;">"GALACTIC_->_EQUATORIAL"</span></div><div><span style="font-family: courier;">"J2000.0"</span></div><div><span style="font-family: courier;">"B (LAT) IN D°M°S°"</span></div><div><span style="font-family: courier;">?->B</span></div><div><span style="font-family: courier;">"L (LONG) IN D°M°S°"</span></div><div><span style="font-family: courier;">?->L</span></div><div><span style="font-family: courier;">192.8595->R</span></div><div><span style="font-family: courier;">27.1284->E</span></div><div><span style="font-family: courier;">32.93117169->C</span></div><div><span style="font-family: courier;">sin^-1 (cos B*cos E*sin (L-C)+sin B*sin E)->D</span></div><div><span style="font-family: courier;">cos B*cos (L-C)->Y</span></div><div><span style="font-family: courier;">sin B*cos E-cos B*sin E*sin (L-C)->X</span></div><div><span style="font-family: courier;">Arg (X+Yi)->T</span></div><div><span style="font-family: courier;">R+T->A</span></div><div><span style="font-family: courier;">A>360⇒A-360->A</span></div><div><span style="font-family: courier;">A÷15->A</span></div><div><span style="font-family: courier;">ClrText</span></div><div><span style="font-family: courier;">"R.A.="</span></div><div><span style="font-family: courier;">A ▶DMS◢</span></div><div><span style="font-family: courier;">"DEC="</span></div><div><span style="font-family: courier;">D▶DMS</span></div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">Example:</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">The star Regulus in the constellation Leo (Alpha Leonis) is located approximately at: </div><div style="font-family: arial;">b: 48°56'03"</div><div style="font-family: arial;">l: 226°25'36"</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">α: 10°08'22.31" (10 hr, 8 min, 22.31 sec)</div><div style="font-family: arial;">δ: 11°58'02.14"</div><div style="font-family: arial;"><br /></div><div style="font-family: arial;">Note: The results are approximated. </div><div style="font-family: arial;"><br /></div></span></div><div><br /></div><div><p><span style="font-family: arial; font-size: medium;"><b>Sources</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"Equatorial coordinate system" Wikipedia. Last Edited April 10, 2023. Accessed December 10, 2023. <a href="https://en.wikipedia.org/wiki/Equatorial_coordinate_system" target="_blank">https://en.wikipedia.org/wiki/Equatorial_coordinate_system</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"Galactic coordinate system" Wikipedia. Last Edited April 21, 2023. Accessed November 23, 2023. <a href="https://en.wikipedia.org/wiki/Galactic_coordinate_system" target="_blank">https://en.wikipedia.org/wiki/Galactic_coordinate_system</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Duffett-Smith, Peter. <u>Practical Astronomy With Your Calculator</u> Second Edition. Cambridge University Press: Cambridge, UK. 1981. </span></p><p><span style="font-family: arial; font-size: medium;">ISBN: 0 521 28411 2 (paperback) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">National Aeronautics and Space Administration (NASA). "Coordinate Calculator" NASA/IPAC Extragalactic Database. Operated by the California Institute of Technology. 2023. Accessed November 26, 2023. <a href="https://ned.ipac.caltech.edu/coordinate_calculator?in_csys=Equatorial&in_equinox=J2000.0&obs_epoch=2000.0&ra=17h45m40.036s&dec=-29d00m28.17s&pa=0.0&out_csys=Galactic&out_equinox=J2000.0" target="_blank">https://ned.ipac.caltech.edu/coordinate_calculator?in_csys=Equatorial&in_equinox=J2000.0&obs_epoch=2000.0&ra=17h45m40.036s&dec=-29d00m28.17s&pa=0.0&out_csys=Galactic&out_equinox=J2000.0</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Westmeier, Tobias. "Conversion of coordinates" Homepage of Tobias Westmeier. The University of Western Australia. Last Modified 26 September 2023. Accessed November 26, 2023. <a href="https://www.atnf.csiro.au/people/Tobias.Westmeier/index.php" target="_blank">https://www.atnf.csiro.au/people/Tobias.Westmeier/index.php</a></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-68028035725754214212024-01-06T00:00:00.000-08:002024-01-06T00:00:00.134-08:00Equatorial to Galactic Coordinates: Updating the Constants <p><span style="color: #800180; font-family: arial; font-size: medium;"><b>Equatorial to Galactic Coordinates: Updating the Constants </b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Introduction</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">There are several coordinate systems used by astronomers to determine the placement of celestial objects, such as stars, galaxies, planets, and black holes, in our night skies. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Equatorial System</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The most common system is the Equatorial System. Imagine a sphere which represents the Universe with the center of the Earth as the center. The coordinates are the right ascension (α) and the declination (δ).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Right ascension (α): The right ascension is the angular distance from the vernal equinox, going eastward traveling with the celestial equator. The 0 point is the vernal equinox. The vernal equinox, which generally takes place around March 20 or 21, is when the sun is over the Earth's equinox heading north. The lengths of daytime and nighttime are equal. For the northern hemisphere, it's the first day of spring, and for the southern hemisphere, it's the first day of autumn. Sometimes, the vernal equinox is called the First Point of Aries (♈). The range of the right ascension is from 0 hours to 24 hours. Each hour is equivalent to 15° (15 degrees).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Declination (δ): The declination is the angular distance north (above) or south (below) the celestial equator. The range of declination is from -90° to +90°.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Galactical System</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The galactic coordinate system focuses on aligning with our Milky Way Galaxy, with our Sun as the center of the sphere. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic Longitude (l): The galactic longitude measures the angular distance from the center of the Milky Way Galaxy, increasing in the eastward direction. The range of the galactic longitude is from 0° to 360°, with the 0° point at the Galactic Center, which lies in the constellation </span><span style="font-family: arial; font-size: medium;">Sagittarius </span><span style="font-family: arial; font-size: medium;">the Archer. (Sagittarius A*)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic Latitude (b): The galactic latitude is the angle northward from the galactic equator, and it's range is from -90° (south pole located in the constellation Sculptor) to 90° (north pole located in the constellation Coma Berenices).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>Practical Astronomy: With Updated Constants</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A popular resource for astronomical calculations is the book Practical Astronomy With Your Calculator by Peter Duffett-Smith. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">On page 48 of Practical Astronomy With Your Calculator, Duffett-Smith provides these equations for converting from equatorial (α, δ) to galactic (l, b) coordinates:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b = arcsin( cos δ × cos 27.4° × cos(α - 192.25°) + cos δ × cos 27.4° )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l = arctan( ( sin δ - sin b × sin 27.4° ) ÷ ( cos δ × sin(α -192.25°) × cos 27.4°) + 33°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note that in calculation, α, δ, b, and l must be in decimal degrees. Usually the coordinates are given in hours-minutes-seconds or degrees-minutes-seconds, and the quantities must be converted before calculation. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The numerical constants? Those are the 1950.0 coordinates of the north galactic pole with α0 = 192.25° = 12h 49m and δ = 27.4° = 27°24'. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Obviously, in 2024, we would be working with the epoch J2000.0 coordinates of the north galactic pole. If we want to work the J2000.0 coordinates in the above formulas, the constants must be changed.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">From the "Conversion of coordinates" page of Tobias Westmeier's webpage, the J2000.0 of the north pole are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">α0 ≈ 192.8595° (12h 51m 26.28s)</span></p><p><span style="font-family: arial; font-size: medium;">δ0 ≈ 27.1284° (27°07'42.24")</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I choose to use these coordinates because it provides more decimal places than what is presented in the Galactic coordinate page of Wikipedia.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">This leaves us with updated equations:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b = arcsin( cos δ × cos 27.1284° × cos(α - 192.8595°) + cos δ × cos 27.1284° )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l = </span></p><p><span style="font-family: arial; font-size: medium;">arctan( ( sin δ - sin b × sin 27.1284° ) ÷ ( cos δ × sin(α -192.8595°) × cos 27.1284°) + C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">We need to determine the value of C.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">I'm going to use our galactic center, Sagittarius A*, as a reference point, with the coordinates as determined by NASA/IPAC Extragalactic Database's Coordinator Calculator tool:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sagittarius A*:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Equatorial Coordinates</span></p><p><span style="font-family: arial; font-size: medium;">α ≈ 266.41681667° (17h 45m 40.036s)</span></p><p><span style="font-family: arial; font-size: medium;">δ ≈ -29.007825° (-29°00'28.17")</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Galactic Coordinates</span></p><p><span style="font-family: arial; font-size: medium;">l ≈ 359.94418679° (359°56'39.072")</span></p><p><span style="font-family: arial; font-size: medium;">b ≈ -0.04610951° (-0°2'45.994")</span></p><p><span style="font-family: arial; font-size: medium;">(Theoretically, this should be l0 = 0°, b0 = 0°).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Substituting the following data into equation for l (only the second equation has C):</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l = </span></p><p><span style="font-family: arial; font-size: medium;">arctan( ( sin δ - sin b × sin 27.1284° ) ÷ ( cos δ × sin(α -192.8595°) × cos 27.1284°) + C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">359.94418679° = </span></p><p><span style="font-family: arial; font-size: medium;">arctan( ( sin -29.007825° - sin -0.04610951° × sin 27.1284° ) ÷ ( cos -29.007825° × sin(266.41681667° - 192.8595°) × cos 27.1284°) + C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">359.94418679° = arctan( (-0.4845538612°) ÷ (+0.7465187073°)) + C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">We have to keep in mind that anytime we are working with astronomical math, we have to mind the coordinate system. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">359.94418679° = atan2(0.7465187073°, -0.4845538612°) + C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">359.94418679° = arg(0.7465187073° - 0.4845538612° × i) + C (where i = √-1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Note: </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">atan2(0.7465187073°, -0.4845538612°) = -32.98698493°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">To put this answer in the range of 0° to 360°:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">-32.98698493° + 360° = 327.0130151°</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">359.94418679° = 327.0130151° + C </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">C = 32.93117169</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Our final updated equations are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">b = arcsin( cos δ × cos 27.1284° × cos(α - 192.8595°) + cos δ × cos 27.1284° )</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">l = </span></p><p><span style="font-family: arial; font-size: medium;">arctan( ( sin δ - sin b × sin 27.1284° ) ÷ ( cos δ × sin(α -192.8595°) × cos 27.1284°) + 32.93117169</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">and will be used in the programs coming up this weekend.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sources</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"Equatorial coordinate system" Wikipedia. Last Edited April 10, 2023. Accessed December 10, 2023. <a href="https://en.wikipedia.org/wiki/Equatorial_coordinate_system" target="_blank">https://en.wikipedia.org/wiki/Equatorial_coordinate_system</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"Galactic coordinate system" Wikipedia. Last Edited April 21, 2023. Accessed November 23, 2023. <a href="https://en.wikipedia.org/wiki/Galactic_coordinate_system" target="_blank">https://en.wikipedia.org/wiki/Galactic_coordinate_system</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Duffett-Smith, Peter. <u>Practical Astronomy With Your Calculator</u> Second Edition. Cambridge University Press: Cambridge, UK. 1981. </span></p><p><span style="font-family: arial; font-size: medium;">ISBN: 0 521 28411 2 (paperback) </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">National Aeronautics and Space Administration (NASA). "Coordinate Calculator" NASA/IPAC Extragalactic Database. Operated by the California Institute of Technology. 2023. Accessed November 26, 2023. <a href="https://ned.ipac.caltech.edu/coordinate_calculator?in_csys=Equatorial&in_equinox=J2000.0&obs_epoch=2000.0&ra=17h45m40.036s&dec=-29d00m28.17s&pa=0.0&out_csys=Galactic&out_equinox=J2000.0" target="_blank">https://ned.ipac.caltech.edu/coordinate_calculator?in_csys=Equatorial&in_equinox=J2000.0&obs_epoch=2000.0&ra=17h45m40.036s&dec=-29d00m28.17s&pa=0.0&out_csys=Galactic&out_equinox=J2000.0</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Westmeier, Tobias. "Conversion of coordinates" Homepage of Tobias Westmeier. The University of Western Australia. Last Modified 26 September 2023. Accessed November 26, 2023. <a href="https://www.atnf.csiro.au/people/Tobias.Westmeier/index.php" target="_blank">https://www.atnf.csiro.au/people/Tobias.Westmeier/index.php</a></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-80733334795276204182023-12-31T20:03:00.000-08:002023-12-31T20:03:00.131-08:00Swiss Micros DM32: Scientific Constants<p><span style="font-family: arial; font-size: medium;"><b>Swiss Micros DM32: Scientific Constants</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="color: #2b00fe; font-family: Fira Sans; font-size: medium;"><b><i>Happy New Year - Wishing you a prosperous and healthy 2024! </i></b></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>Scientific Constants</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The state constants.d32 loads eight scientific constants to eight global registers. On the DM32, global registers, (numbered -100 to -999, note the negative numbers here), are registers that can be accessed in any state ("calculator").</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The eight constants featured are:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">-900: Earth's Gravity constant: g = 9.80665 m/s^2</span></p><p><span style="font-family: arial; font-size: medium;">-901: Molar Gas constant: R = 8.314462618 J/(K mol)</span></p><p><span style="font-family: arial; font-size: medium;">-902: Planck constant: h = 6.62607015E-34 J/Hz</span></p><p><span style="font-family: arial; font-size: medium;">-903: Newtonian Universal Constant: G = 6.67430E-11 m^3/(kg s^2)</span></p><p><span style="font-family: arial; font-size: medium;">-904: Avogadro constant: Na = 6.02214076E23 mol^-1</span></p><p><span style="font-family: arial; font-size: medium;">-905: Speed of Light: c = 299,792,458 m/s</span></p><p><span style="font-family: arial; font-size: medium;">-906: Boltzmann constant: k = 1.380649E-23 J/K</span></p><p><span style="font-family: arial; font-size: medium;">-907: Elementary Charge constant: e = 1.602176634E-19 C</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Program Labels:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">LBL L: Load the constants</span></p><p><span style="font-family: arial; font-size: medium;">LBL H: help file, press [ R/S ] between each description</span></p><p><span style="font-family: arial; font-size: medium;">LBL V: view all the numerical value of constants</span></p><p><span style="font-family: arial; font-size: medium;">LBL O: obtain a single constant. Enter a number from 0-7.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">0: g</span></p><p><span style="font-family: arial; font-size: medium;">1: R</span></p><p><span style="font-family: arial; font-size: medium;">2: h</span></p><p><span style="font-family: arial; font-size: medium;">3: G</span></p><p><span style="font-family: arial; font-size: medium;">4: Na</span></p><p><span style="font-family: arial; font-size: medium;">5: c</span></p><p><span style="font-family: arial; font-size: medium;">6: k</span></p><p><span style="font-family: arial; font-size: medium;">7: e</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The labels are not global, but the scientific constants are. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Store the register number (-900 to -907) in the variable i. Press RCL (i) to obtain the constant. </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">[ Link to download constants.d32 ]</span></p><p><span style="font-family: arial; font-size: medium;">[ <a href="https://drive.google.com/file/d/1MQWOTwQvc2WrIlU56pw5txWrMrs0dSnk/view?usp=sharing " target="_blank">Link to download constants: here</a>] </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Source</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">"2018 CODATA Recommended Values of the Fundamental Constants of Physics and Chemistry" NIST SP 959. June 2019. Retrieved December 2, 2023 https://physics.nist.gov/cuu/pdf/wallet_2018.pdf</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.comtag:blogger.com,1999:blog-9169922911599301079.post-19234413601411612972023-12-30T00:00:00.000-08:002023-12-30T00:00:00.130-08:00HP 15C (CE) and TI-84 Plus CE Triangle, Square, and Sawtooth Waves<p><span style="font-family: arial; font-size: medium;"><b>HP 15C (CE) and TI-84 Plus CE Triangle, Square, and Sawtooth Waves</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Almost New Years... thank you for all your support in 2023!</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>The Periodic Waves Featured</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Let:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">A = amplitude of the wave</span></p><p><span style="font-family: arial; font-size: medium;">P = period of the wave</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Triangle:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtozjkH19kOlkcvSlEKzth5arh2LI8cyabJyYkfowxNEb-DnjIOSAgkckyOxvAU4C7w1OaHgPW6otd4jO1hKEyP43X69X1TLGTfRMmc7-lgMVFERVJuq8bL9JSCkXaGvIY8eLPVA4t2P_phLlT04Xp1lCkHWPDS9KlnX573l16gie_i6q1COuOwAKUgFI/s677/ti%2084%20triangle%20wave%20picture.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="677" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtozjkH19kOlkcvSlEKzth5arh2LI8cyabJyYkfowxNEb-DnjIOSAgkckyOxvAU4C7w1OaHgPW6otd4jO1hKEyP43X69X1TLGTfRMmc7-lgMVFERVJuq8bL9JSCkXaGvIY8eLPVA4t2P_phLlT04Xp1lCkHWPDS9KlnX573l16gie_i6q1COuOwAKUgFI/w640-h302/ti%2084%20triangle%20wave%20picture.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">TW(A,P,x) = (2 × a ÷ π) × arcsin(sin (2 × π × x ÷ p))</span></p><p><span style="font-family: arial; font-size: medium;">Domain: [ -A, A ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Square:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7z0dRkmjesHucxIz6I9qfoDqAZSPbttsH-om13MgXgsogIBnbcgMwF-4ogXrzQpcpZFkV0sqCQeSn4WCO9mDzlsZX9BXT39vAVkaCRTz_0iiXytpUjqjMKqVglmcGwrsKzYJCsQDBWlpEibaBBzM3RCyGntpcV_uo8ZPXmIzMk27fbkvjSpBH3NUt4W0/s1051/ti%2084%20square%20wave%20picture.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="671" data-original-width="1051" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7z0dRkmjesHucxIz6I9qfoDqAZSPbttsH-om13MgXgsogIBnbcgMwF-4ogXrzQpcpZFkV0sqCQeSn4WCO9mDzlsZX9BXT39vAVkaCRTz_0iiXytpUjqjMKqVglmcGwrsKzYJCsQDBWlpEibaBBzM3RCyGntpcV_uo8ZPXmIzMk27fbkvjSpBH3NUt4W0/w640-h408/ti%2084%20square%20wave%20picture.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SW(A,P,x) = a × sgn(sin(2 × π × x ÷ p)) = a × (-1)^floor(2 × x ÷ P)</span></p><p><span style="font-family: arial; font-size: medium;">Domain: [ -A, A ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sawtooth:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7OBqk7TbRe4bYNyVMg3376D8MubJRt20ZbXNJjKeDNelC8pXdTXZSr1w9VcEfjgUExGhXdCBHA6OLdMmVzX9BdlgVkNMPPfr6wd88eiF0J_YmW7Zv01Iu5ktB3M6KdHy8Am2aFGlCt0nG5FGVKiFTEqrvFro4bLeZ7asQF37jNMANR4eJ7gK4PnuTYOQ/s1045/ti%2084%20sawtooth%20wave%20picture.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="709" data-original-width="1045" height="434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7OBqk7TbRe4bYNyVMg3376D8MubJRt20ZbXNJjKeDNelC8pXdTXZSr1w9VcEfjgUExGhXdCBHA6OLdMmVzX9BdlgVkNMPPfr6wd88eiF0J_YmW7Zv01Iu5ktB3M6KdHy8Am2aFGlCt0nG5FGVKiFTEqrvFro4bLeZ7asQF37jNMANR4eJ7gK4PnuTYOQ/w640-h434/ti%2084%20sawtooth%20wave%20picture.jpg" width="640" /></a></div><br /><p><br /></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">SAW(A,P,x) = A × frac(x ÷ P) </span></p><p><span style="font-family: arial; font-size: medium;">Domain: [ -A, A ]</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">The programs presented only allow for non-negative arguments (x>0). The TI-84 Plus CE program PRDWAVES offer calculations and graphs.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>HP 15C Program Code</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">LBL A: Triangle Wave</span></p><p><span style="font-family: arial; font-size: medium;">LBL B: Square Wave</span></p><p><span style="font-family: arial; font-size: medium;">LBL C: Sawtooth Wave</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Registers Used:</span></p><p><span style="font-family: arial; font-size: medium;">R1 = amplitude (A)</span></p><p><span style="font-family: arial; font-size: medium;">R2 = period (P)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Load A and P in R1 and R2 and then load x in the x stack. X must be non-negative or an error occurs (Error 0).</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Step | Key Code | Key</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Triangle Wave</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">001 | 42, 21, 11 | LBL A</span></p><p><span style="font-family: courier; font-size: medium;">002 | 43, _5, _8 | CF 8</span></p><p><span style="font-family: courier; font-size: medium;">003 | 43, 30, _2 | TEST 2 (x<0?)</span></p><p><span style="font-family: courier; font-size: medium;">004 | __, __, 11 | √x</span></p><p><span style="font-family: courier; font-size: medium;">005 | __, __, _2 | 2</span></p><p><span style="font-family: courier; font-size: medium;">006 | __, __, 20 | ×</span></p><p><span style="font-family: courier; font-size: medium;">007 | __, 43, 26 | π</span></p><p><span style="font-family: courier; font-size: medium;">008 | __, __, 20 | ×</span></p><p><span style="font-family: courier; font-size: medium;">009 | 45, 10, _2 | RCL÷ 2</span></p><p><span style="font-family: courier; font-size: medium;">010 | __, __, 23 | SIN</span></p><p><span style="font-family: courier; font-size: medium;">011 | __, 43, 23 | SIN^-1</span></p><p><span style="font-family: courier; font-size: medium;">012 | __, __, _2 | 2</span></p><p><span style="font-family: courier; font-size: medium;">013 | __, __, 20 | ×</span></p><p><span style="font-family: courier; font-size: medium;">014 | 45, 10, _1 | RCL÷ 1</span></p><p><span style="font-family: courier; font-size: medium;">015 | __, 43, 26 | π</span></p><p><span style="font-family: courier; font-size: medium;">016 | __, __, 10 | ÷</span></p><p><span style="font-family: courier; font-size: medium;">017 | __, 43, 32 | RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Square Wave</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">018 | 42, 21, 12 | LBL B</span></p><p><span style="font-family: courier; font-size: medium;">019 | 43, _5, _8 | CF 8</span></p><p><span style="font-family: courier; font-size: medium;">020 | 43, 30, _2 | TEST 2 (x<0?)</span></p><p><span style="font-family: courier; font-size: medium;">021 | __, __, 11 | √x</span></p><p><span style="font-family: courier; font-size: medium;">022 | __, __, _2 | 2</span></p><p><span style="font-family: courier; font-size: medium;">023 | __, __, 20 | ×</span></p><p><span style="font-family: courier; font-size: medium;">024 | 45, 10, _2 | RCL÷ 2</span></p><p><span style="font-family: courier; font-size: medium;">025 | __, 43, 44 | INT</span></p><p><span style="font-family: courier; font-size: medium;">026 | __, __, _1 | 1</span></p><p><span style="font-family: courier; font-size: medium;">027 | __, __, 16 | CHS</span></p><p><span style="font-family: courier; font-size: medium;">028 | __, __, 34 | x<>y</span></p><p><span style="font-family: courier; font-size: medium;">029 | __, __, 14 | y^x</span></p><p><span style="font-family: courier; font-size: medium;">030 | 45, 20, _1 | RCL× 1</span></p><p><span style="font-family: courier; font-size: medium;">031 | __, 43, 32 | RTN</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Sawtooth Wave</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">032 | 42, 21, 13 | LBL C</span></p><p><span style="font-family: courier; font-size: medium;">033 | 43, _5, _8 | CF 8</span></p><p><span style="font-family: courier; font-size: medium;">034 | 43, 30, _2 | TEST 2 (x<0?)</span></p><p><span style="font-family: courier; font-size: medium;">035 | __, __, 11 | √x</span></p><p><span style="font-family: courier; font-size: medium;">036 | 45, 10, _2 | RCL÷ 2</span></p><p><span style="font-family: courier; font-size: medium;">037 | __, 42, 44 | FRAC</span></p><p><span style="font-family: courier; font-size: medium;">038 | 45, 20, _1 | RCL× 1 </span></p><p><span style="font-family: courier; font-size: medium;">039 | __, 43, 32 | RTN </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Technique: If you require entries to be nonegative, you can use the sequence:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">... commands. ..</span></p><p><span style="font-family: courier; font-size: medium;">CF 8 (turns complex mode off)</span></p><p><span style="font-family: courier; font-size: medium;">TEST 2 (x<0?)</span></p><p><span style="font-family: courier; font-size: medium;">√x (causes an error, specifically Error 0; skipped if x is non-negative)</span></p><p><span style="font-family: courier; font-size: medium;">... commands ... </span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><b>TI-84 Plus CE Program PRDWAVES</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">(spaces added for clarity)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Func</span></p><p><span style="font-family: courier; font-size: medium;">Radian</span></p><p><span style="font-family: courier; font-size: medium;">FnOff</span></p><p><span style="font-family: courier; font-size: medium;">"2023-11-28 EWS"</span></p><p><span style="font-family: courier; font-size: medium;">1→A</span></p><p><span style="font-family: courier; font-size: medium;">1→P</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 0</span></p><p><span style="font-family: courier; font-size: medium;">"AMP = "+toString(A)+","+"PRD = "+toString(P)→Str1</span></p><p><span style="font-family: courier; font-size: medium;">Menu(Str1,"ENTER PARAMETERS",1,"TRIANGLE WAVE",2,"SQUARE WAVE",3,</span></p><p><span style="font-family: courier; font-size: medium;">"SAWTOOTH WAVE",4,"EXIT",E)</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 1</span></p><p><span style="font-family: courier; font-size: medium;">Input "AMPLITUDE? ",A</span></p><p><span style="font-family: courier; font-size: medium;">Input "PERIOD? ",P</span></p><p><span style="font-family: courier; font-size: medium;">Goto 0</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 2</span></p><p><span style="font-family: courier; font-size: medium;">"2*A/π*sin^-1(sin(2*π*X/P))"→Y1</span></p><p><span style="font-family: courier; font-size: medium;">Goto C</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 3</span></p><p><span style="font-family: courier; font-size: medium;">"A*(-1)^iPart(2*X/P)"→Y1</span></p><p><span style="font-family: courier; font-size: medium;">Goto C</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl 4</span></p><p><span style="font-family: courier; font-size: medium;">"A*fPart(X/P)"→Y1</span></p><p><span style="font-family: courier; font-size: medium;">Goto C</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl C</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Menu("CALCULATE","F(X)",F,"GRAPH",G,"NEW PROBLEM",0,"EXIT",E)</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl F</span></p><p><span style="font-family: courier; font-size: medium;">Equ>String(Y1,Str2)</span></p><p><span style="font-family: courier; font-size: medium;">Disp Str2</span></p><p><span style="font-family: courier; font-size: medium;">Input "X≥0,X? ",X</span></p><p><span style="font-family: courier; font-size: medium;">If X<0</span></p><p><span style="font-family: courier; font-size: medium;">Then</span></p><p><span style="font-family: courier; font-size: medium;">Disp "X CAN NOT BE NEGATIVE"</span></p><p><span style="font-family: courier; font-size: medium;">Pause</span></p><p><span style="font-family: courier; font-size: medium;">ClrHome</span></p><p><span style="font-family: courier; font-size: medium;">Goto F</span></p><p><span style="font-family: courier; font-size: medium;">end</span></p><p><span style="font-family: courier; font-size: medium;">Y1(X)→Y</span></p><p><span style="font-family: courier; font-size: medium;">Disp "Y = ", Y</span></p><p><span style="font-family: courier; font-size: medium;">Pause </span></p><p><span style="font-family: courier; font-size: medium;">Goto C</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl G</span></p><p><span style="font-family: courier; font-size: medium;">0→Xmin</span></p><p><span style="font-family: courier; font-size: medium;">10→Xmax</span></p><p><span style="font-family: courier; font-size: medium;">ZoomFit</span></p><p><span style="font-family: courier; font-size: medium;">DispGraph</span></p><p><span style="font-family: courier; font-size: medium;">Stop</span></p><p><span style="font-family: courier; font-size: medium;"><br /></span></p><p><span style="font-family: courier; font-size: medium;">Lbl E</span></p><p><span style="font-family: courier; font-size: medium;">Disp "BYE."</span></p><p><span style="font-family: courier; font-size: medium;">Stop</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Notes:</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Y1: [vars], Y-VARS, 1: Function..., 1: Y1 (captial Y with subscript 1)</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><a href="https://drive.google.com/file/d/16vnL51rvDmlHygrAyVpjtKHrVp8RJG18/view?usp=sharing" target="_blank">Download PRDWAVES.8xp here</a><br /></span></p><p><br /></p><p><span style="font-family: arial; font-size: medium;"><b>Examples</b></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Let P = 2, A = 1</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X = 1</span></p><p><span style="font-family: arial; font-size: medium;">Triangle: 0.0000</span></p><p><span style="font-family: arial; font-size: medium;">Square: -1.0000</span></p><p><span style="font-family: arial; font-size: medium;">Sawtooth: 0.5000</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X = 2.5</span></p><p><span style="font-family: arial; font-size: medium;">Triangle: 1.0000</span></p><p><span style="font-family: arial; font-size: medium;">Square: 1.0000</span></p><p><span style="font-family: arial; font-size: medium;">Sawtooth: 0.2500</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">X = 4.8 </span></p><p><span style="font-family: arial; font-size: medium;">Triangle: 0.4000</span></p><p><span style="font-family: arial; font-size: medium;">Square: 1.0000</span></p><p><span style="font-family: arial; font-size: medium;">Sawtooth: 0.4000</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">Eddie</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p><p><span style="font-family: arial; font-size: medium;">All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. </span></p><div><br /></div>Edward Shorehttp://www.blogger.com/profile/13278913865743064653noreply@blogger.com