Sunday, September 24, 2017

HHC 2017 In Review

HHC 2017 In Review

Hello Nashville, TN!


HHC 2017 took place on September 16 and 17, 2017 in Brentwood, TN.  If you have not gone to a HHC conference, and you love calculators and math, I strongly encourage you to attend.  The conferences take place typically around the latter half of September. 


Disclaimer

I will give a summary of each of the talks here, accompanied by a YouTube video produced by http://www.hpcalc.org/.  The hpcalc.org website is run by Eric Rechlin.  I am under a non-disclosure agreement, which means that I will not be able to discuss certain details of the conference due to confidentiality.

Programming Contests

There were two programming contests, which is presented during the conference, both for the conference attendees and the MoHPC forum.  For fun, please click on the links below.

Subject:  Happy Numbers

Subject: Egyptian Fractions


Day 1:  September 16, 2017

Jim Johnson:  HP 25-LP Panamatik’s New Woodstock Low-Power Upgrade Kit


The classic HP Woodstock Calculators (HP-21, PP-22, HP-25, HP-25C, HP-27, HP-29C) had rechargeable battery packs that also came with the AC plug in battery pack.  The ACT chip in the Woodstock calculators could get damaged if the AC plugged in without the battery or the faulty battery.  Panamatik created a new HP-25 LP kit to replace the ACT chip.  The ACT chip not only revives your Woodstock calculator but also adds features such as:

* 80 character alpha-numeric text.  When you are reviewing your programs, you will see the function name rather than the character code.
* The calculator will have a sleep mode.  This allows the calculator to last up to 10 days before recharging.
* A clock is added, which also adds the ability to set alarms.
* All memory becomes continuous (saved when shut off).

Gene Wright – Non-HP Desktop Scientific Calculators


During the height of scientific calculators in the 1970s, desktop versions of scientific calculators were manufactured.  Aside from the HP-9820, HP-9805A, HP-9815A, HP-9815S, and HP-9825A, Wright highlighted the follow scientific desktops:

* Compucorp 324G:  portable scientific calculator

* Rockwell 350:  8 digit calculator, algebraic

* Monroe 1920:  14 digit calculator, algebraic, linear regression.  Two keys, [ I ] and [ II ] are mapped to two switch selectors. 

The [ I ] key can either execute DMS>θ, r>θ (convert to degrees), xy>θr (rectangular to polar), π, Clr 1-3 (clear registers 1, 2, and 3), Σ (add data points). 

The [ II ] key can used for θ>DMS, θ>r (convert to radians), θr>xy (polar to rectangular), LOG (common logarithm, antilog is available via [INV] [ II ]), σ/mean (calculates standard deviation – stored in register 9 and mean – stored in register 8), -Σ (remove data points).
 
* Electronika MK-45:  features factorial and storage arithmetic, algebraic

* Sharp PC 1001: programmable calculator, 64 steps

* Victor VS 230:  extremely rare desktop scientific calculator

* Commodore 1540:  10 digits with 2 digit exponents, 2 memory registers

Gene Wright – New ROMs for the HP-41CL


An update on the HP 41CL, a replacement CPU board for the fullnut versions for the HP 41C.  The new version of the HP 41CL includes:

* Formula evaluation with an equation library
* Total Rekall:  adds additional function such as XEQ+ and LAST_F (last 5 operations).  There is an additional 5 registers available for emergency purposes.
* HP 67 Fun:  game programs ported from the HP 67.  Chess, Moon Lander, One Arm Bandit, and other games.
* Partial Differential Equations
* Differential Geometry
* Recursive FROOT (root) and FINTG (integrals)
* XROM rom
* Ladybug rom:  makes the 41C is an integer binary calculator
* Test Statistics Solution Rom
* PPC 9: PPC Statistics ROM

Sylvian Cote – 41CL Self-Update


Sylvian’s presentation is very detailed about the 41CL.  A 41CL version 5 is being currently developed with the target date to be released in late 2017-early 2018.  It is the going to be the last version produced.  Version 5 will have the RAM size of 1,024 KB, with flash size of 8 MB, and the number of flash pages will increase to 1,024, the largest of the 41CL. 

The update can be completed all at once or in parts. 


Daniel McDonald – The End Is Near or I Love Pessimism


McDonald addresses a very important question:  what is going to happen to our calculator collection when we die?  How can we ensure the knowledge we gained won’t be lost to future generations? 

Hopefully, when the planet finally switches to an all-app world, there will still be room for handheld calculators with keyboards, or at the very least, enjoy a renaissance (or several) like Model T cars, typewriters, and vinyl albums.

Bob Prosperi – Searching… for calculators


Want that latest calculator or trying to find the elusive calculator for your collection?  Look no further than the tips and tricks presented by Bob Propseri.  Search terms, wildcards, what phrases get the best results (be specific, most of the time), and the use of quotes and minus signs are discussed here. 

Sometimes, the information you are looking for is on a website that is no longer currently maintained.  A tool to try the Wayback Machine, https://archive.org/web/ where over 305 billion archived sites have been achieved.  Your mileage may vary.

On the next eBay or auction site search, if the description contains “I don’t know how to test”, Prosperi suggest just to skip that item because it is most likely broken.

Namir Shammas – PRNGs For Calculators


There is a method on how calculators and computers generate random numbers, typically between 0 and 1 on calculators. Calculators and computers use a PRNG, a pseudo-random number generator to generate random numbers.  While computers use integer-based methods, calculators use floating number-based methods.  The latter generates less “random” values but is forgiven because we call for less random numbers on calculators. 

Regarding integer-based methods, a large integer is generated, then it is divided by another large integer to arrive at the random number. 

Using Matlab, Shammas tested various PRNGs for the ability to generate random numbers.  Patricianly, a million random numbers were generated on each test.  The PRNGs were scored by a penalty factor. 

Some examples of PRNGs are:

* frac(( 1111 + (9997 -1111)*r) * r)
* frac(997 * r)
* frac(π + r)^3
* frac(111/(π + r))

Where frac is the fraction function and r is a seed number.  PRNGs can get really complex, some involve IF-THEN-ELSE routines while others involve more than one seed.

Eric Rechlin – HP Calculator Achieve Twentieth Anniversary


Rechlin tells the history of www.hpcalc.org, launched on August 21, 1997.  Rechlin also accounts about the beginnings of storing HP calculator programs on websites.  Congratulations on 20 years, Eric!

Definitely check out this site www.hpcalc.org.

Note:  Any of my HP Prime programs that I do on this blog is also available for download (author:  Eddie Shore).  Much appreciation and thanks Eric!

Gene Wright – Don’t Make Me Wait


Wright discusses the mathematical perils of waiting, particularly situations where there is a long line and only one server.  Wright discusses queueing theory and the weighing the costs of service (number of servers, which is seen) and the cost of waiting (unseen).  Calculations quickly get complex where more than one server is involved.

Gene Wright – Commodore Scientific Calculators


Did you know that Commodore (1954 – 1994) made computers and calculators?  They did.  Watch this video and learn about the Commodore 1489, SR-37, SR-4148, SR-7919, PR-50, and others.  My personal favorite is the M 55. 

The M 55 (1976) stands out because it offered the error function, Bessel functions, log gamma, matrix operations, and Leguerre polynomials.  The N-60 (1976) specialized in navigation.  The S-61 (1976) specialized in statistics.  The SR-4921 (1975) was Commodore’s RPN model.

A good place for older calculator manuals, including Commodore, is Katie Wesserman’s site http://www.wass.net/manuals/. 

Richard Nelson – Not So Simple Power Calculations


This talk covers Ohm’s Law, calculating effective power, and the problem with load power versus pot rotation.  The pot is referred to a potientmeter, an electrical contact that serves a voltage divider.  In the case that the potientmeter is used in a system of two terminals, then the potientmeter becomes a rheostat (resistance adjustor).  Nelson covers a subject that is not discussed in electronic engineering class.

End of Day 1 – we’ve been going from 8:00 AM to 9:00 PM. 

Day 2:  September 17, 2017

Richard Schwartz – Log Tables


Before handheld calculators (1970s) we had to use tables and slide rules to assist us in calculations.  Log tables were provided by the government to students which had calculated common logarithms (base 10) to four decimal places.  Schwartz discusses the rounding errors found in the tables and how they can be addressed.

Bob Prosperi – HP 75 Update


The HP 75 (1982 – 1986) is enjoying a Renaissance.  There were two versions of the HP 75:  the HP 75C (1982) and the HP 75D (1983 – 1986).  There are also several emulators of the HP 75.  The hardware is large but is a beauty to hold. 

Original specs of the HP 75:

* Programming Language:  BASIC
* CMOS Capricorn CPU coprocessor
* 16,000 byte memory plus 8,000 bytes module available
* AC Port with 3 ROM slots
* Works with the HP-IL and PIL-BOX

You can join a discussion group for the HP 75:  https://groups.io/g/hp75

Namir Shammas – Halley-Ostrowski Root-Seeking Method


Dedicated to Bill Zimmerly.

Methods are numerically finding the root of the equation f(x) = 0 include the well-known Bisection Method, Newton’s Method (the most famous and used), Halley’s Method, and Ostrowski’s Method.

Shammas talks about combing methods to get generate a method to get to the solution faster (less iterations) and more accurately.  Highlighted are the Halley-Ostrowski Method and the Ostrowski-Lagrange Method. 

Jack Schwartz – EduCalc: A Look Back


Schwartz talks and reminiscences about EduCalc, a well embraced store that operated in Laguna Niguel, CA from May 24, 1976 to December 31, 1997.  EduCalc was one of the places to go and contact for HP calculators and documentation. 

Fun fact:  Richard Nelson used to work for EduCalc, and he did voices message detailing events and news for EduCalc.  Go to the video in this section and go to the 50:36 to hear a sample.  Really neat.

If only I visited EduCalc when it was open before it closed its doors in 1997.  And I live near Laguna Niguel! 

Eddie Shore – Extending the HP-12C: Programming for Scientific Applications
This is my first time I talked at an HHC conference, where I covered how we can use the programming features of the HP-12C to take it beyond financial applications and to save as much space as possible.  I covered how to type π, absolute value, the modulus function, finding the number of digits in an integer, how to simulate subroutines, and other topics.


Documentation:

Another check mark off of my bucket list. 

Don Shepherd – Do Not Fold, Spindle, or Mutilate

Punch Cards

Punch cards had a long history, the first design in 1725, with automated processing available in the late 1800’s.  At first, punch cards stored vital data and statistics, until around the 1950s where punch cards became command programming statements. 

Although punch cards came in various shapes and sizes, the typical punch card had eight rows of the digits 0 through 9, with space on top.  The space on top held punches that dictate which characters were used, first the alphabet (A-Z), then numbers (0-9), finally assorted characters (. , $).

To run a program or store information, a lot of cards were used. 


A particular card was the Wang Calculator card, where each punch card had seventy nine rows of numbers in Octal base (0, 1, 2, 4, 10 (8 in decimal), 20 (16 in decimal), and 40 (32 in decimal)).

A particularly neat way to punch cards was to use the IBM Port-A-Punch.  The stylus was used to punch holes in the cards without mess. 

I didn't know that HP Manuals from the 1970s were pretty small and handheld.  Here is two of them for the HP 33E and early financial calculators.

 Goodies:  Radio Shack EC-4000 (TI-57), TI-35 Plus, Sharp EL-506G.  This conference always have excellent door prizes.


Can’t wait for HHC 2018!

Eddie


This blog is property of Edward Shore, 2017.

Thursday, September 21, 2017

Retro Review: Texas Instruments TI-35 PLUS

Retro Review:  Texas Instruments TI-35 PLUS



Essentials

Company:  Texas Instruments
Type:  Scientific
Year: 1986
Battery:  A76 x 2
Digits: 10
Memory Registers: 3, 2 temporary for certain functions and 1 permanent. Storage arithmetic commands SUM and EXC are included. 

Thank you for Bob Patton.  I won this calculator as one of the door prizes on last week’s HHC 2017.

Like the last retro review, I am going to describe the features by the modes available on the calculator.

Mode 1: Decimal Mode (Normal)

This is the normal mode where most of the mathematical operations are available.
The [ a ] and [ b ] keys are temporary registers for various functions, such as:

Number of Combinations:  n [ a ], r [ b ], [ 2nd ] [ ÷ ] (nCr)
Number of Permutations:  n [ a ], r [ b ], [ 2nd ] [ * ] (nPr)
Rectangular to Polar Conversions:  x [ a ], y [ b ], [ 2nd ] [ b ] (R>P); r stored in [ a ], θ stored in [ b ]
Polar to Rectangular Conversions: r [ a ], θ [ b ], [ 2nd ] [ a ] (P>R); x stored in [ a ], y stored in [ b ]

Mode 2:  Binary Mode

Entering Binary Mode converts the number into a binary integer.  Arithmetic operations are available.  The maximum binary number is 511 (2^9 – 1), and binary numbers are 10 bits including a signed bit (leftmost). 

Mode 3:  Octal Mode

Entering Octal Mode converts the number into an octal integer.  Arithmetic operations are available.  

Mode 4:  Hexadecimal Mode

Entering Hexadecimal Mode converts the number into a hexadecimal integer.  Arithmetic operations are available.  In this mode, the [ sin ], [ cos ], [ tan ], [ 1/x ], [ a ], and [ b ] are remapped to the hexadecimal digits A, B, C, D, E, and F, respectively.

Bob Patton gives this amazing demonstration of the Hexadecimal mode: 

[MODE] 4 [ tan ] [ 0 ] [ b ] [ b ] [ a ] [ a ] [STO]  (stores COFFEE_16 in memory)
[ tan ] [ 0 ] [ tan ] [ 0 ] [ sin ]  (inputs COCOA_16)

Repeat:
[ SUM ] [ 0 ] [ RCL ] [ = ] [ SUM ] [ +/- ]
(Note what happens while repeating this loop.  You can try a similar key stroke loop on similar calculators.  Thank you, Bob!)

Mode 5:  Complex Number Mode

Store the real part in temporary register [ a ], the imaginary part in temporary register  [  b ].  Arithmetic operations and polar/rectangular conversions are available.  Other math functions work on the components only.

Mode 6:  Statistics Mode

The TI-35 Plus offers 1-variable statistics with the standard measurements of mean, standard deviation (σn-1), population deviation (σn), and sums. The only way to clear the stat data is to exit stat mode, then enter it again.

An added feature is the three normal distribution probability functions.  Strangely, these functions do not rely on the data entered in the stat registers, and assume that the standard parameters apply (mean is zero, variance is one).

P(t):  lower tail probability
Q(t):  upper tail probability
R(t):  probability from 0 to z

Keyboard and Display

The keys are nice and responsive.  Over time the key markings wearing off.  I like the white font on the dark gray keys.  I wish there was a little more contrast for the secondary functions, which are black on dark gray. 

The display is nice and crisp. 

Final Verdict

I like the TI-35 Plus, it is a step up from the TI-30 series by adding complex number arithmetic and integer conversions.  However, the TI-35 Plus lacks the Boolean functions found on the TI-34.  It is a matter of what features are desired. 

Eddie


This blog is property of Edward Shore, 2017.

Retro Review: Sharp EL-506G

Retro Review:  Sharp EL-506G



Essentials

Company:  Sharp
Type:  Scientific
Year: 1992
Battery:  LR44 x 2, back case is screwed in
Digits: 10
Memory Registers: 7 (A, B, C, D, X, Y, M).  M is the independent register and is the only register available in all calculator modes.  Storage arithmetic commands M+ and M- are included. 
Type of Entry:  Algebraic (called D.A.L. for Direct Algebraic Logic by Sharp)

Thank you for Bob Patton.  I won this calculator as one of the door prizes on last week’s HHC 2017 (a post will be coming shortly).

I am going to describe the features by the modes available on the calculator.

Mode 0: Normal Mode

This is the normal mode where most of the mathematical operations are available.  Here you can convert integers to and from decimal, binary, octal, and hexadecimal mode.  The maximum binary number is 511 (2^9 – 1), and binary numbers are 10 bits including a signed bit (leftmost).  In binary, octal, and hexadecimal sub-modes, the Boolean functions NOT, AND, OR, XOR, and XNOR are available.

It is also in this mode where you can enter and work with fractions.  Fraction parts are separated by a small “r”.  Unfortunately, you cannot convert directly from decimal approximation to fractions.

A wild thing about the algebraic operating system is the display.  Most calculators will have you type the full expression on one line and give the answer on the second.  The EL-506G is however, one line.  Yes, you still enter expressions as you would write them but there is no way to go back and edit them.  During calculation, the function name or symbol will appear on the left hand the screen.  Multiplication is shown by *, and division is shown by /.  Implied multiplication is allowed, indicated by (*).  It takes a little getting used to.



On the EL-506G, Implied Multiplication gets higher priority than multiplication used by the multiply key [ x ].  So:

6 / 2 ( 1 + 2 ) = returns 1

While

6 / 2 * (1 + 2) = returns 9.

I like how the percent key works on the EL-506G, allowing to chain multiple calculations. 

Conversions and Constants

The EL-506G has 32 constants and 32 conversions.  If you have an EL-506G and need a listing, please email me at ews31415@gmail.com.

Mode 1:  Complex Mode

The typical set of functions available for complex mode are present: arithmetic, 1/x, and x^2.  The [a b/c] key is mapped to i (√-1), while the [D°M’S] key is mapped to ∠.

Complex mode has two sub-modes: rectangular and polar.  You can convert and change sub-modes by the use of the [→rθ] key.  [→rθ] converts to polar, while the shifted function ([2ndF] (→xy)) converts to rectangular.

Mode 2: Simultaneous Equations – Linear Systems

This modes solves 2 x 2 or 3 x 3 systems.  The matrix is set up as follows:

Ax = B where

A = [ [a1, b1, c1] [a2, b2, c2] [a3, b3, c3] ], B = [ [ d1 ] [ d2 ] [ d3 ] ]

For 2 x 2 systems, set a3, b3, c1, c2, c3, and d3 all to zero. 

For each linear system solved, the determinant of A is also calculated.

Mode 3:  Statistics Mode

When entering statistics, you will be asked to choose a model:

0 (SD):  1 Variable Statistics
1 (a+bx):  Linear Regression, y = a + bx
2 (…+cx^2):  Quadratic Regression, y = a + bx + cx^2
3 (e^x):  Exponential Regression, y = a * e^(bx)
4 (ln x): Logarithmic Regression, y =  a + b ln x
5 (a*x^b): Power Regression, y = a * x^b
6 (1/x): Inverse Regression, y = a + b/x

The [ STO ] key is mapped to the comma to enter bivariate data.
The [ M+ ] is for data entry.
The [ 2ndF ] (M-) is to erase data.

Keyboard

The keyboard feels quite nice, as the keys require a light touch.  Everything is very responsive. 

Final Verdict

The only tick I have is that the lack of editing algebraic expressions, when you only have one line to work with.  Other than that, this calculator is enjoyable to use.

Eddie

I have two more retro reviews in the upcoming weeks:  TI-35 Plus and Radio Shack EC 4000 (TI-57 clone).  I also can’t wait to share with you what went on during HHC 2017.

It is a year off from next, but if you want to spend a weekend and have a massive geek, calculator, and math fest all rolled into one, the HHC 2018 will be next September.  I have so much fun at these conferences!  Please bug me as new information become available.


This blog is property of Edward Shore, 2017.

Saturday, September 9, 2017

Next Week... and Plans for October 2017

I'm so excited, can't want for next week's HHC 2017 calculator conference in Nashville!  It is my annual calculator conference I attend.  I am also giving a short talk on the HP 12C this year: expanding the use of the HP 12C to include applications beyond finance.

http://hhuc.us/2017/

If you can't make it, I will let you know some details (that I can disclose) when I get back.

What I am planning to do for October is to spend at least two weeks working with the Python programming language.  I am aiming to work with either a Raspberry Pi or QPython3 android app (it's free) or both.


Eddie

This blog is property of Edward Shore, 2017

Wednesday, September 6, 2017

Fun with the TI-80

Fun with the TI-80


TI-80 Program D2DMS - Decimal to Degrees-Minutes-Seconds

Variables:

Decimal Format:
D = decimal

DMS Format:
H = degrees/hours, M = minute, S = seconds

INPUT “DEC:”,D
IPART D→H
IPART (60*FPART D)→M
60 * FPART (60 * FPART D)→S
DISP “H,M,S:”,H,M,S

TI-80 Program DMS2D - Degrees-Minutes-Seconds to Decimal

Variables:

Decimal Format:
D = decimal

DMS Format:
H = degrees/hours, M = minute, S = seconds

INPUT “H:”,H
INPUT “M:”,M
INPUT “S:”,S
H + M/60 + S/3600 → D
DISP “DEC:”,D

TI-80 Program QUADRAT - Quadratic Equation

Variables:

A, B, C are coefficients of the equation Ax^2 + Bx + C, where the discriminant D:

D = B^2 – 4*A*C
If D≥0, then the roots are real and stored in X and Y.

If D<0, then the roots are complex and are in the form of conjugates X ± Yi.  X is the real part, Y is the imaginary part.



DISP “AX^2+BX+C=0”
INPUT “A:”,A
INPUT “B:”,B
INPUT “C:”,C
B^2 – 4AC → D
DISP D 
-B / (2A) → E
IF D≥0
THEN
E + √D/(2A) → X
E - √D/(2A) → Y
DISP “R1:”,X
DIPS “R2:”,Y
ELSE
E → X
√-D / (2A) → Y
DISP “RE:”,X
DISP “IM :”,Y
END

Annuity Factors

Variables:
I = periodic interest rate
N = number of payments/periods/deposits

TI-80 Program USFV – Annuity Future Value Factor

INPUT “I:”,I
INPUT “N:”,N
( (1+.01)^N – 1)/(.01I) → F
DISP F

TI-80 Program USPV – Annuity Present Value Factor

INPUT “I:”,I
INPUT “N:”,N
(1 – (1 + .01I)^-N)/(.01I) → P
DISP P

Two Dimensional Vector Operations

Let two vectors be defined as V1 = [A, B] an V2 = [C, D].  The program calculates the dot product, stored in E, norm of V1, stored in F, norm of V2, stored in G, and the angle between V1 and V2 in degrees, stored in H.

TI-80 Program VECTOR2

DEGREE
DISP “V1:”
INPUT A
INPUT B
DISP “V2:”
INPUT C
INPUT D
AC + BD → E
√(A^2 + B^2) → F
√(C^2 + D^2) → G
COS^-1 (E /(F*G)) → H
DISP “NORM V1:”, F
DISP “NORM V2:”, G
PAUSE
DISP “DOT:”, E
DISP “ANGLE:”, H

Simplistic Logistic Regression

Fit data (x,y) to the equation:

Y = 1 / (A + B*e^(-X))


TI-80 Program SIMPLOG

INPUT “L1:”, L1
INPUT “L2:”, L2
e^-L1 → L1
1/L2 → L2
LINREG(aX+b) L1, L2
a→A: b→B
DISP “1/(B+Ae^X)”,A,B
PAUSE
DISP “CORR^2”,r^2





Eddie


This blog is property of Edward Shore, 2017

Monday, September 4, 2017

Retro Review: Texas Instruments TI-80

TI-80


TI-80 (left), TI-84 Plus CE (right)
Look how thin the TI-80 is
Retro Review: Texas Instruments TI-80

First, thank you Nano for the TI-80 (along with giving me a pair of slide rules and an astronomy poster)!  Much appreciated!
  
Essentials

Company:  Texas Instruments
Years:  1995
Type:  Graphing, Programming
Memory:  7,034 bytes
Operating System: Algebraic
Memory Registers: 27 (A-Z, θ)
Screen:  Monochrome

Batteries:  2 CR2032 batteries

Graphing Modes:  Function (4), Parametric (3).  Table included. 

Regressions:  6: Linear (ax + b), Quadratic, Linear (a + bx), Logarithmic, Exponential, Power

Lists: Up to 99 entries per lists, 6 lists available (L1 through L6)

Matrices: none

Complex Numbers:  none

Keyboard

The keyboard is what one would expect on a Texas Instruments graphing calculator: nice and responsive. 

Screen

The screen is small.  Not kidding.  The screen is only 48 x 64 pixels big, accompanying 8 lines of 16 characters.  That means that the font is small.  What is wild is that the pi symbol (π) does not conform to the rest of the font, and is twice as long as the rest of the characters.

The screen is still bigger than the mini-graphing calculators such as the Casio fx-6300g or the Hewlett Packard HP-9g.

Is the TI-80 a simplified TI-81?

For the most part, no.  Sure, the TI-80 does not have matrices and hyperbolic functions (sinh, cosh, etc) like the TI-81.  However, the TI-80 has fractions (see the next section), integer division and remainder function, random integer, a complementary table mode, and lists.  The number of stat plots increased to 3, which they don’t have to depend on the statistics mode.

As far as programming memory, the TI-80 beats the TI-81: 7,034 bytes to 2,400 bytes.  Also, you can go beyond 37 programs for the TI-80, as the names are not restricted to one character.

Fractions

The TI-80 has a dedicated fraction menu, which allow users to convert between improper and proper form, as well as conversion between fraction and decimal approximation.  The Manual Simplification mode allows fractions to not be automatically simplified on calculation. 

To enter fractions, the format is:  A _ B / C
Note that the slash is bold.  Merely pressing the division key will not register the fraction.

To separate the whole part from the fraction, press [ 2nd ] [ + ] (UNIT_).

To separate the numerator from the denominator, press [ 2nd ] [ ÷ ] (b/c).

Example:  Enter 2 3/4
Keystrokes:  2 [ 2nd ] [ + ] 3 [ 2nd ] [ ÷ ] 4

According to Datamath (http://www.datamath.org/Graphing/TI-80.htm ), the TI-80 would get replaced with the TI-73 in 1998.  This may mean that the TI-80 became the base for the TI-73 series (TI-73, TI-73 explorer).

Lists

The TI-80 allows for 6 lists, each with a 99 element capacity.  Arithmetic can be operated on two same-sized lists, on an element-by-element functions.  Lists functions include sorting, dimension, minimum, maximum, sum of the elements, product of the elements, and sequence generation.

Programming

Programming is fairly basic for the TI-81.  Commands:
If-Then-Else-End Structure (IF, THEN, ELSE, END)
Quick if structure
For-End structure (no IS>, DS< this time) (FOR, END)
Labels:  one character and local labels (LBL, GOTO)
Subroutines (PRGM_, RETURN)
Drawing commands include points, shading (three types, general, Y<, Y>)

Since the only built-in calculus function of the TI-80 is numerical derivation (NDERIV), two programs for Newton’s Method and Simpson’s Rule are presented below.

TI-80 Program:  SOLVEY1  (Newton’s Method)

80 bytes
The equation is stored in Y1.  The program solves for X in Y1(X) = 0

INPUT “GUESS:”, X
LBL 0
X-Y1/NDERIV(Y1,X,X)→N
IF ABS (X-N)>1E-10
THEN
N→X
GOTO 0
END
N→X
DISP “X = “, X

Example: X^2-3X+1, guess X = 3
Result:  X = 2.618033989

TI-80 Program: SIMPY1 (Integral, Simpson’s Rule)

140 bytes
The equation is stored in Y1.  The program calculates ∫(Y1,X,A,B)

RADIAN
INPUT “A:”,A
INPUT “B:”,B
INPUT “N (EVEN):”,N
(B-A)/N→H
0→T
FOR(I,1,N-1)
A+IH→X
T+2*Y1→T
IF FPART(I/2)≠0
2*Y1+T→T
END
(T+Y1(A)+Y1(B))H/3→T
DISP “INTEGRAL:”,T

Example: X^2-3X+1, with A = 0 to B = 5 and N = 10
Result:  X = 9.166666667

Final Verdict

The TI-80 is a nice introductory calculator, and thanks to programming a lot can be done with it.  I wish the screen was bigger and degree/degrees-minutes-seconds conversions were available, but other than that, it was a great calculator which provides a lot of features (maybe not as intimidating as more advanced calculators). 

It is a nice calculator to add to the collection, and I thank you Nano immensely. 

Eddie


This blog is property of Edward Shore, 2017.

Friday, September 1, 2017

TI-84 Plus CE: Fitting Points to an Ellipse

TI-84 Plus CE: Fitting Points to an Ellipse

Back to one of my favorite subjects: curve fitting.



The program ELLIPFIT attempts to fit a parametric curve for a collection of points (x, y) to an ellipse using the following equations:

x = a * cos t + b
y = c * sin t + d

where the independent variable is t.  The program also plots the estimated line and the scatter plot.  I decided to keep the correlation (r^2) separate, so we can tell how well the line fits both the x and y data. 

The program uses the range of 0 ≤ t ≤ 2*π, where t is in radians.

The user is asked to provide two lists, x and y.   The list of t values is determined by the atan2, angle, or arg function of the complex number point x + y*i.  The angle is adjusted to the range of [0, 2*π].

Quadrant I: x ≥ 0, y ≥ 0, angle(x + y*i)
Quadrant II: x < 0, y ≥ 0, angle(x + y*i)
Quadrant III: x < 0, y < 0, angle(x + y*i) + 2*π
Quadrant IV: x ≥ 0, y < 0, angle(x + y*i) + 2*π

TI-84 Plus CE Program ELLIPFIT

Notes:

L1: list 1, [ 2nd ] [ 1 ]; L2: list 2, [ 2nd ] [ 2 ], etc.  X1T, Y1T are from the [ vars ], Y-VARS, Parametric submenu

[square] is from [2nd] [ y= ] (stat plot) , MARK submenu, option 1

The complex variable i = √-1 is found by pressing [ 2nd ] [ . ].

Program:

"ELLIPTICAL FIT"
"2017-08-31 EWS"
Param:Radian:a+bi
Input "X LIST: ",L2
Input "Y LIST: ",L3
FnOff
L2→L1
For(I,1,dim(L1))
angle(L2(I)+L3(I)*i)→T
If L3(I)<0
Then
T+2π→T
End
T→L1(I)
End
PlotsOff
cos(L1)→L4
LinReg(ax+b) L4,L2
a→A:b→B:r²→E
"Acos(T)+B"→X1T
ClrHome
Disp "X = A*cos(T)+B"
Disp A
Disp B
Disp "CORR: "
Pause E
sin(L1)→L4
LinReg(ax+b) L4,L3
a→C:b→D:r²→F
"Csin(T)+D"→Y1T
ClrHome
Disp "Y = C*sin(T)+D"
Disp C
Disp D
Disp "CORR: "
Pause F
FnOn 1
PlotsOn 1
GraphColor(1,RED)
Plot1(Scatter,L2,L3,[square],GREEN)
0→Tmin
2π→Tmax
ZoomStat

(Obviously use the colors and makers you like.   If you are working with a monochrome TI-83/TI-84, ignore the color commands.)

You can get a download here:

Example 1

A perfect circle:

X
Y
0
1
1
0
0
-1
-1
0

Results:
x = cos t (r^2 = 1)
y = sin t (r^2 = 1)




Example 2

X
Y
1.0
0.0
0.5
0.5
0.0
1.0
-0.5
0.5
-1.0
0.0
-0.5
-0.5
0.0
-1.0
0.5
-0.5

Results:
x = 0.8535533906 cos t (r^2  ≈ 0.97140)
y = 0.8535533906 sin t  (r^2 ≈ 0.97140)

 


Eddie


This blog is property of Edward Shore, 2017.

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