Eddie's Math and Calculator Blog: September 2018

Sunday, September 23, 2018

One Week to HHC 2018

One Week to HHC 2018

It's only one week to HHC 2018, the annual HP calculator conference. This year's conference will be in San Jose, California. As always I am excited.

http://hhuc.us/2018/

Eddie

HP 48G: Stefanescu Horatiu: Intersection of the Diagonals of a Quadrilateral

HP 48G: Stefanescu Horatiu: Intersection of the Diagonals of a Quadrilateral

The following program, written by Stefanescu Horatiu, calculates the intersection point of the two diagonals of a quadrilateral (partulator in Romanian).

The program takes place in a directory PATRULATERDIAGONALE. In order to type in the program, you will need to create a directory by using the CRDIR command.

This program also works on the HP 49G series (48gii, 49G, 49g+) and the HP 50g.

HP 48G Program PATRULATERDIAGONALE - Stefanescu Horatiu

Note: You are going to notice how all the subroutines flow together, as the first program calls the next program. You will need to enter and store all the programs for the entire routine to work correctly.

On a personal note, I like how the text is spelled out one letter at time. Hoartiu accomplishes this by using a FOR-NEXT structure which includes the commands 1 I SUB 1 DISP. (with I as the counter variable).

The text of the program is in Romanian.

The program is presented here with permission from the author, with full credit going to Stefanescu Horatiu. I thank Horatiu in allowing me to feature his work on my blog.

STARTDIAGONALE:

<< CLEAR CLLCD 1 110 FOR I
"ACEST PROGRAM CALCUL
EAZA COORDONATELE PUN
CTULUI DE INTERSECTIE
A DIAGONALELOR UNUI
PATRULATER OARECARE."
1 I SUB 1 DISP
NEXT 0 WAIT
INTRODUCERE >>

INTRODUCERE: (User input screen)

<< CLLCD
"COORDONATE PATRULATER"
{"Ax" "Ay" "Bx"
"By" "Cx" "Cy" "Dx"
"Dy" } { 2 4 } { }
{ } INFORM DROP
OBJ→ DROP 'DY' STO
'DX' STO 'CY' STO
'CX' STO 'BY' STO
'BX' STO 'AY' STO
'AX' STO CLLCD
EMURILE >>

EMURILE: (the start of the calculation routines)

<< 'CY-AY' →NUM 'M1' STO
'-AX*(CY-AY)' →NUM 'M2' STO
'CX-AX' →NUM 'M3' STO
'-AY*(CX-AX)' →NUM 'M4' STO
ENURILE >>

ENURILE:

<< 'BY-DY' →NUM 'N1' STO
'-DX*(BY-DY)' →NUM 'N2' STO
'BX-DX' →NUM 'N3' STO
'-DY*(BX-DX)' →NUM 'N4' STO
ESURILE >>

ESURILE:

<< 'N1-N3*M1/M3' →NUM 'S1' STO
'N3*(M2-M4)/M3+N4-N2' →NUM 'S2' STO
PURILE >>

PURILE:

<< 'S2/S1' →NUM 'PX' STO
'(PX*M1+M2-M4)/M3' →NUM 'PY' STO
REZULTATE >>

REZULTATE: (display the results)

<< CLLCD 1 59
FOR I
"Coordonate punct de
intersectie ale dia
gonalelor: P(x,y)"
1 I SUB 1 DISP NEXT 4 FIX
"P(" PX + →STR ";" +
→STR PY + →STR ")"
+ →STR 5 DISP 0 WAIT
STERG >>

STERG: (cleanup, purge working variables)

<< { AX AY BX BY CX
CY DX DY PX PY M1
M2 M3 M4 N1 N2 N3
N4 S1 S2 } PURGE
CLLCD CLEAR >>

Instructions:

Set your calculator the folder PATRULATERDIAGONALE. Run STARTDIAGONALE and enter the coordinates. The rest of the program runs automatically. Start with the left hand corner and go clockwise.

Note: I typed Horatiu's program on an HP 49G. In REZULTATE, for some reason I couldn't get the FIX 4 to take effect, even when I switched the calculator to Approximate mode. So in order to get both PX and PY on the screen, I added a carriage return character (↲, [right shift] [ 2 ]) after the semicolon. This creates a new line allowing both coordinates to be displayed.

Example:

Example 1: (Horatiu's example)
A: (ax, ay): (2, 10)
B: (bx, by): (11, 12)
C: (cx, cy): (13, 6)
D: (dx, dy): (1, 4)

P: (px, py): (6.46875, 8.375)
FIX 4: (6.4688, 8.3750)

Example 2: (my own example)
A: (ax, ay): (0, 8)
B: (bx, by): (5, 12)
C: (cx, cy): (7, 7)
D: (dx, dy): (2, 1)

P: (px, py): (3.72649999999, 7.4625)
FIX 4: (3.7265, 7.4625)

Source:

Horatiu, Stefanescu "Calculul Coordonatelor Punctului de Intersectie A Diagonalelor Unui Partulater Oarecare" 2018.

Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

Casio Desktop Calculators: Calculating at a Very Fast Speed

Casio Desktop Calculators: Calculating at a Very Fast Speed

Introduction: Wow That's Fast!

Recently, there is a discussion on the Museum of HP Calculators forum on "postfix algebraic scientific calculators still in production". The conversation turned to two-key rollover which allowed for fast typing on the calculator. A member ijabott, directed us to a three minute snippet of a YouTube video (https://www.youtube.com/watch?v=WwGL4Z__Ufc&feature=youtu.be). The video featured Asuka Kamimura, a champion of speed calculating, quickly adding a long list of numbers with great accuracy. I was blown away on how she quickly keyed in those numbers. The video explained that Kamimura was going 9 keystrokes a second.*

**Thank you Mark Hardman for pointing out my error (on minute). The sentence is now correct.

The video also explained that are calculator clubs in Japanese high schools that practice calculator speed typing for seven hours on Saturdays and Sundays. There are also calculator speed contests in Japan. If anyone reading this has the link or information for the 2018 or even the upcoming 2019 contest, please let me know.

The video also shows a technique on how fast calculating can be accomplished (starts at the 2:59 mark of the above video):

Thumb works on the 0 key only.

The index finger covers the 1-4-7 keys, along with the 00 and any keys on the left side of the keyboard.

The middle finger covers the decimal point, and the row with the 2-5-8 keys.

The ring finger covers the 3-6-9 row, along with the subtraction, multiplication, and division keys. The ring finger also has the equals key.

Finally, little finger is for the plus key.

Regarding the setup and the keys on the calculator, your mileage may vary. The setup present for right-hand users, hence for left-handed users will have to adjust accordingly (thumb works on the plus key, index works with 3-6-9, middle has 2-5-8, ring has 1-4-7, and little has the 0 key for left-handed users).

The Calculators That Allow for Fast Typing

The calculator shown in the video is a Casio ND-26S (0:45). It is a Japanese model, also designated as a "Study Cal". Also featured is the Casio AZ-25S (3:33), a "Study Cal". According to Casio, "Study Cal" are sold to schools only.

Here is a picture of the ND-26S from the Casio Calculator Collectors website: http://www.casio-calculator.com/Museum/Pages/NNN/ND-26S/Casio%20ND-26S.html

Here in the United States, Casio (and Canon) sells calculators that allow for fast typing. If you are interested, look for the larger desktop type of calculators. Pictured below are two examples:

Casio WS-320MT
Casio JF-100BM

Casio WS-320MT (left), Casio JF-100BM (right)

Note: I think all the newer keyboards on Casio calculators are designed for fast typing, even the scientific and graphing ones. (fx-991EX Classwiz, fx-CG50)

Want to Give it a Shot?

Try adding the columns as fast and accurately as you can.

For me, it currently takes me about a 1:20 to add up the 40 numbers in each of the blue boxes on my left hand (my non-dominate hand, I'm normally right-handed). This is after 30 minutes of practice.

Sources

Videos:

"Japanese people take their calculators very seriously" Posted by Henrik Nieslen on October 26, 2014. https://www.youtube.com/watch?v=WwGL4Z__Ufc&feature=youtu.be

This segment is part of the Japanology series.

"2013 06 13 BEIGN Japaonlogy Calculators" Posted by 13blackmercury on September 4, 2013. https://www.youtube.com/watch?v=1_GVkR0SITo

This particular episode was aired on June 13, 2013.

Discussion on HP Museum of Calculators:

"Postfix algebraic scientific calculators still in production" HP Museum of Calculators Forum. Thread began on September 13, 2018. http://www.hpmuseum.org/forum/thread-11385.html

Calculators (links all retrieved on September 23, 2018):

"ND-26S" Casio Calculator Collectors. http://www.casio-calculator.com/Museum/Pages/NNN/ND-26S/Casio%20ND-26S.html

AZ-26S Product Page. Casio. https://casio.jp/dentaku/products/AZ-26S/ (page is in Japanese)

WM-320MT Product Page. Casio. https://www.casio.com/products/calculators/desktop/wm-320mt (United States)

JF-100BM Product Page. Casio. https://www.casio.com/products/calculators/desktop/jf-100bm (United States)

Have fun! Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

Tuesday, September 18, 2018

TI-84 Plus CE: Storing Names in a Concentrated String

TI-84 Plus CE: Storing Names in a Concentrated String

Introduction

The program STRNAMES allows the user to store a list of names in a single string. There are only 10 string variables for the TI-84 Plus CE (and in fact, all the the TI-83 and TI-84 families), so if you need to store more than 10 names, a workaround is needed.

This program uses two strings: Str1 and Str2. Str1 is a temporary string variable used to store and edit the list of names. Str2 is the master list of all the names.

In order to make this work, we will need to note where in the string the names start and the length of the names. The two lists used are L₁, the position of each name, and L₂ for the length of each name.

In this program, each name is separated by space.

You will notice that Str2 starts with a space, and the lists L₁ and L₂ have a 0. The TI-84 Plus CE does not allow us to store empty strings or lists.

STRNAMES The Menu

1. Add a Name: Add a name to the list
2. Delete Last Name: Deletes the last name on the list
3. Clear/Initialize: Clears all the variables. I recommend you start with this option every time you work with a new list of names. Also, if you use other programs or the list or strings for other things, run the Clear/Initialize before beginning.
4. Review: List all the names in order.
5. Erase Any Name: You can erase any name in the list (1st name, 2nd name, 3rd name, etc).
6. Exit: Quits the Program

TI-84 Plus CE Program STRNAMES

"2018-09-18 EWS"
Lbl 0
Menu("MENU","ENTER A NAME",A,"DELETE LAST NAME",B,"CLEAR/INITIALIZE",C,"REVIEW",D,"ERASE ANY NAME",E,"EXIT",F)

Lbl A
Input "NAME: ",Str1
augment(L₁,{length(Str2)+1})→L₁
augment(L₂,{length(Str1)}→L₂
Str2+Str1+" "→Str2
Disp "ADDED",Str2,"NAMES:",dim(L₁)-1
Pause
Goto 0

Lbl B
If dim(L₁)≠1
Then
dim(L₁)→I
L₂(I)→B
length(Str2)→C
sub(Str2,1,C-B-1)→Str2
dim(L₁)-1→dim(L₁)
dim(L₂)-1→dim(L₂)
Disp "DONE.",Str2,"NAMES:",dim(L₁)-1
Else
Disp "LIST IS EMPTY."
End
Pause
Goto 0

Lbl C
" "→Str2
{0}→L₁
{0}→L₂
Disp "CLEARED"
Pause
Goto 0

Lbl D
For(I,2,dim(L₁))
L₁(I)→A
L₂(I)→B
dim(L₁)→C
toString(I-1)+"/"+toString(C-1)+": "+sub(Str2,A,B)→Str1
Disp Str1
Wait 0.5
End
Pause
Goto 0

Lbl E
Input "ENTRY NUMBER:",I
I+1→I
dim(L₁)→D
L₂(I)→E
If D=I
Then
Goto B
Else
L₁(I)→A
L₁(I+1)→B
length(Str2)→C
sub(Str2,1,A-1)+sub(Str2,B,C-B)+" "→Str2
For(K,I+1,D)
L₁(K)-E-1→L₁(K-1)
L₂(K)→L₂(K-1)
End
dim(L₁)-1→dim(L₁)
dim(L₂)-1→dim(L₂)
Disp "DONE.",Str2,"NAMES:",dim(L₁)-1
Pause
End
Goto 0

Lbl F
Disp "END PROGRAM"

Example

Try playing with this program.

Example list:

1. Start by initializing, choose option 3.

2. Enter EDDIE. Choose option 1. Press [ 2nd ] [alpha] and type EDDIE. Quotes are not needed (since the Input command will be stored to a string). Str2 = " EDDIE "

3. Enter ANN. Choose option 1. Str2 = " EDDIE ANN "

4. Enter TERRY. Choose option 1. Str2 = " EDDIE ANN TERRY "

5. Let's remove ANN from the list. In our example, ANN is the second name. Choose option 5. Enter 2. The result, Str2 = " EDDIE TERRY "

6. Enter MARK. Choose option 1. Str2 = " EDDIE TERRY MARK "

7. Review the list of names. Choose option 4. The screen will show:

1/3 EDDIE
2/3 TERRY
3/3 MARK

Continue with the example however you want.

Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

Sunday, September 16, 2018

HP 20S and HP 21S: Precession

HP 20S and HP 21S: Precession

Introduction

The program PRECESS estimate the new position (right ascension (RA), declination (δ)) of a celestial object given their position in Epoch 2000 with the object’s proper notion.

Estimation formulas:

Change in RA and δ before accounting for proper notion

ΔRA = m + n * sin RA * tan δ (in seconds)

= 3.07496 + 1.33621 * sin RA * tan δ (for epoch 2000)

Δδ = (15 * n) * cos RA (in arcseconds)

= 20.0431 cos RA (epoch 2000)

With m = 3.07496 seconds and n = 1.33621 seconds (for epoch 2000)

For other epochs:

1900: m = 3.0731, n = 1.33678

2100: m = 3.07682, n = 1.33564

Then:

RA_new = (RA_old + Y * (ΔRA + RA_proper) / 3600 ) / 15 (hours)

δ_new = (δ_old + Y * (Δδ + δ_proper) / 3600 (degrees)

Y = years from 2000 (or the appropriate epoch)

For the HP Prime and TI-84 Plus CE versions, click here: http://edspi31415.blogspot.com/2018/09/hp-prime-and-ti-84-plus-ce-precession.html

HP 20S and HP 21S Program: Precession

The key codes for both calculators are the same.

STEP KEY KEY CODES

01 LBL D 61, 41, d

02 DEG 61, 23

03 RCL 0 22, 0

04 →HR 51, 54

05 × 55

06 1 1

07 5 5

08 = 74

09 STO 0 21, 0

10 RCL 1 22, 1

11 →HR 51, 54

12 STO 1 21, 1

13 3 3

14 . 73

15 0 0

16 7 7

17 4 4

18 9 9

19 6 6

20 + 75

21 1 1

22 . 73

23 3 3

24 3 3

25 6 6

26 2 2

27 1 1

28 × 55

29 RCL 0 22, 0

30 SIN 23

31 × 55

32 RCL 1 22, 1

33 TAN 25

34 = 74

35 STO 5 21, 5

36 2 2

37 0 0

38 . 73

39 0 0

40 4 4

41 3 3

42 1 1

43 × 55

44 RCL 0 22, 0

45 COS 24

46 = 74

47 STO 6 21, 6

48 RCL 0 22, 0

49 + 75

50 RCL 4 22, 4

51 × 55

52 ( 33

53 RCL 5 22, 5

54 + 75

55 RCL 3 22, 3

56 ) 34

57 ÷ 45

58 3 3

59 6 6

60 0 0

61 0 0

62 = 74

63 ÷ 45

64 1 1

65 5 5

66 = 74

67 →HMS 61, 54

68 STO 7 21, 7

69 R/S 26

70 RCL 1 22, 1

71 + 75

72 RCL 4 22, 4

73 × 55

74 ( 33

75 RCL 6 22, 6

76 + 75

77 RCL 3 22, 3

78 ) 34

79 ÷ 45

80 3 3

81 6 6

82 0 0

83 0 0

84 = 74

85 →HMS 61, 54

86 STO 8 21, 8

87 RTN 61, 26

Instructions

Store the following values in the registers:

R0: Initial RA in HH.MMSSSS format

R1: Initial δ in DD.MMSSSS format

R2: RA proper notion

R3: δ proper notion

R4: number of years from 2000. For 2022, store 22. For 1978, store -22.

Result:

R7: New RA in HH.MMSSSS format, press [ R/S ] to get

R8: New δ in DD.MMSSSS format

Examples

Estimate the RA and δ of Regulus (Alpha Leonis) and Sadalmelik (Alpha Aquarii) for 2020 (Y = 20). (data from Wikipedia)

Regulus (Leo the Lion ♌)

Epoch 2000: RA = 10h 8m 22.311s, δ = +11° 58’ 0.195”

Proper Notion: RA_prop = -0.016582 arcsec/yr, δ_prop = 0.00556 arcsec/yr

(arcsec = “)

Results:

RA_2020 ≈ 10h 8m 26.56557s (shown as 10°08’26.56557”)

‘δ_2020 ≈ +11° 52’ 6.06118”

Sadalmelik (Aquarius the Water Bearer ♒)

Epoch 2000: RA = 22h 5m 47.03593s, δ = -0° 19’ 11.4568”

Proper Notion: RA_prop = 1.216667 * 10^-3 arcsec/yr, δ_prop = -0.00939 arcsec/yr

Result:

RA_2020 ≈ 22h 5m 51.14225s

δ ≈ -0° 13’ 19.5407”

Convert mas/yr to arcsec/yr:

For RA: (x/15) /1000

For δ: x/1000

Sources:

Jones, Aubrey. Mathematical Astronomy with a Pocket Calculator John Wiley & Sons: New York. Printed in Great Britain. 1978. ISBN 0 470 26552 3

Meeus, Jean. Astronomical Algorithms William-Bell, Inc. Richmond, VA 1991. ISBN 0-943396-35-2

Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

HP 20S and HP 21S: Qualifying Loan Amount (28:36 ratio)

HP 20S and HP 21S: Qualifying Loan Amount (28:36 ratio)

Introduction

The program presented in today's blog entry will calculate the qualifying loan amount given the following:

* Loan's annual interest rate and term (in years)
* The borrower's monthly gross income
* The borrower's monthly non-property related debt (credit cards, auto loans, store bought appliances on credit, etc). Do not include utilities or phone bills.
* The estimated monthly property tax and insurance. For this program, combine the two amounts.

Before running the program, store the following amounts in the following registers:

R0: Monthly Income
R1: Monthly Debt
R2: Monthly Property Taxes and Insurance
R3: Annual Interest Rate
R4: Term

The down payment is not taken into consideration.

The result is the loan amount using the standard 28:36 ratio (stored in register R5). The 28:36 ratio is the guideline that the borrower spends no more than 28% of their income on housing expenses, and no more than 36% of their income on all debt service.

HP 20S and HP 21S Program: Qualifying Loan Amount

The key codes for most steps are the same. Lines where the key codes are different are noted, particularly the percentage function.

STEP KEY KEY CODE
01 LBL E 61, 41, E
02 FIX 2 51, 33, 2
03 RCL 0 22, 0
04 × 55
05 3 3
06 6 6
07 % HP 20S: 51,14 HP 21S: 51, 53
08 = 74
09 - 65
10 RCL 1 22, 1
11 = 74
12 STO 6 21, 6
13 RCL 0 22, 0
14 × 55
15 2 2
16 8 8
17 % HP 20S: 51,14 HP 21S: 51, 53
18 = 74
19 STO 7 21, 7
20 RCL 6 22, 6
21 INPUT 31
22 RCL 7 22, 7
23 X≤Y? 61, 42
24 SWAP 51, 31
25 STO 8 21, 8
26 RCL 2 22, 2
27 STO - 8 21, 65, 8
28 1 1
29 - 65
30 ( 33
31 1 1
32 + 75
33 RCL 3 22, 3
34 ÷ 45
35 1 1
36 2 2
37 0 0
38 0 0
39 ) 34
40 Y^X 14
41 ( 33
42 1 1
43 2 2
44 +/- 32
45 × 55
46 RCL 4 22, 4
47 ) 34
48 = 74
49 ÷ 45
50 ( 33
51 RCL 3 22, 3
52 ÷ 45
53 1 1
54 2 2
55 0 0
56 0 0
57 ) 34
58 = 74
59 × 55
60 RCL 8 22, 8
61 = 74
62 STO 5 21, 5
63 RTN 61, 26

Example

R0: Monthly Income = $4,485.00
R1: Monthly Debt = $375.00
R2: Monthly Property Taxes and Insurance = $126.83
R3: Annual Interest Rate = 5%
R4: Term = 30 years

Result: $207,288.60

Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

Saturday, September 15, 2018

HP 20S and HP 21S: Approximating Stopping Distances

HP 20S and HP 21S: Approximating Stopping Distances

Introduction

We can approximate the stopping distance (in feet) of a vehicle on dry pavement given the vehicle's speed (in miles per hour, mph) by the formula:

y = 3.85714285714*10^-2 * x^2 + 1.44504201681 * x + 0.64915966369

or

y = 27/200 * x^2 + 1.44504201681 * x + 0.64915966369

y: stopping distance on dry pavement, feet
x: speed of vehicle, mph

Assumptions:

* The vehicle is assumed to be a passenger vehicle.

* The reaction time is 1 second and the deceleration rate is 28 ft/s.

The program listed rounds all results to one decimal place.

HP 20S and HP 21S Program: Stopping Distance

The key codes for both calculators are the same in this program.

STEP KEY KEY CODE
01 LBL B 61, 41, b
02 STO 0 21, 0
03 x^2 51, 11
04 × 55
05 2 2
06 7 7
07 ÷ 45
08 7 7
09 0 0
10 0 0
11 + 75
12 RCL 0 22, 0
13 × 55
14 1 1
15 . 73
16 4 4
17 4 4
18 5 5
19 0 0
20 4 4
21 2 2
22 0 0
23 1 1
24 6 6
25 8 8
26 1 1
27 + 75
28 . 73
29 6 6
30 4 4
31 9 9
32 1 1
33 5 5
34 9 9
35 6 6
36 6 6
37 3 3
38 9 9
39 = 74
40 STO 1 21, 1
41 FIX 1 51, 33, 1
42 RTN 61, 26

Examples

Input: 25 mph, Result: 60.9 ft

Input: 40 mph, Result: 120.2 ft

Input: 65 mph, Result: 257.5 ft

Note: This time I am writing this blog entry direct in the Blogger compose box. When I transfer text from either Jarte or WordPad to Blogger, all the formatting is lost. And I don't want to format my text twice. I will still save a backup copy. I am very happy that Blogger compose box allows me to select special characters for the math symbols I need (the happy face is appropriate because it makes me happy!)

Source:

Glover, Thomas J. Pocket Ref 4th Edition. Sequoia Publishing, Inc. Littleton, CO. 2012

Eddie

HP 20S and HP 21S: Rounding Numbers

HP 20S and HP 21S: Rounding Numbers

Introduction

The following program will allow the user to round any positive number to any number of decimal places, regardless of fixed decimal settings.

This is based off the algorithm:

x_rounded = int(10^n * x + 0.5) ÷ 10^n

Note: You can check out the programs for the HP 12C and DM 41L/HP 41C here:
http://edspi31415.blogspot.com/2018/08/hp-12c-platinum-and-dm-41l-rounding.html

HP 20S and HP21S Program: Rounding Numbers

Key codes for both calculators are the same.

Step Key Key Code
01 LBL C 61, 41, C
02 10^x 51, 12
03 STO 0 21, 0
04 SWAP 51, 31
05 × 55
06 RCL 0 22, 0
07 + 75
08 . 73
09 5 5
10 = 74
11 IP 51, 45
12 ÷ 45
13 RCL 0 22, 0
14 = 74
15 RTN 61, 26

Instructions

Enter x, press [INPUT], enter n (number of decimal places)

Examples

For these examples, I have set the calculator in ALL setting ( [right shift], [ ) ] )

Example 1: Round π to 4 places.

π [ INPUT ] 4 [XEQ] (C)

Result: 3.1416

Example 2: Round e^2.2 to 6 places

2.2 [e^x] [INPUT] 6 [XEQ] (C)

Result: 9.025013

Note: I typed this blog entry by using the Jarte word processor (http://www.jarte.com/index.html). I am using the free version for the first time (there is also a paid version). Jarte is based off of WordPad, but adds spell check and nicer editing features.

Source:

Keith Oldham, Jan Myland, and Jerome Spanier An Atlas of Functions Second Edition, Springer. 2009 ISBN 978-0-387-48806-6

Eddie

All original content copyright, © 2011-2018. 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. Please contact the author if you have questions.

HP 20S and 21S: Heron's Triangle

HP 20S and 21S: Heron's Triangle

Introduction

The following program calculates the area of a triangle knowing the three lengths. The area is determined by Heron's formula:

Area: √(s * (s - a) * (s - b) * (s - c)) where s = (a + b + c)/2
Store the lengths of the triangle in registers R0, R1, and R2 respectively.
Results are stored in the following registers:
R3: s
R4: area

HP 20S and 21S Program: Heron's Triangle

The key codes for both calculators are the same.

STEP KEY KEY CODE
01 LBL A 61, 41, A
02 RCL 0 22, 0
03 STO 3 21, 3
04 RCL 1 22, 1
05 STO+3 21, 75, 3
06 RCL 2 22, 2
07 STO+3 21, 75, 3
08 2 2
09 STO÷3 21, 45, 3
10 RCL 3 22, 3
11 STO 4 21, 4
12 RCL 3 22, 3
13 - 65
14 RCL 0 22, 0
15 = 74
16 STO×4 21, 55, 4
17 RCL 3 22, 3
18 - 65
19 RCL 1 22, 1
20 = 74
21 STO×4 21, 55, 4
22 RCL 3 22, 3
23 - 65
24 RCL 2 22, 2
25 = 74
26 STO×4 21, 55, 4
27 RCL 4 22, 4
28 √ 11
29 STO 4 21, 4
30 RTN 61, 26

Example

R0 = 17, R1 = 18, R2 = 21. Result: Area: 148.833238744

Note: I switched computers last week. For the last few years, I used Microsoft Word but for the time being I am going to use WordPad. Let's see how this goes. Fortunately I can still can use Unicode characters with Alt+X. For example, I can type 221A, then type [Alt] + [ X ] to get the square root character. Unfortunately, WordPad doesn't have spell check.

Eddie

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Sunday, September 9, 2018

Retro Review: Calculated Industries Qualifier Plus IIImx, Model 3440

Retro Review: Calculated Industries Qualifier Plus IIImx, Model 3440

General Information

Company: Calculated Industries

Type: Finance/Banking

Display: 9 digit alpha-numeric display

Power: 2 LR44 or 2 A76 batteries

Memory: 1 independent memory (store, recall, M+, M-)

Years: 2004 – late 2000s

Original Cost: $49.95

Documentation: Manual, though it is no longer available online

Introduction and Features

The Qualifier Plus IIImx is a finance calculator that seems to be made for a specific client, World Savings. The model has a World Savings logo on it, and any Armadillo Gear protective cover that came with it.

Interesting to note that in 2006 that Wachovia Corporation purchased Golden West Financial Corporation, World Savings’ parent corporation, only for Wachovia itself to be purchased by Wells Fargo in 2008. [[S1]]

Let’s get to the regular known features of the Qualifier Plus IIImx:

* Time Value of Money (payments are assumed to be monthly, but can be adjusted), this can include price and down payment

* Amortization of Loans

* Interest Only Payment Calculations

* Payment Calculations: P&I (principal and interest), PITI (principal, interest, property tax, property insurance), TOTAL (PITI plus monthly expenses)

* Qualifying Loan Amounts (two slots to store two ratios, Qual 1 defaults to the standard 28:36 debt/income ratio)

* Rent vs. Buy Analysis: given monthly rent, loan amounts, property tax, property insurance, the renter’s income tax bracket

* Date calculations: 2-digit year entry. I’m not sure what this time period covers because the pocket guide doesn’t state. Through entering various dates and using www.dayoftheweek.org, the dates seem to range from January 1, 1960 (Friday) to December 31, 2059 (Wednesday).

One neat thing with the Qualifier Plus IIImx (this really goes for all the Calculated Industries financial and real estate calculators) is that some of the entries can determine percentage rates or dollar amounts without additional key strokes. Generally, any entry of 100 or less is treated as a percent, above 100 is treated as dollars.

Example:

20 [ Dn Pmt ] sets the down payment at 20% of the price

20000 [ Dn Pmt ] sets the down payment at $20,000

Other keys that work this way: [ Shift ] [ 7 ] (annual property tax), [Shift] [ 8 ] (annual property insurance), [Shift] [ 9 ] (annual mortgage insurance)

So far, so good. Now let’s get to the controversy…

Negative Amortization: The MARM Loans

I am grateful that when I bought the calculator it still had its pocket reference guide [[S2]] otherwise I would have no idea what all the MARM keys were about. I still don’t understand all the details, but the MARM keys calculates such loans that were called “pick-a-payment” loans, which were popular and heavily advertised during the housing boom in the mid to late 2000s.

In general, “pick-a-payment” loans allowed borrowers to set a payment where the payment is less than the interest charged for the initial period of the loan. Any interest that wasn’t paid was tacked to the end the loan. Furthermore, none of the principal has been paid down during the initial time. I think you can see the problem, by paying too low in the beginning resulted in a higher loan balance (principal plus unpaid interest). Furthermore, MARM loans are rate adjustable. Even with the presence of caps, it’s not all that comforting when the deferred interested and delay of paying off principal are taken into account.

In 2010, Wells Fargo (having acquired World Savings and Wachovia) made a minimum of $50 million in a class action lawsuit over these types of loans [[S3]], including promises to modify any loans of the borrowers who made such “pick-a-payment” type of mortgages. Wells Fargo would get in trouble again 2012 when the loan modifications were denied to a lot of affected borrowers. [[S4]]

It shouldn’t be surprising to see why Calculated Industries discontinued this model and took down any documentation for this calculator.

My personal take: if the mortgage or loan has any hint of negative amortization – RUN! Don’t even consider it.

Verdict

Because of the controversial and perhaps infamous nature of some of this calculator’s features, I am not going to issue a verdict or recommendation.

Sources:

[[S1]] Wells Fargo. “World Savings is Now Wells Fargo” https://www.wellsfargo.com/about/corporate/worldsavings/ Retrieved September 5, 2018

[[S2]] Calculated Industries. Model 3440: Pocket Reference Guide. 2004 Guide is not available online.

[[S3]] Orlofsky, Steve – Editor. “Wells Fargo to settle lawsuit over pick-a-payment loans” Reuters. December 14, 2010. https://www.reuters.com/article/wellsfargo-settlement/wells-fargo-to-settle-lawsuit-over-pick-a-payment-loans-idUSN1427719820101215?feedType=RSS Retrieved September 5, 2018.

[[S4]] Reckard, E. Scott. “Wells Fargo settlement over ‘pick-a-pay’ home loans is challenged”. Los Angeles Times. December 11, 2012. http://articles.latimes.com/2012/dec/11/business/la-fi-wells-suit-20121211 Retrieved September 9, 2018.

Eddie