Fun With the TI-59

Fun With the TI-59

The following programs can be used on the TI-58C, TI-58, TI-59, TI-66, and any applicable emulator such as the RCL 58, RCL 59, and TI-5x. 

Vieta's Formula

Given the roots α, β, and γ we can calculate the coefficients of the general cubic equation a*x^3 + b*x^2 + c*x + d = 0 by:

s1 =  α + β + γ
s2 = α * β + β * γ + α * γ
p = α * β * γ

And the coefficients are:

a = 1
b = -s1
c = s2
d = -s3

The program displays a, b, c, and d.

TI-59 Program Vieta's Formula

000 76 LBL
001 11 A
002 42 STO
003 01 01
004 91 R/S
005 76 LBL
006 12 B
007 42 STO
008 02 02
009 91 R/S
010 76 LBL
011 13 C
012 42 STO
013 03 03
014 91 R/S
015 76 LBL
016 15 E
017 01 1
018 42 STO
019 04 04
020 91 R/S
021 43 RCL
022 01 01
023 85 +
024 43 RCL
025 02 02
026 85 +
027 43 RCL
028 03 03
029 95 =
030 94 +/-
031 42 STO
032 05 05
033 91 R/S
034 43 RCL
035 01 01
036 65 *
037 53 (
038 43 RCL
039 02 02
040 85 +
041 43 RCL
042 03 03
043 54 )
044 85 +
045 43 RCL
046 02 02
047 65 *
048 43 RCL
049 03 03
050 95 =
051 42 STO
052 06 06
053 91 R/S
054 43 RCL
055 01 01
056 65 *
057 43 RCL
058 02 02
059 65 *
060 43 RCL
061 03 03
062 95 =
063 94 +/-
064 42 STO
065 07 07
066 91 R/S

Example

Input:  α = 3, β = -5, γ = 6
Results: a = 1, b= -4, c = -27, d = 90

Random Numbers

Generate random numbers between 0 and 1 with this psuedorandom number generator.  You will need to enter a seed to start out.

Instructions:  enter a seed, [ RST ], [ R/S ].  Keep pressing [ R/S ] to generate additional random numbers.

TI-59 Program:  Psuedorandom Number Generator

000 85 +
001 89 PI
002 95 =
003 45 Y^X
004 05 5
005 95 =
006 22 INV
007 59 INT
008 91 R/S
009 81 RST

Source:  HP 25 Application Programs.  Hewlett Packard, 1975

Distance to the Horizon

This program computes the distance to an object, in nautical miles, given both the height of object (in feet) and height of the observer's eyes (in feet).

Formula:   

distance = 1.144 * ( √HE + √H )

Instructions.   Enter HE, [ RST ], [ R/S ], enter H, [ R/S ]

TI-59 Program: Distance to the Horizon

000 34 SQRT
001 85 +
002 91 R/S
003 34 SQRT
004 95 =
005 65 *
006 01 1
007 93 .
008 01 1
009 04 4
010 04 4
011 95 =
012 91 R/S
013 81 RST

Example

Input:  HE = 9.5 ft, H = 222 ft
Results:  20.57126091 n.m.

Source: 
"Distance To Or Beyond Horizon" (HAV 1-06A)  HP 65 Navigation Pac -1.  Hewlett Packard.  1974

Atmospheric Refraction

This program calculates atmospheric refraction of the light passing through the Earth's atmosphere given the apparent altitude of the light source, such as a star.

R = 1/(tan (h0 + 7.31/(h0 + 4.4)) 

The angle is in degrees.   Enter the apparent altitude, h0, in degrees, minutes, seconds format (DD.MMSSSS).  The result, R, is in arcminutes. 

000 60 DEG
001 88 DMS
002 42 STO
003 00 00
004 85 +
005 07 7
006 93 .
007 03 3
008 01 1
009 55 /
010 53 (
011 43 RCL
012 00 00
013 85 +
014 04 4
015 93 .
016 04 4
017 95 =
018 30 TAN
019 35 1/X
020 42 STO
021 01 01
022 91 R/S
023 81 RST

Example:

Input:  h0 = 43'24".  Enter as .4324
Result:  R = 26.63496931'

Source:
Meeus, Jean.  Astronomical Algorithms.  Willams-Bell Inc:  Richard, VA 1991 ISBN 0-943396-35-2

Head Winds and Cross Winds

The program calculates head winds and cross winds given :

* wind velocity (K)
* the direction wind from due north, clockwise, in degrees (D)
* the plane's heading direction angle from due north, clockwise, in degrees (D)
* any adjustment for the compass (V)

Head Wind: HW = K * cos(D - HDG - V)
Cross Wind:  RCW = K * sin(D - HDG - V)

Instructions:
Enter K, [ R/S ], enter D, [ R/S ], enter HDG, [ R/S ], enter V, [ R/S ]

Cross wind is displayed.  Press [ x<>t ] to get head wind.

Note:  As a program step, CP clears the t register. 

TI 59 Program:  Cross Winds and Head Winds

000 60 DEG
001 29 CP
002 32 X<->T
003 91 R/S
004 75 -
005 91 R/S
006 75 -
007 91 R/S
008 95 =
009 37 P->R
010 91 R/S
011 81 RST

Example

Input:
K = 25 mph
D  = 240 mph
HDG = 280 mph
V = 0

Results:
Cross Wind:  -16.09699024 mph [ x<>t ]
Head Wind:  19.1511108 mph

Source:
"Head Winds and Cross Winds"   HP 65 Aviation Pac 1.  Hewlett Packard, 1974

Eddie


All original content copyright, © 2011-2020.  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.

TI-59: Geometric Areas

TI-59: Geometric Areas

Introduction

The program calculates areas of planar geometric shapes.  The following user keys are defined:

A:  Enter A or radius.

B:  Enter B

C:  Enter C

D:  Display the total area

E:  Clear the total area

A':  Calculate the area of an Ellipse:  π*A*B.  For a circle, A = B

B':  Calculate the area of a Rectangle:  A*B.  For a square, A = B

C':  Calculate the area of a Triangle using Heron's Formula. 
S = (A + B + C)/2; √(S * (S - A) * (S - B) * (S - C))

D':  Calculate the area of Sector of a Circle:  π*B°*A^2/360
A:  radius, B: angle in degrees

E':  Calculate the area of a Regular Polygon:  (B * A^2)/(4 * tan(180°/B))
A:  length of a side, B:  number of sides (degrees)

Each calculation will add to the total area.

Memory Registers:

R01:  A
R02:  B
R03:  C
R04:  total area
R05:  S = (A + B + C)/2

The program is for the TI-58C, TI-58, TI-59, their emulators, and TI-66.

TI-59 Program:  Geometry Areas

000 76 LBL
001 11 A
002 42 STO
003 01 01
004 91 R/S
005 76 LBL
006 12 B
007 42 STO
008 02 02
009 91 R/S
010 76 LBL
011 13 C
012 42 STO
013 03 03
014 91 R/S
015 76 LBL
016 14 D
017 43 RCL
018 04 04
019 91 R/S
020 76 LBL
021 15 E
022 25 CLR
023 42 STO
024 04 04
025 91 R/S
026 76 LBL
027 16 A'
028 89 PI
029 65 *
030 43 RCL
031 01 01
032 65 *
033 43 RCL
034 02 02
035 95 =
036 44 SUM
037 04 04
038 91 R/S
039 76 LBL
040 17 B'
041 43 RCL
042 01 01
043 65 *
044 43 RCL
045 02 02
046 95 =
047 44 SUM
048 04 04
049 91 R/S
050 76 LBL
051 18 C'
052 53 (
053 43 RCL
054 01 01
055 85 +
056 43 RCL
057 02 02
058 85 +
059 43 RCL
060 03 03
061 54 )
062 55 /
063 02 2
064 95 =
065 42 STO
066 05 05
067 65 *
068 53 (
069 43 RCL
070 05 05
071 75 -
072 43 RCL
073 01 01
074 54 )
075 65 *
076 53 (
077 43 RCL
078 05 05
079 75 -
080 43 RCL
081 02 02
082 54 )
083 65 *
084 53 (
085 43 RCL
086 05 05
087 75 -
088 43 RCL
089 03 03
090 54 )
091 95 =
092 34 SQRT
093 44 SUM
094 04 04
095 91 R/S
096 76 LBL
097 19 D'
098 60 DEG
099 89 PI
100 65 *
101 43 RCL
102 02 02
103 65 *
104 43 RCL
105 01 01
106 33 X²
107 55 /
108 03 3
109 06 6
110 00 0
111 95 =
112 44 SUM
113 04 04
114 91 R/S
115 76 LBL
116 10 E'
117 53 (
118 01 1
119 08 8
120 00 0
121 55 /
122 43 RCL
123 02 02
124 54 )
125 60 DEG
126 30 TAN
127 65 *
128 04 4
129 95 =
130 35 1/X
131 65 *
132 43 RCL
133 02 02
134 65 *
135 43 RCL
136 01 01
137 33 X²
138 95 =
139 44 SUM
140 04 04
141 91 R/S

Example

5 [ A ]  6 [  B ]

[2nd] [ A' ]   Result:  94.24777961  (area of an ellipse with A = 5, B = 6)

[2nd] [ B' ]  Result:  30  (area of a rectangle with A = 5, B = 6)

9 [ C ]

[2nd] [ C' ]  Result: 14.14213562  (area of a triangle with A = 5, B = 6, C = 9)

9 [ A ] 60 [ B ]

[2nd] [ D' ]  Result: 42.41150082 (area of a circular sector A = 9, B = 60°)

9 [ A ] 8 [ B ]

[2nd] [ E' ]  Result:  391.1025971 (area of a polygon with a side length of 9 and 8 sides)

[ D ]  Total Area:  571.9040132

[ E ] clears total area

Eddie

All original content copyright, © 2011-2020.  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.

Retro Review: Texas Instruments TI-66

Retro Review:  Texas Instruments TI-66

Quick Facts

Company:  Texas Instruments
Years in Production: 1982 to 1985
Original Price: I estimate the original price to be from $70 to $100
Battery:  2 x LR44 or 2 x AR76
Type:  Scientific, Keystroke Programmable
Operating System: AOS
Number of Digits: 10
Memory:  512 steps, which can be allocated to a maximum of 64 memory registers
Accessories: Carrying Case, PC-200 Printer

I paid $7.99 at a Goodwill in Cerritos, CA.  The calculator came with the carrying case, User Guide, and Quick Start Guide, all boxed up.  What a lucky find!

The Next Generation of TI-58C

The TI-66 was slated to be the next generation of the TI-58C of 1978.  Virtually the keyboard design and commands of the TI-58C are present in the TI-66, but there are some differences:

*  The TI-66 is an landscape form with a gray keyboard, where as the TI-58C (and the related TI-58 and TI-59 has a black keyboard).

*  The TI-66 lacks a card reader.

*  The TI-66 also lacked a slot for modules. 

*  However, the TI-66 runs on coin batteries (AR76 or LR44), which can be found easily.  The TI-58C family had rechargeable battery packs, which cannot be easily purchased (few vendors sell them online).

*  In learn mode, when a step is registered, the TI-66 displays the key you just pressed with its mnemonic. 

Programming With The TI-66

Keystroke programming is fairly simple with the TI-66.  As I mentioned before, the TI-66 displays a mnemonic when a key stroke is registered (think HP 42S, HP 41C, or HP 32SII).  Examples are:

[ x^2 ] displays x↑2
[ π ] displays PI
[ Σ+ ] displays Σ+
[ √x ] displays √x

However, when it comes to programming the TI-66, patience is key!  The TI-66 takes on average, 1.5 seconds to register a new keystroke in learn (LRN) mode.  This is not for the speedy programmers among us.  This is my down point about the calculator, but it is not a deal breaker.

Other Programming Features

*  User labels A, B, C, D, and E; along A', B', C', D', and E'.  There are five keys dedicated to user labels.

*  Local labels have an unusual scheme.  They are defined by (almost) any key that is not a numeric key.  Therefore, we have labels such as 1/x, sin, and ÷.   This is carries over from the 1970s TI programmables (TI-57, TI-58, TI-58C, and TI-59). 

* 10 user flags: 0-9.

*  Indirect addressing

*  Storage arithmetic:  SUM (STO+), INV SUM (STO-), Prd (STO*), INV Prd (STO÷)

*  Comparisons:  compare the value in the display with register t.  Store amounts in register t with [ x<> t ].  Example:  a [ x<>t ] b [ 2nd ] (x≥t) tests whether b ≥ a).

*  An [ OP ] key gives access to additional functions and printing commands. 

A Partial List of OP Commands

OP 01 - 08 deal with printing, while 09 is not a valid code.

OP 10:  sign(x)
OP 11:  variance(x), variance(y)
OP 12:  slope, intercept  (linear regression)
OP 13:  correlation (linear regression)
OP 14:  x'  (predict x, linear regression)
OP 15:  y' (predict y, linear regression)

OP 2#:  increase register R0# (0-9) by 1
OP 3#:  decrease register R0# (0-9) by 1

Keyboard

Other than registering new programming commands, the keys are immediately responsive.  The keys are nice to the touch. 

Verdict

I would recommend the TI-66, especially if you want a TI-58, TI-58C, or TI-59, but don't want to deal with 1970s rechargeable batteries, or you are on a budget.  It is a very nice, feature rich calculator to have. 

Eddie

All original content copyright, © 2011-2019.  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.

HP 32SII and TI-66: Curve Fitting

HP 32SII and TI-66:  Curve Fitting

Introduction

The curve fitting program uses the linear regression module to determine the parameters b ("intercept") and m ("slope") in non-linear curves using following transformations:

Logarithmic Regression:  y = b + m * ln x
Transformations:  ( ln x, y, b, m )

Inverse Regression:  y = b + m / x
Transformations:  ( 1/x, y, b, m )

Exponential Regression:  y = b * e^(m * x)
Transformation:  ( x, ln y, e^b, m )

Power Regression:  y = b * x^m
Transformation:  ( ln x, ln y, e^b, m )

Geometric (Exponent) Regression:  y = b * m^x
Transformation:  ( x, ln y, e^b, e^m )

Simple Logistic Regression:  y = 1 / (b + m * e^(-x))
Transformation:  ( e^(-x), 1/y, b, m )

HP 32SII Program:  Curve Fitting

Note:
1.  This can be adapted into the HP 35S under one label.  Just take note of the where the label points are.
2.  The total amount of bytes used is 90.
3.  Flags 1 and 2 are used.  If flag 1 is set, e^m is calculated as slope.  If flag 2 is set, e^b is calculated as intercept.

Program:
// Initialize - LBL X
LBL X
CF 1
CF 2
CLΣ
0
RTN

// Calculation - LBL Y
LBL Y
b 
FS? 2
e^x
STO B
VIEW B
m
FS? 1
e^x
STO M
VIEW M
r 
STO R
VIEW R
RTN

// Logarithmic Regression - LBL L
LBL L
LN 
R/S
GTO L

// Inverse Regression - LBL I
LBL I
1/x
R/S
GTO I

// Exponential Regression - LBL E
LBL E
SF 2
x<>y
LN 
x<>y
R/S
GTO E

// Power Regression - LBL P
LBL P
SF 2
LN 
x<>y
LN 
x<>y
R/S
GTO P

// Geometric/Exponent Regression - LBL G
LBL G
SF 1
SF 2
x<>y
LN
x<>y
R/S 
GTO G

// Simple Logistic Regression - LBL S
LBL S
+/-
e^x
x<>y
1/x 
x<>y
STOP 
GTO S

Instructions:
1.  Clear the statistics data and flags by pressing [XEQ] X.
2.  Enter data points, run the proper label, and press [ Σ+ ] or [ Σ- ].

For example, for Logarithmic fit:
y_data [ENTER] x_data [XEQ] L [ Σ+ ]

Subsequent Data:
y_data [ENTER] x_data [R/S] [ Σ+ ]

This scheme allows for undoing data:
y_data [ENTER] x_data [XEQ] L [ Σ- ]

3.  Calculate intercept (B), slope (M), and correlation (R), press [XEQ] Y.

TI-66 Program:  Curve Fitting

Notes:
1.  This program should be able to entered on a TI-58, TI-58C, or TI-59.  At the time of the posting, I have not done it, so I don't have the key codes.
2.  94 steps are used.  [INV] [SBR] is merged into the RTN step.
3.  Flags 1 and 2 are used.  If flag 1 is set, e^m is calculated as slope.  If flag 2 is set, e^b is calculated as intercept.

Program:
// Initialize - key [ A ]
000 LBL
001 A
002 INV
003 ST.F
004 01
005 INV
006 ST.F
007 02
008 CSR
009 0
010 RTN

// Calculation - key [ A' ]
011 LBL
012 A'
013 OP
014 12
015 INV
016 IF.F
017 02
018 (   // left parenthesis
019 INV
020 LN X
021 LBL
022 (  // left parenthesis
023 STO
024 08
025 R/S
026 X<>T
027 INV
028 IF.F
029 01
030 )  // right parenthesis
031 INV
032 LN X
033 LBL
034 )  // right parenthesis
035 STO 
036 07
037 R/S
038 OP
039 13
040 STO
041 09
042 RTN

// Logarithmic Regression - key [ B ]
043 LBL
044 B
045 LN X
046 X<>T
047 R/S
048 RTN

// Inverse Regression - key [ C ]
049 LBL 
050 C
051 1/X
052 X<>T
053 R/S
054 RTN

// Exponential Regression - [ D ]
055 LBL 
056 D
057 ST.F
058 02
059 X<>T
060 R/S
061 LN X
062 R/S
063 RTN

// Power Regression - [ B' ]
064 LBL
065 B'
066 ST.F
067 02
068 LN X
069 X<>T
070 R/S
071 LN X
072 R/S
073 RTN

// Geometric/Exponent Regression - [ C' ]
074 LBL
075 C'
076 ST.F
077 01
078 ST.F
079 02
080 X<>T
081 R/S
082 LN X
083 R/S
084 RTN

// Simple Logistic Regression - [ D' ]
085 LBL
086 D'
087 +/-
088 INV
089 LN X
090 X<>T
091 R/S
092 1/X
093 R/S
094 RTN

Instructions:
1.  Clear the statistics data and flags by pressing [  ].
2.  Enter data points: enter x, run the proper label, enter y, press [R/S] and press [2nd] ( Σ+ ) or [INV] [2nd] ( Σ+ )  (for  Σ- ).

For example, for Logarithmic fit:
x_data [ B ] y_data [R/S]  [2nd] (Σ+)

This scheme allows for undoing data:
x_data [B] y_data [R/S] [INV] [2nd] (Σ+)

3.  Calculate intercept (B), slope (M), and correlation (R), press [2nd] [ A' ].

Examples

All results are rounded.

Example 1: Logarithmic Regression
Data (x,y):
(33.8, 102.4)
(34.6, 103.8)
(36.1, 105.1)
(37.8, 106.9)

Results:
B:  -33.4580
M:  38.6498
R:  0.9941

y ≈ -33.4580 + 38.6498 ln x

Example 2:  Inverse Regression
Data (x,y):
(100, 425)
(105, 429)
(110, 444)
(115, 480)

B:  823.80396
M:  -40664.72143
R:  -0.91195

y ≈ 823.80396 - 40664.72143/x

Example 3: Simple Logistic Regression
Data (x,y):
(1, 11)
(1.3, 9.615)
(1.6, 8.75)
(1.9, 8.158)
(2.6, 7.308)

B: 0.14675
M: -0.15487
R:  -0.99733

y ≈ 1 / (0.14675 - 0.15487*e^(-x))

Eddie

All original content copyright, © 2011-2019.  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.