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.

Wednesday, August 30, 2017

TI-84 Plus CE: Fitting a Parametric Line

TI-84 Plus CE:  Fitting a Parametric Line

The program PARLIN attempts to fit a parametric line for a collection of points (x(t), y(t)) using the following equations:

x = a * t + b
y = c * 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. 

TI-84 Plus CE Program PARAM

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

Program:

Param
Input "T LIST: ",L1
Input "X LIST: ",L2
Input "Y LIST: ",L3
FnOff
PlotsOff
LinReg(ax+b) L1,L2
a→A:b→B:r²→E
"AT+B"→X1T
ClrHome
Disp "X = A*T + B"
Disp A
Disp B
Disp "CORR: "
Pause E
LinReg(ax+b) L1,L3
a→C:b→D:r²→F
"CT+D"→Y1T
ClrHome
Disp "Y = C*T + D"
Disp C
Disp D
Disp "CORR: "
Pause F
min(L1)-5→Tmin
max(L1)+5→Tmax
FnOn 1
PlotsOn 1
GraphColor(1,BLUE)
Plot1(Scatter,L2,L3, [square] ,ORANGE)
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 also download the program here:


Example 1

Fit the data to a parametric line:

T
X
Y
1
2.3
-3.0
2
2.8
-2.6
3
3.2
-2.3
4
3.7
-1.9
5
4.2
-1.6

Results:  
x = 0.47*t + 1.83 (r^2 ≈ 0.998)
y = 0.35*t – 3.33 (r^2 ≈ 0.997)




Example 2

Fit the data to a parametric line:

T
X
Y
1
-1.0
1.000
2
1.0
1.250
4
5.3
1.746
8
13.6
2.825
16
30.1
4.275

Results:
x = 2.075268817 * t – 3.066666667 (r^2 ≈ 0.99997)
y = 0.2196827957* t + 0.857166667 (r^2 ≈ 0.99145)



Eddie


This blog is property of Edward Shore, 2017.

Retro Review: Texas Instruments TI-35 PLUS

Retro Review:  Texas Instruments TI-35 PLUS Essentials Company:  Texas Instruments Type:  Scientific Year: 1986 Batter...