HP 17BII+ and TI-84 Plus CE Python: Zeta Approximation

HP 17BII+ and TI-84 Plus CE Python:  Zeta Approximation

Zeta Function

zeta(x) = Σ(1 ÷ (n^x), n =1 to ∞)

We are going to use the approximation:

zeta(x) = Σ(1 ÷ (n^x), n =1 to w) where w = intg(10^((a + 2) ÷ x)

where a is the number of decimal places desired.  The higher the accuracy, the longer the calculation takes.  Also the lower x is, the longer the calculation takes.

This is for all x > 0.

HP 17BII+ Formula ZETA

ZETA=0×L(W:10^IP((ACC+2)÷X))+Σ(N:1:G(W):1:INV(N^X))

Examples:

ACC =3, X = 2;  Result:  ZETA = 1.63

ACC =3, X = 3.5;  Result:  ZETA = 1.13

ACC =3, X = 8.7;  Result:  ZETA = 1.00

TI-84 Plus CE Python:  zeta.py

# 2021-12-07 ews

# zeta function approximation

from math import *

print("zeta function approximation")

x=eval(input("x? "))

a=eval(input("# places? "))

w=int(10**((a+2)/x)

z=0

n=1

while n<w:

  z+=(n**x)**-1

  n+=1

z=round(z,a)

print("zeta = "+str(z))

Eddie

All original content copyright, © 2011-2022.  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 17BII+ and Numworks: Payment of a Loan with an Unusual First Period

 HP 17BII+ and Numworks: Payment of a Loan with an Unusual First Period

The First Payment Is Not Due in a Month

In finance, the first payment of a loan is not due at the end of a month from signing. This happens when all payments are due at a certain date, such as the 30th/31st or 1st of each month, regardless of when the loan papers are signed.  Loans of this type are referred to odd period loans or partial period loans.  Every payment after the first follows the conventional month time line.

HP 17BII+ Formula:  Partial Period Loan 

The following HP 17BII+ formula deals with calculating odd period loans.  This solver formula is directly from the HP 17BII+ Financial Calculator User's Guide, pg. 196 (see source):

ODD:  PV×(I%÷100×FP(DAYS÷30)+1)=-IF(DAYS<30:(1+I%÷100)×PMT:PMT)×UPSV(I%:N)-FV×SPPV(I%:N)

In the solver, the percent sign is a character used in variables, not a function.  PV, FV, PMT, I%, N are all valid variables in the HP 17BII+ solver.  The variables:

N:  number of payments

DAYS:  number of days in the first period, from 0 to 59.

I%:  the periodic interest rate.   For monthly payments, divide the annual interest rate by 12.

PV:  the loan amount

FV:  the balloon amount

PMT:  payment

This formula follows the cash flow convention:  negative amounts for cash outflows, positive amounts for cash inflows.

Numworks Script:  Partial Period Loan

oddperiod.py

My Numworks script:  https://my.numworks.com/python/ews31415/oddperiod

# 2021-11-14 EWS

# odd period

from math import *

print("Loan with partial period")

print("0 - 59 days")

print("Monthly Payments")

n=float(input("N: n? "))

rate=float(input("I/YR:  rate? "))

pv=float(input("PV: loan amt? "))

fv=float(input("FV: balooon pmt? "))

days=float(input("DAYS: odd period? "))

r=rate/1200

if days<30:

  j=1+r

else:

  j=1

f=days/30-int(days/30)

w=r*f+1

  

# uspv

u=(1-(1+r)**(-n))/r

# sppv

s=(1+r)**(-n)

pmt=(pv*w+fv*s)/(j*u)

# rounding

pmt=-int(pmt*100+.5)/100

# result

print("Payment: "+str(pmt))

Note:   the cash flow convention is followed

Examples

Loan 1:

Inputs:

N = 60

DAYS = 10

PV = $58,425.10

I%/YR = 4.48%  (annual rate), for the HP 17BII+, divide this by 12

FV = $0.00 (no balloon payment)

Result:  PMT:  -1,085.99  

Loan 2:

Inputs:

N = 240

DAYS = 40

PV = $16,956.00

I%/YR = 7.02%  (annual rate), for the HP 17BII+, divide this by 12

FV = $500.00 (enter -500.00 for HP 17BII+)

Result:  PMT:   -130.96

Source

HP 17BII+ Financial Calculator User's Guide.  Ed. 2.  Hewlett Packard.  San Diego, CA  2004

http://h10032.www1.hp.com/ctg/Manual/c00363348

All original content copyright, © 2011-2022.  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 17BII+: Update to Normal CDF Formula - Don Phillips

 HP 17BII+:  Update to Normal CDF Formula - Don Phillips

On March 31, 2019, I posted a formula calculate the normal cumulative distributive function (normal CDF) for x ≥ 0:

http://edspi31415.blogspot.com/2019/03/hp-17bii-normal-distribution-and-random.html

Don Phillips provided us with an updated formula to include negative values of x.   Much gratitude for allowing me to post this formula:

NCDF=L(ANS:1-EXP(-ABS(X)^2÷2)÷SQRT(2×PI)×(.4361836×L(T:INV(1+.33267×ABS(X)))-.1201676×G(T)^2+.9372980×G(T)^3))×0+IF(X<0:1-G(ANS):G(ANS))

Example Calculations:

X = -2.50,  NCDF = 0.00622

X = -1.50, NCDF = 0.06680

X = -0.50, NCDF = 0.30855

X = 0.00, NCDF = 0.50000

X = 0.50, NCDF = 0.69145

X = 1.00, NCDF = 0.84135

X = 2.00, NCDF = 0.97724

Thank you Don, Eddie. 

All original content copyright, © 2011-2021.  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. 

Casio fx-115ES Plus: Ten Tips

 Casio fx-115ES Plus:  Ten Tips

This blog entry covers both the original and the current 2nd Edition of the Casio fx-115 ES Plus.  Here are ten things to help you know about some of the advanced features of the fx-115 ES Plus, including some things to watch out for.  

I believe this also covers the fx-991 ES Plus 2nd Edition (NOT the Classwiz).  

Tip 1:  Integer Division and Modulus

Find the quotient and remainder of a division problem by pressing [ALPHA] [ []/[] ] (÷R).   We can use this calculate the modulo of two positive numbers (use caution with negative numbers).

Example 1:  364 mod 20 = 4

364÷R20 returns 18, R = 4

(18 * 20 + 4 = 364)

Example 2:  178.5 mod 18.5 = 12 

178.5÷R18.5 returns 9,R=12

(9 * 18.5 + 12 = 178.5)

Tip 2:  Solving Quadratic Equations Also Calculates the Extrema Point

Solving quadratic equations in EQN mode will present the point of the parabola's extrema point (minimum or maximum).  Keep on pressing [ ↓ ] or [ = ].

[ Mode ],  5:  EQN,  3:  aX^2+bX+c=0

Example 1:  4 * x^2 + 13 * x + 5 = 0

[ 4, 13, 5]

X1 = (-13+√89)/8   (MthIO mode)

X2 = (-13-√89)/8

X-Value Minimum = -13/8

Y-Value Minimum = -89/16

Example 2:  -2 * x^2 + 5 * x + 10 = 0

[-2, 5, 10]

X1 = (5+√105)/4

X2 = (5-√105)/4

X-Value Maximum = 5/4

Y-Value Maximum = 105/8

Please note that results and coefficients are not stored in variables.  This goes for all the equations in EQN mode, including finding roots of a polynomial and solving simultaneous equations.  

Tip 3:  Solving Quadratic Inequalities

The Inequality mode solves inequalities for quadratic and cubic equations.  

[ MODE ], [ ↓ ], 1: INEQ,  1 for quadratic equation/2 for cubic equation, select inequality:

1:  >0

2:  <0

3:  ≥0

4:  ≤0

Example:  Solve x^3 + 2 * x - 3 > 0

[1, 0, 2, -3], option 2

Result:  1<X

Tip 4:  The Percent Function

The percent function ( [ SHIFT ] [ ( ] (%) ) just divides the argument by 100.  This can lead to puzzling results when working addition and subtraction problems involving percent.

8 + 10% returns 8.1   (10% converts it to 0.1)

8 - 10% returns 7.9

To add and subtract percents properly, do this instead:

8(1 + 10%) returns 8.8

8(1 - 10%) returns 7.2

Tip 5:  Limited Powers in Complex Mode

In complex mode (CMPLX), the only powers available to be calculated are x^2 and x^3.   To take any complex number to any real power will require the use of De Moivre's formula:

(x + yi)^n = r^n * cos θ + i * r^n * sin θ

My suggestion to use COMP mode, with the Rec and Pol conversions.  In CMPLX mode, rectangular/polar conversions do not store results.  In COMP mode, rectangular/polar conversions store results in the following variables:

X:  x, r

Y:  y, θ

Tip 6:  Solve Equations for Any Variable

We can use the general solver in COMP mode to solve for any variable.  The syntax is:

equation, variable;  press [ SHIFT ], [ CALC ] (SOLVE)

If variable is omitted, the variable to be solved for assumed to be X.

If the equation does not contain an equals sign (=), the solver finds the root for equation, assuming equation=0.

The entries and results are stored in variables. 

In Radians mode:

Example 1: y = x * sin x  with y =0.5

We are solving for x, so we can eliminate the variable argument.

Y=X*sin(X), [ SHIFT ], [ CALC ]

Enter 0.5 for Y

Enter a guess for X, I chose 1.

Result:  X = 0.7408409551, L-R = 0

Example:  2 * a - b = 3 * c, solve for b when a = 2 and c = -1.

2A-B=3C, B, [ SHIFT ], [ CALC ]

Enter 2 for A

Enter -1 for C

Enter a guess for B, I chose 1 (again).

Result:  B = 7, L-R = 0

Caution:  Some equations can not be solved on the fx-115 ES Plus.  In particular, involving integrals and derivatives.  

Tip 7:  The Repeating Decimal Bar

I think this may be only calculator (yet), that allows the use to easily type in a bar to represent repeating decimals.  

Example:

1.45454545454545454545....   can be typed with 1.45 with the bar over the 45, or 1, [ . ], [ ALPHA ], [ √ ] ( bar ) 45

Pressing [ = ] returns 16/11 (assuming MthIO is set).  Repeated uses of [ S←→D ] gives 1.(45), 1.454545455, 16/11.

Tip 8:  Integer Part and Greatest Integer Function (Floor)

Int ( [ ALPHA ] [ + ] ):  Returns the integer part of a number

Intg ( [ALPHA] [ - ] ):  Returns the floor function of a number, the largest integer that does not exceed the given number.  

Example 1:

Int(-12.96) returns -12

Intg(-12.96) returns -13

To find the (calculator) fractional part of a number, enter n - Int(n).  

Tip 9:  Use CALC to Formula Evaluation

In addition to the Table mode, using [ CALC ] in COMP mode allows the user to evaluate a formula using different expressions.   As long as you keep pressing [ = ], the prompting for variables and calculations repeat.  The latest values are updated in the memory registers.

Expressions may take the form of:

variable = expression

To results are stored in the designated variable.

Example:   Evaluate for y when x = 0.2, x = 0.7, and x = 1.2 when y = x^3 + 15 * log x

Y=X^3+15*log(X)   

[ CALC ]

Enter 0.2 for X, [ = ]

Result #1: -10.49255007, [ = ]

Enter 0.7 for X, [ = ]

Result #2: -2.6665294, [ = ]

Enter 1.2 for X, [ = ]

Result #3:  -0.5402813093 

Press [ AC ] to exit.

Tip 10:  Previous Answers are Stored Two-Deep in COMP Mode

In COMP mode, we have both Ans and PreAns ([ALPHA], [ Ans ]).  PreAns recalls the answer from two calculations ago.  

Be careful, switching modes with most likely clear the PreAns register (zero).  Also, PreAns is only available in COMP mode.

Bonus:  Checking the fx-115ES Plus 2nd Edition's ID  (2nd Edition only)

You can see the calculator's ID along with a bar code which allows to test whether the calculator is a genuine Casio calculator.  

I hope you find these tips helpful,

Eddie

All original content copyright, © 2011-2021.  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: Radio Shack EC-4027

Retro Review:  Radio Shack EC-4027

Quick Facts:

Company:  Radio Shack

Year Introduced:  1993

Type:  Scientific, Formula Programming

Memory:  40 steps

Operating System:  Algebraic

Memory Registers:  7, A through F, M

Batteries:  2 x LR44 (357)

Equivalent Of:  Sharp EL-5020

Background

From the 1970s to about the 1990s (maybe early 2000s), Radio Shack sold OEM equivalents of calculators from Sharp, Casio, and Texas Instruments, and the EC-4027 is no exception.  One advantage to buying Radio Shack is that the price tends to be cheaper but with equivalent quality of the original.

An Update to the Sharp EL-5100

The EC-4027 (and the Sharp EL-5020) is a scientific calculator which holds multi-step formulas.   There are no switches, everything is keys this time.  The following modes offered are:

*  Normal:  Computational mode

*  AER:  Program and store formulas

* ∫dx:  Integral Mode

* STAT 1:  Single-variable statistics mode

* STAT 2:  Linear Regression, y = a+bx

Base conversions and fractions are added.  

Like the EL-5100, expressions are entered algebraically as you would write it down.   A frustrating part is that the entire expression is not shown on the screen, regulating functions to the sides of the screen, which makes editing expressions difficult if not impossible.

Integration and Loops but With Less Memory

The memory of the EC-4027 is half of the EL-5100:

* 40 steps instead of 80

* Only two formulas can be stored instead of five

We do get comparisons against the M register, all six comparisons (<, ≤, =, >, ≥, ≠).  If the condition is met, the formula is starts over from the beginning, creating a loop.   

There is a separate mode for integration.  Either formula 1 or 2 can be called, and Simpson's Rule is used.  Any function that can be integrated is in terms of M.  

I wish the memory wasn't halved but instead increased.  Also, expand the ALPHA characters to include the entire alphabet.  But, the EC-4027 serves it's purpose.

Sources:

Toth, Viktor T. "Radio Shack EC-4027"  2000-2018.  https://www.rskey.org/ec4027  Last accessed April 9, 2021

Voidware.  "Sharp EL-5020" http://www.voidware.com/calcs/el5020.htm  Last accessed April 9, 2021. 

Eddie

All original content copyright, © 2011-2021.  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: Sharp EL-5100

Retro Review:  Sharp EL-5100

Company:  Sharp

Year Introduced:  1979

Type:  Scientific, Formula Programming

Memory:  80

Operating System: Algebraic

Memory Registers: 11, A through J, M

Background

I have to give a shout out to the Pasadena Antique Mall in Pasadena, California.   The EL-5100 was a lucky find for me, and the ladies at the counter were kind enough to let me walk quickly to nearby Target to get batteries so the EL-5100 can be tested.  The calculator tested perfectly!  If you are in the greater Los Angeles area, the Pasadena Antique Mall is great place to visit for all things retro.  

Landscape and Thin Calculator

The EL-5100 is a light weight calculator in a silver, thin design.  The calculator is well built and the keys are solid.   The keys are arranged in three sections, from left to right:

*  Scientific functions

*  Number keypad and arithmetic functions

*  Storage and alpha keys:  A-J, M

A staple of calculators from the 1970s is the physical mode switch.   The EL-5100 has one mode switch:

* AER:  Program and store formulas

* COMP:  Computational mode

* STAT:  Statistics mode, including linear regression  (y = a + bx)

Formula Storage

The EL-5100 can store up to five formula areas, with 80 steps allocated between them.   The formulas can be separate or stored as a chain of formulas.  An example of the chain formula:

c = √(a^2 + b^2)

d = c / (b + c)

would be stored as:

(switch to AER mode, CA)

1; f(A,B)=√(A^2+B^2) STO C ◣

2; C ÷ (B + C) STO D

(switch back to COMP)

Press [ COMP ] 

(an example)

A =?   (pressing COMP again takes the last value of A)

Example:  Let A = 19, B = 79

[COMP]

A = ?   19 [COMP]

B = ?   79 [COMP]

1; ANS 1 = 81.25269226  (C)

[2nd F]  2;  

2;  ANS 1 = 0.507028563  (D)

An alternative way to chain formulas (multistep):

1; f(A,B)=√(A^2+B^2) STO C,  C ÷ (B + C) STO D

Example:  Let A = 19, B = 79

[COMP]

A = ?   19 [COMP]

B = ?   79 [COMP]

1; ANS 1 = 81.25269226  (C)  [COMP]

2; ANS 2 = 0.507028563  (D)

You can store immediate results, however, they will end the execution.  However, this is still handy when you are using the M register and the M+ feature.

* Note:  In AER mode, the [ COMP ] key is the comma.  

Statistics Mode

In STAT mode, it was common for Sharp calculators to assign data entry keys to the M register keys.

[ RM ] becomes CD  (clear data)

[ →M ] becomes the comma for bivariate data (x,y)

[ M+ ] becomes DATA for storing data

The multiplication key can be used to store data with frequency greater than.  However, you can do mathematical operations as long as they are enclosed in parenthesis.

Even though the variable keys A-J are not available during STAT mode, the stat values are stored in the following variables and can be used later in COMP mode.

E = n

F = ∑x

G = ∑x^2

H = ∑xy

I = ∑y

J = ∑y^2

Sharp EL-5100 vs TI-68

The EL-5100 ushered in a category of formula storage calculators.  Here is a comparison table between 1979's EL-5100 and 1989's TI-68.

EL-5100		TI-68
1979	Year of Introduction	1989
3 x SR44/LR44/357	Batteries	1 x CR2032
landscape	Form	portrait
5, sequential	Number of Storage Areas	1 at a time, as memory allows
80	Number of Steps	440 (55 registers)
y = a + bx, r	Linear Regression	y = SLP x + ITC, COR
A through J, M	Variable Names	variable names up to 3 characters
chain formulas, physical mode switch	Unique Features	complex numbers, base conversions, integrals, solver, conversions

Verdict

The EL-5100 is a simple calculator which is a joy to use.  

Eddie

All original content copyright, © 2011-2021.  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 71B: Population Deviation Derivation and Program

HP 71B:  Population Deviation Derivation and Program 

Derivation

The standard formula for the population deviation for a set of statistical data is given by:

σx = √( Σ(x - μ)^2 / n)

where μ is the mean, where μ = Σx / n

Σx = the sum of all the data points
 n = the number of data points

If this function needs to be programmed, using the definition as will probably require the use of two FOR structures: one for the mean, and one for the deviation.  Is there a way to use a formula where a FOR structure can be saved?

Turns out, the answer is yes. 

σx = √( Σ(x - μ)^2 / n)
= √( Σ(x^2 - 2*x*μ + μ^2) / n)

Note that:
Σ( f(x) + g(x) ) = Σ f(x) + Σ g(x)
For a constant, a:   Σ( a * f(x) ) = a * Σ f(x)
And:  Σ a = a * n   (sum from 1 to n)

Then:

σx = √( Σ(x - μ)^2 / n)
= √( Σ(x^2 - 2*x*μ + μ^2) / n)
= √( (Σ(x^2) -  2*μ*Σx + Σ( μ^2 )) / n)
= √( (Σ(x^2) -  2*μ*Σx + n*μ^2) / n) 
= √( (Σ(x^2) -  2*Σx*Σx/n + n*(Σx)^2/n^2 ) / n) 
= √( (Σ(x^2) -  2*(Σx)^2/n + (Σx)^2/n) / n)
= √( (Σ(x^2) -  (Σx)^2/n ) / n)

The above formula allows to use a sum and sum of square of data points in calculating population deviation, eliminating the need for an additional FOR structure. 
 
Standard deviation follows a similar formula:
sx = √( (Σ(x^2) -  (Σx)^2/n ) / (n - 1))

HP 71B Program:  Population Deviation

File:  PDEV
20 N=0
22 A=0
24 B=0
30 INPUT "X? ";X
40 N=N+1
50 A=A+X
60 B=B+X^2
70 INPUT "DONE? NO=0"; C
80 IF C=0 THEN 30
90 M=A/N
95 S=SQR((B-A^2/N)/N)
100 DISP "MEAN= ";M
105 PAUSE
110 DISP "PDEV= ";S
120 END

Example

Data Set:  150, 178, 293, 426, 508, 793, 1024

MEAN = 481.7142857
PDEV = 300.6320553

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.

Estimating the Boiling Point at Various Elevations

Estimating the Boiling Point at Various Elevations

Equation

We can estimate the boiling point of water, accurate to the nearest tenth (one decimal point), by the formula:

y = 4.299969165*10^-8 * x^2 – 0.0035531324 * x + 100.0049216

Where:

x = elevation in meters

y = boiling point of water in degrees Celsius (°C)

This equation was derived using quadratic regression analysis of 27 sample points, testing points for elevations from -305 m to 6629 m.

If you are working with US units, you can use the following unit conversions:

1 ft = 0.3048 m

Conversion to Celsius:  °C = (°F – 32) * 5/9

Examples

x = -152 m (approx. -498.687664 ft), y ≈ 100.5 °C

x = 4115 m (13500.65617 ft), y ≈ 86.1 °C

x = 6325 m (20751.31234 ft), y ≈ 79.3°

Source:

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

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.

Algebra: Multiplying a * b Trick (Using the Difference between a and b)

Algebra:  Multiplying a * b Trick (Using the Difference between a and b)

Can we find a formula to find products where two values are an equal-distant apart

The Values of a and b Differ by 2

Let a and b be real numbers which differ by 2, that is b – a = 2.  Here I am assuming that b > a. 

Let n be the midpoint between a and b.  That is:

n = b – 1 and

n = a + 1

Therefore:

b = n + 1

a = n - 1

Then:

a * b

= (n - 1) * (n + 1)

= n^2 - n + n – 1

= n^2 - 1

Example:  51 * 49

Notice that:

51 – 49 = 2, and

51 - 1 = 50

49 + 1 = 50

Hence:

51 * 49 = 50^2 – 1 = 2499

Can we expand this included products of a * b, where the difference is b – a = 2 * w

The Values of a and b Differ by 2*w

Let’s look at a more general case. 

Let b – a = 2*w

Then:

b = n + w and a = n – w

Then:

a * b

= (n – w) * (n + w)

= n^2 – n*w + n*w – w^2

= n^2 – w^2

Example:  37 * 43.

43 – 37 = 6

w = 6/2 = 3

Then:

n = 43 – 3 = 37 + 3 = 40

Then:

37 * 43 = 40^2 – 3^2 = 1600 – 9 = 1591

Try another example:  57 * 49

57 – 49 = 8

8 / 2 = 4

57 – 4 = 53, 49 + 4 = 53

Then:

57 * 49 = 53^2 – 4^2 = 2809 – 16 = 2793

In summary for a * b with b > a.

Let w = (b – a)/2 and n = a + w or n = b – w

Then a * b = n^2 – w^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.

Retro Review: TI-60X

Retro Review: TI-60X

TI-60X.  Yes I forgot the multiplication sign here.

Company:  Texas Instruments

Years:  1991 – 1995? 2000?

Year of my TI-60X:  1991 (specifically week 46, November 1991)

Type:  Scientific, Formula Storage

Number of Steps: 96, shown in units of registers (12 registers of 8 steps each)

Operating System: Algebraic

Memory Registers: 12 (A through I, X, Y, Z)

Regressions Available:  Linear

Chipset:  Toshiba T9838

Battery: 1 CR2032

My late Uncle Ralph bought a TI-60X for me in 1992 (I think it was in ’92).  It was my first year of high school.  Uncle Ralph encouraged my love for calculators. (Thanks for all you did for me Uncle)

A Rich Feature Set

The TI-60X operates in Algebraic mode.  Simply, type in the expression as its written, and press [ =/ENTER ]. 

The TI-60X isn’t programmable in the traditional sense (keystroke or BASIC) but rather you can store formulas (A = π * B^2, for example) for later use.  I think the TI-60X is the first of its kind to store formulas.  Today, formula storage is a feature of the Sharp EL-520W.  More on this later.

You have your standard linear regression capabilities.  However, instead of the usual labels a, b, and r, you have ITC (intercept), SLP (slope), and COR (correlation) respectively.  If find these labels much helpful since calculators sometimes tend to switch the roles of a and b in linear regression mode.  Entry is rather easy, just enter the data point and press [ Σ+ ] and you are good to go.  No separate declaration of stats mode needed.

Equation:  y = INT + SLP * x

The Base conversions are on the TI-60X as well.  We also get the logical functions AND, OR, XOR, XNOR, NOT, and 2’s (compliment).  The TI-60X distinguishes the variables A-F from the hexadecimal A-F by assigning the latter set to the 3^rd functions of the reciprocal, square, square root, and the trigonometric keys.  On the screen, hexadecimal letters are in bold while storage registers are not.

Fractions are included, as well as the decimal to/from fraction conversion.  The TI-60X has the following additional conversions:

* degrees, decimal-minute-seconds

* polar, rectangular coordinates

* inches, centimeters

* gallons, liters (litres)

* pounds, kilograms

* degrees Fahrenheit (°F), degrees Celsius (°C)

The Blocky Display

Can we talk about the display for a moment?  The text on the TI-60X’s screen is blocky.  According to the Datamath Calculator Museum, the character layout is 5 x 4 dots instead of the usual 7 x 5.  This display could be a throwback to the calculator display of the 1970s and 1980s where the numbers were made of linear segments. 

The article from Datamath on the TI-60X:  http://www.datamath.org/Sci/Modern/TI-60x.htm 

Formula Programming, Simultaneous Equations, and Integration

Up to 12 formulas can be stored, and they can have the labels A, B, C, D, E, F, G, H, I, X, Y, and Z.  The formulas can have more than one variable. Pressing [SOLVE] allow the user to calculate the formula, with each independent variable being prompted.  If there is a numerical value in the independent variable, the TI-60X will display it as a default choice. 

When the “SOLVE YN?” and “REVIEW YN?” prompts appear, the plus key acts as NO and the equals keys acts as YES. 

Integration is pretty easy.  At the appropriate prompted variable, press [2^nd] [ , ] (dx) to insert the dx indicator.  You will be asked for a lower limit, upper limit, and the number of intervals.  I am assuming Simpson’s method but I’m not 100% sure.

Simultaneous equations of 2 x 2 and 3 x 3 linear systems are offered.  Execution takes up 2 or 3 registers respectively.   Solutions are stored in X, Y, and for 3 x 3 systems, Z. 

Example: y = 2 * x * sin x

Enter the formula:

Change to Radians mode by pressing [3^rd] [LOG] (DR>) until the R indicator is displayed. 

Press [2^nd] [ EE ] (FMLA).  At the “NAME?” prompt, press [ ( ] for Y (ALPHA is automatically turned on at this point) and enter the equation.

Calculate y(π/3).  Press [SOLVE].  At X, enter π/3.  Result:  Y = 1.813799364.

Integrate y(x) from 0.5 to 1, use 20 intervals.  Call up the Y= formula again, press [SOLVE].  At the X= prompt, clear the number and enter dx.  Enter the required parameters.  After calculation, the TI-60X displays Y = 0.521068842.  The integral is now stored in Y.

Final Verdict

For what it’s set out to do, the TI-60X accomplishes it rather well.  The calculator is rich with features and there is some storage for some formulas.  I also like the bolder blocky numbers in the display, they are easier to read.  I think the TI-60X launched the advanced scientific calculator genre which is now common place. 

Yes, this calculator is worth collecting.  I’m not sure what the prices are to purchase a used on from eBay, Amazon, or other shopping website, but I imagine it’s not expensive.  (I think the 60X was about $30-$40 when it was sold new back in the 1990s). 

Thank you for comments and support.  Until next time,

Eddie

This blog is property of Edward Shore, 2017.

Right Triangle: Finding the Dimensions Knowing Only Area and Perimeter: finding a general formula

Right Triangle:  Finding the Dimensions Knowing Only Area and Perimeter: finding a general formula

Problem:  Given the area of a right triangle (R) and perimeter (P), find the dimensions of the right triangle (a, b, and the hypotenuse c). 

Three facts about right triangles:

(I)  Area:  R = 1/2 * a * b

(II)  Perimeter:  P = a + b + c

(III) Pythagorean Theorem:  a^2 + b^2 = c^2

The task is to find a, b, and c:

Step 1:

Of (I): 

1/2 * a * b = R

a * b = 2 * R

Step 2:

Then from (II):

a + b + c = P

a + b = P – c

Step 3:

Squaring both sides:

(a + b)^2 = (P – c)^2

Step 4:

Expanding the left side:

a^2 + 2*a*b + b^2 = (P – c)^2

2*a*b + a^2 + b^2 = (P – c)^2

With a^2 + b^2 = c^2 (III) and a*b=2*R (Step 1):

2*(2*R) + c^2 = (P – c)^2

Simplify:

4*R + c^2 = P^2 – 2*P*c + c^2

4*R = P^2 – 2*P*c

c = (P^2 – 4*R)/(2*P)

Step 5: 

Rearrange (I) to solve for a (we could solve for b but the procedure is similar)

1/2 * a * b + R

a = (2*R)/b

Step 6: 

Use (III) and Step 5 to solve for b:

a + b + c = P

a + b = P – c

(2*R)/b + b = P – c

2*R + b^2 = b*(P – c)

(at this point, c is known)

b^2 – b*(P – c) + 2*R = 0

Using the quadratic formula:

b = ( (P-c) ± √((P-c)^2 – 8*R) )/2

In conclusion:

c = (P^2 – 4*R)/(2*P)

b = ( (P-c) ± √((P-c)^2 – 8*R) )/2

a = (2*R)/b = P – a - c

Example: 

Given R = 6 and P = 12

c = (12^2 – 4*6)/(2*12) = 5

b = ( (12-5) + √((12-5)^2 – 8*6) )/2 = 4

a = 12 – 5 – 4 = 3

c = (12^2 – 4*6)/(2*12) = 5

b = ( (12-5) - √((12-5)^2 – 8*6) )/2 = 3

a = 12 – 5 – 3 = 4

Solutions:

a = 3, b = 4, c = 5

or

a = 4, b = 3, c =5

Eddie

This blog is property of Edward Shore, 2016

Review of FreeCalcFxc

Review: FreeCalcFxC

Platforms: iPhone and iPod Touch, will run on an iPad

Versions Available:
Free Version
$0.99 Scientific Version
$0.99 Financial Version

The only difference between the Free Version and the Scientific Version is that the Free Version is ad-supported.

Keyboard

The keyboard is a simple layout of 34 keys. The keys are labeled with one function. To access the shift function, press the gold shift key. The names of the shifted function replace the primary functions. Kudos for simplicity, however, my personal preference is to see both the primary and shift functions at the same time.

RPN and Algebraic Mode

The default mode is RPN (Reverse Polish Notation), but you can always enter an algebraic formula by pressing the "=f" key. The "=f" becomes the "=" to terminate entry of the formula.

Many, many, many calculators are available

Accessing the Focused Calculator list gives many calculators such as Math and Trig (the main calculator), Time Value of Money, Bonds, Statistics, Probability and Conversion calculators. For me the Conversion calculators leave a little to be desired, since there are no direct conversion keys attached to the default keyboard (luckily, that can be remedied!).

In addition to the Focused Calculators, CalcFxC gives formula template calculates. Among these formula calculators you have Percent Change, Distribution Functions, and the Quadratic and Cubic Equations.

The keyboard gives a good response when the "keys" are pressed. The screen is a two line (adjustable) screen which displays the y-stack and x-stack. The stack is four levels.

Help can be accessed by pressing and holding a key.

Real Numbers and Limits

The calculator operates on real numbers only. So, entering √-1 will return an error. As a consequence, the polynomial solvers return only real roots. The numbers range in the order of -10^-308 to 10^308.

There are no fractions or exact values of trig functions.

Math and Trig Keyboard

This keyboard contains functions usually not found a standard scientific calculator:

sqrtpi: takes the square root of the number then multiplies it by π
exmp1: e^x - 1, known on Hewlett Packard Calculators as the EXM1 function
log1p: ln(x + 1), known on Hewlett Packard Calculators as the LNP1 function
jn: Bessel Function of the First Kind, with x on the y-stack and the order n on the x-stack. jn also returns the Bessel Function of the Second Kind.
quad: Takes three arguments from the stack (a, b, c of ax^2+bx+c) and returns the real roots.

If you want to access the hyperbolic functions, you will need to call the Math and Hyperbolic calculator.

Memory

The calculator has 27 memories: memories a through z, and a special register ra. Storage and recall arithmetic can be performed on register ra - no idea why (except for maybe programming limitations) CalcFxC decided to restrict this feature to one register.

Programmability in the Form of Customizable Calculators

CalcFxC does not offer "traditional" macro or program capability. Instead, CalcFxC offers the ability to edit and create custom keyboards. You can redefine the key's name and help screen, along with it's formula. You have access to all of the functions. To use the stack arguments, use rgx(), rgy(), rgz(), and rgt() for the x, y, z, and t stacks respectively. This is a fun feature for those who has ever wanted to design their own calculators, and I am one of them!

To emulate the stack operations properly, you will need to define the formulas for each stack.

For example, if I designate the comb function as the Combination function, I would use the following formulas:
x Formula: combin(rgy(),rgx())
y Formula: rgz()
z Formula: rgt()
t Formula: rgt()
Last x Formula: rgx()

Functions can be copied and pasted. You will need some experience with RPN calculators to take advantage of this feature.

Final Word

This app is enjoyable to use. I am probably going to spend an afternoon or evening making a custom calculator. RPN fans, this is a good calculator app to get.

Since I am not a fan of ads, I will pay the $0.99 to get the non-ad version.

4.5 of 5 stars.

Eddie


This blog is property of Edward Shore. 2012.