Casio fx-6500P Program Library 2025

Casio fx-6500P Program Library 2025

Last birthday, I reviewed the rare classic, the Casio fx-6500G:

https://edspi31415.blogspot.com/2024/03/spotlight-casio-fx-6500g.html

Parabola Area and Maximum Point: Program P1: Steps 114

Area Under a Parabola set up by the equation:

y = -((x – a)*(x – b)) = -x^2 + p*x – q

p = a + b

q = a * b

Cls

“-((X-A)×(X-B))”

“A”? →A

“B”? → B

A+B → P

AB → Q

-B^3 ÷ 3 + B² P ÷ 2 – Q B + A^3 ÷ 3 - A² P ÷ 2 + Q A → R

“AREA:”

R ◢

“MAX PT:”

P ÷ 2 →X ◢

-((X-A)×(X-B)) → Y

The caret symbol ^ stands for [x^y].

Example:

y = -((x + 4) * (x – 2)) = -x^2 – 2*x + 8

A = -4, B = 2

Area: 36

Maximum Point: (-1, 9)

Circular Sector: Arc Length and Sector Area: Program: P2: Steps: 59

“RADIUS”? →R

“ANG(°)”? → T

RTπ÷180 →L

RL÷2 →A

“ARC LENGTH:”

L ◢

“AREA:”

A

The degree character is generated by the [° ‘ “] key.

Example:

R = 10.5, T (angle) = 120°

Results: Arc length = 21.99114858, Area = 115.45353

Integer Division: Program: P3: Steps: 51

“INT÷”

“X>0”? →X

“M>0”? →M

Int(X÷M)→Q

X-M×Q→R

Q ◢

“REM”

R

Examples:

43 Int÷ 11 = 3 Rem 10

7263 Int÷ 1849 = 3 Rem 1716

Hint: To find out the number of steps in a single program? Simply scroll down the last character and hold down the [ MDisp ] key. Kind of neat because this works outside of programming mode. I think this key was available on most Casio graphing calculators well into the fx-7700G (single G) and fx-9700Gα (E,M,H) series in mid 1990’s.

95% Population Proportion: Program P4: Steps: 96

X successes out of population N

“95 PRCT PROP”

“X”? → X

“N”? → N

X ÷ N → P

√(P(1-P))→ M

1.959963984 M ÷ √N → H

P – H → L

L + 2H → H

“LOW:”

L ◢

“HIGH:”

H

Example:

X = 850, N = 1176

Interval:

LOW: 0.6972058859

HIGH: 0.7483723454

Interval:

Source: HP 21S Stat/Math Calculator: Owner’s Manual. Hewlett Packard. 3^rd Edition. June 1990.

Power Generated by a Wind Turbine: Program P5: Steps: 82

“WIND PWR”

“RADIUS (M)”? →R

“SPEED (M÷S)”? → V

“DENSITY”? →P

π × R² × P × V^3 ÷ 2 → W

“POWER:”

W

Example:

R = 8.18 m, V = 4.48 m/s, P = 1.2 kg/m³

Result: 11340.74989 W

Source: Sharp Electronics Corporation Conquering The Sciences: Applications for the SHARP Scientific Calculator EL-506A Sharp Corporation. Osaka, Japan. 1986. pp.75-77

Round to Nearest Integer (display only): Program P6: Steps: 11

?→N

Fix 0

Rnd

Norm

Examples:

N = 19.273 → 19

N = 44.8273 → 45

N = -2.82 → -3

That’s it. I wish you all a wonderful day. Thank you,

Eddie

All original content copyright, © 2011-2025. 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.

Swiss Micros DM41X and fx-6500G: Complex Gudermannian Function and Its Inverse

Swiss Micros DM41X and fx-6500G: Complex Gudermannian Function and Its Inverse

Introduction

The Complex Gudermannian Function and the inverse are calculated as:

gd(x + yi) = u +vi where:

i = √-1

u = arctan( sinh x / cos y) = angle( cos y + i*sinh x )

v = arctanh( sin y / cosh x )

gd^-1(u + vi) = x + yi where:

i = √-1

x = arctanh( sin u / cosh v )

y = arctan( sinh v / cos u ) = angle(cos u + i*sinh v )

Notes:

* The calculator is set to radians mode during program execution.

* The arctangent function is handled using the rectangular to polar conversion (using the angle part). Doing so will increase the range between -π to π. The results are normalized.

* The results may not necessarily be the only answer but an attempt to get the principle branch.

Swiss Micros DM41X: Gudermannian and Inverse Gudermannian Functions

The DM41X is similar to the Hewlett Packard HP 41C series. Assuming we have no mathematical modules plugged in, the hyperbolic functions must be programmed as they were not included in the original function set.

Keeping with RPN notation, the imaginary part is placed on the Y stack and the real part is placed on the X stack. The memory registers used:

R01 = X

R02 = Y

R03 = U

R04 = V

gd(X + Yi) = U + Vi

The hyperbolic functions operate on real values only, and the in the Gudermannian and its inverse functions handle the real and imaginary parts separately.

DM41X: Hyperbolic Sine Routine: SINH

01 LBL^T SINH

02 ENTER↗

03 E↗X

04 X<>Y

05 CHS

06 E↗X

07 -

08 2

09 /

10 RTN

11 END

DM41X: Hyperbolic Cosine Routine: COSH

01 LBL^T COSH

02 ENTER↗

03 E↗X

04 X<>Y

05 CHS

06 E↗X

07 +

08 2

09 /

10 RTN

11 END

DM41X: Hyperbolic Arctangent Routine: ATANH

01 LBL^T ATANH

02 ENTER↗

03 ENTER↗

04 1

05 +

06 X<>Y

07 CHS

08 1

09 +

10 /

11 LN

12 2

13 /

14 RTN

15 END

Now to the main programs:

DM41X: Complex Gudermannian Function: CDG

01 LBL^T CGD

02 RAD

03 STO 01

04 X<>Y

05 STO 02

06 RCL 01

07 XEQ^T SINH

08 RCL 02

09 COS

10 R-P

11 X<>Y

12 STO 03

13 RCL 02

14 SIN

15 RCL 01

16 XEQ^T COSH

17 /

18 XEQ^T ATANH

19 STO 04

20 RCL 03

21 RTN

22 END

DM41X: Inverse Complex Gudermannian Function: CGDI

01 LBL^T CGDI

02 STO 03

03 X<>Y

04 STO 04

05 RAD

06 RCL 03

07 SIN

08 RCL 04

09 XEQ^T COSH

10 /

11 XEQ^T ATANH

12 STO 01

13 RCL 04

14 XEQ^T SINH

15 RCL 03

16 COS

17 R-P

18 X<>Y

19 STO 02

20 RCL 01

21 RTN

22 END

Casio fx-6500G: Gudermannian and Inverse Gudermannian Functions

The code can easily be adapted to other Casio calculators.

gd(X + Yi) = U + Vi

In these program listings, the real and imaginary parts are handled separately. For the fx-6500G (and same for the fx-7000G, 7500G, and 8000G), the Rectangular to Polar (Pol(x,y)) conversion stores the radius in the variable I and angle (θ) in the variable J. For the early Casio models, switch to Radians mode by pressing [ MODE ] [ 5 ].

gd(X + Yi) → U + Vi

Code:

Rad

“GD(X+YI)”

“X”:? → X

“Y”:? → Y

Pol(cos Y, sinh X)

J → U

tanh^-1 (sin Y ÷ cosh X) → V

“U + VI=”

U ⊿

V

gd^-1(U + Vi) → X + Yi

Code:

Rad

“GD^-1(U+YI)”

“U”:? → U

“V”:? → V

tanh^-1 (sin U ÷ cosh V) → X

Pol(cos U, sinh V)

J → Y

“X + YI=”

X ⊿

Y

Examples

Results are rounded to six decimal places. Be aware only one answer is given.

1. gd(3 + 4i) ≈ 1.635952 – 0.075314i

2. gd(-7 + 2i) ≈ -1.571555 + 0.001658i

3. gd(0 + 3i) ≈ 3.141593 + 0.142068i

4. gd(-3 + 0i) ≈ -1.471304 + 0i

Sources

“The Complex Gudermannian Function” analyticphysics.com. Uploaded June 16, 2021. Accessed June 23, 2024. https://analyticphysics.com/Complex%20Variables/The%20Complex%20Gudermannian%20Function.htm

“Gudermannian function” Wikipedia. Last Edited May 23, 2024. Accessed June 20, 2024.

https://en.wikipedia.org/wiki/Gudermannian_function#:~:text=The%20Gudermannian%20function%20relates%20the,sector%20is%20%CF%95%20%3D%20gd%20%CF%88.

Eddie

All original content copyright, © 2011-2024. 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.

Spotlight: Casio fx-6500G

 

Spotlight: Casio fx-6500G

For my birthday, I present a review of the Casio fx-6500G.

Quick Facts

Model: fx-6500G

Company: Casio

Timeline: 1986 – 1988

Type: Graphing Scientific Calculators

Power: 3 x CR2032

Programming Memory: 486 steps at default

Number of Memory Registers: 26 at default

Screen Size: 96 x 32 pixels

Graph Types: Function, Scatter plot, Histogram, Linear Regression Plot, Point Plot

Linear Regression

Base Operations and Logic Functions

Hyperbolic Functions

Screen Sizes and Memory of Casio’s Early Calculators

fx-7000G (1985)	422 bytes, up to 78 registers	96 x 64 pixels
fx-6500G (1986)	486 bytes, up to 86 registers	96 x 32 pixels
fx-7500G (1988)	4006 bytes, up to 526 registers	96 x 64 pixels
fx-6300G (1991)	400 bytes, up to 76 registers	40 x 23 pixels

(measures from rskey.org, Casio fx-6300G manual, Casio fx-7500G manual)

Other Features

Like the other early Casio graphing calculators, including the fx-7000G, fx-7500G, and later the fx-6300G, the fx-6500G has the a similar structure.

The screen of the fx-6500G is just as wide of the screens of the fx-7000G and fx-7500G, but half of the height. The screen of the fx-6500G is still bigger than the fx-6300G and graphs take the entire screen, which I appreciate.

There are four statistical modes:

SD1: single-variable statistics analysis mode

SD2: single-variable statistics graphics mode for Histograms, data lines, and normal curves

LR1: linear regression analysis mode, with the regression equation y = A + Bx

LR2: linear regression graphics mode for scatter plots and linear regression trend lines

The defragment mode ( [ MODE ] [ . ] {Defm}) can allow an additional 60 registers at the expense of programming steps. Each new register costs 8 programming steps. Array registers are accessed in the format A[#], where A is the letter of memory and # is the number of registers away from the variable.

For example:

A[0] accesses A

A[1] accessed B

A[2] accesses C

A[25] accesses Z

A[26] accessed the first expanded memory, the same as Z[1]

# can be a negative integer. Array-type memories allow for indirect registers.

The programming command set is relatively simple, and most of it has remained throughout the entire Casio graphing and programming calculator set:

There are 10 program slots: P0 through P9.

: separates program lines from each other. The carriage return by pressing [ EXE ] also terminates the line.

◢ is the run/stop symbol. Any quoted text or numeric value is shown as the calculator stops. Press [ EXE ] to continue.

⇒ is the jump command and is used for quick If-Then-Else structures. The syntax is:

condition ⇒ do if the condition is true : (or ◢) jump to here if the condition is false.

Goto and Lbl: goto and label. There are ten labels available in each for each program: Lbl 0 through Lbl 9.

Prog: Prog executes another program as a subroutine. An implied “return” is automatically executed at the end of program.

Isz: Increment and skip. Adds 1 to a variable and skips the next command if the new value is 0.

Isz variable : do if var=var+1≠0 is true : (or ◢) skip to here if the var=var+1=0

Dsz: Decrement and skip. Subtracts 1 from a variable’s value and skips the next command if the new value is 0. If find Dsz particularly useful in simple For-Next loops.

Dsz variable : do if var=var-1≠0 is true : (or ◢) skip to here if the var=var-1=0

Final Thoughts

The calculator looks nice and clean. The fx-6500G offers all of the features of the fx-7000G and fx-7500G (and fx-6300G less the fractions) in a scientific calculator size. I like the fact the graphs do fill the entire screen. Programs and calculation modes have up to four lines. The fx-6500G is the way to handle a smaller-sized graphing calculator, which makes it a very sought, harder to find, calculator.

Eddie

All original content copyright, © 2011-2024. 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.