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.

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.

DM42, Free42, HP 42S: Birthday Probability Function

DM42, Free42, HP 42S:  Birthday Probability Function

The Age Old Birthday Question

You probably have read or heard about when there is 23 random people in a room, half of the time someone shares a birthday.   This is the classic birthday problem.   

Consider a room with 3 people and assume a 365 day year calendar.   What are are the odds that no one shares a birthday?

For the first person, they clearly have any day of the calendar.

For the second person, they only have 364 days out of the calendar.

For the third person, they only have 363 days available.

The probability that no one shares a birthday is:

P = 365/365 * 364/365 * 363/365

= (365 * 364 * 363) / (365^3)

≈ 0.99180

About 99.180% chance none of the three people share a birthday. 

Note that:

365/365 * 364/365 * 363/365

= (365/365) * (365 - 1)/365 * (365 - 2)/365

=  1 *  (365/365 - 1/365) * (365/365 - 2/365)

=  1 *  (1 - 1/365) * (1 - 2/365)

The derivation above leads to the formula stated by Persi Diaconis and Brain Skyrms (pg. 20 from Ten Great ideas About Chance): 

P = 1 * (N - 1)/C * (N - 2)/C * ...  =  Π( 1 - m/C, m = 1 to N-1)

C = number of categories (examples: days in a calendar year, minutes in an hour, number of places, etc...)

N = sample population

P = probability that sample population does not share a category (examples:  number of people that don't share the same birthday, number of people from a city that are not in the same location, etc...)

Π is the product function.

In our example above, C is the number of days in a 365 day calendar and N is the number of people.  The program BDAY makes the product calculation.

DM42/HP 42S/Free42/Plus42 Program:  BDAY

N and C are prompted.  

00 { 58-Byte Prgm }

01▸LBL "BDAY"

02 "CATEGORIES?"

03 PROMPT

04 STO 02

05 1

06 STO 01

07 "N?"

08 PROMPT

09 1

10 -

11 STO 03

12▸LBL 00

13 1

14 RCL 03

15 RCL÷ 02

16 -

17 STO× 01

18 DSE 03

19 GTO 00

20 "PROB= "

21 ARCL 01

22 AVIEW

23 RCL 01

24 .END.

A Quicker Calculation

Gratitude to Thomas Klemm, this next program is listed here by permission.

A shorter way to calculate this probability (only limited to how large a calculator can handle numbers) is:

P = PERM(C,N) / (C^N)  =  C! / ( (C - N)! * C^N )

DM42/HP 42S/Free42/Plus42 Program:  BDAYC  (compact)

Enter C on the Y stack and N on the X stack before running the program.

00 { 9-Byte Prgm }

01 RCL ST Y

02 X<>Y

03 PERM

04 X<>Y

05 LASTX

06 Y↑X

07 ÷

08 END

Examples

1.  Probability that 40 people do not share a birthday (assume a 365 day calendar):

C =  365, N =  40

Probability: 0.10877

Only about 10.877% chance no one in 40 people share a birthday.  

2.  Probability that 3 cards drawn do not share the same suit:

C = 4  (4 suits in a deck of cards), N =  3

Probability:  0.37500

About 37.5% chance no three cards share the same suit.

3.  A bowl has 50 numbered balls.   16 people draw a ball from the bowl and then places the ball back in the bowl.

C = 50, N = 16

Probability:  0.06751

Only about 6.751% of the time all 16 people draw different numbered balls.  

Sources

Diaconis, Persi and Brian Skyrms  Ten Great Ideas About Chance  Princeton University Press:  Princeton, New Jersey.  2018.  ISBN 978-0-691-19639-8

"(42S/DM42/Free42/Plus42) Birthday Probability Function"  The Museum of HP Calculators.   https://www.hpmuseum.org/forum/thread-19535.html.  Retrieved February 11, 2023.  

This blog turns 12 tomorrow, so excited!

Eddie 

All original content copyright, © 2011-2023.  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. 

Birthday Blog: Fun Facts About Me

Fun Facts About, me, Eddie Shore, the author of Eddie's Math and Calculator Blog:

1.  I have a Bachelor's Degree in Accounting and a Master's Degree in Mathematics, both from Cal Poly Pomona.

2.  I don't have a favorite sport.

3. My favorite video games are Super Mario Maker, Super Mario Brothers, Mario Kart, Millipede, and Joust.

4. My favorite colors are sky blue, denim blue, forest green, and gold.

5. For you zodiac fans, my zodiac sign is Pisces.  Both of my parents are Geminis, and most of my closest friends are Scorpios.

6. Chocolate chip cookies are my weakness.

7. My four favorite go-to music artists are Earth, Wind & Fire, Stevie Wonder, Janet Jackson, and Sheryl Crow.

8. At home, I have two dogs and three cats. 

9.  I'm Irish and Mexican.

10.  Every morning I write what I want to accomplish for the day.  I go through a lot of Post-Its.

11. The beach is my sanctuary.

12. The mathematics section of university library is to me what Disneyland is to most people, only I don't have to pay $60 for an admission ticket. ;)  My favorite library is the Honnold Mudd Library in Claremont (Claremont Colleges).

13. I can't live without music.  Or calculators.

14. My dream car is a Ferrari. 

15. I prefer tea over coffee.

16. My turn ons are honesty, warmth, kindness, intelligence, and a love for life.

17. My turn offs are dishonesty, arrogance, racism, sexism, and ageism.

18. My bucket list grows by the day.

19. I am very close to my family. 

20. My favorite vacation spot so far is Maui.

21. My favorite number is pi (π), partly because my birthday is March 14 (the day that this blog is posted).

22. I want to go to Greece, Italy, Ireland, and New Zealand.  I'd probably wouldn't return home. 

23. My guilty pleasure is the Real Housewives of New Jersey.  #TeamMargaretJosephs

24. I'm nearsighted and prefer glasses to contacts.

25. I prefer wine over beer, but I do enjoy a good ale.  My favorite shot is Fireball.

26. My newest favorite YouTube channel is Doctor Mike. Favorite of all time is both Cinemasins and Music Video Sins.

27. My favorite calculators are the HP Prime, HP 42S, HP 12C, TI-84 Plus CE and Casio fx-991EX.

28. I am a Press Your Luck addict. Big Bucks, no whammies!

29. I have two dogs and three cats.

30. My music tastes are kind of eccentric, but I learn towards rock, alternative, and some R & B.  I do have a Spotify account. 

31.  My favorite fruits of cherries, applies, and strawberries.

32.  My favorite holiday used to be Christmas, now it's Halloween.

33.  A hobby I like but don't do enough of is art.  I'm drawn to glass art, mythological art, and fantasy art. 

34.  My favorite movie is Ghostbusters - the 1984 original one.

35.  My favorite pie is apple. 

36.  My favorite fonts are Arial, Courier, Futura, and Banschrift.

37.  I lived in Southern California all my life.

38.  Starting and writing on this blog is one of the most fun things I am very fortunate to do, and I thank you for reading and supporting this blog. 

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.

Google Celebrates Olga Ladyzhenskaya

Google Celebrates Olga Ladyzhenskaya 

Today, March 7, 2019, Google honored the Russian mathematician Olga Ladyzhenskaya.  Ladyzhenskaya was born on March 7, 1922 (passed away on January 12, 2004).  She is known for her work in partial differential equations, particularly providing a rigorous proof of the finite difference method for the Navier-Strokes equations. 

Happy Birthday Olga! And thank you for your contributions to mathematics and science.

Wikipedia articles:

Bio on Olga Ladyzhenskaya
https://en.wikipedia.org/wiki/Olga_Ladyzhenskaya

Navier-Strokes Equations
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

Finite Difference Method
https://en.wikipedia.org/wiki/Finite_difference_method

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.