Eddie's Math and Calculator Blog: Casio Prizm

Showing posts with label Casio Prizm. Show all posts

Saturday, June 17, 2017

Casio fx-CG50 Review (updated 3/2/2018)

Casio fx-CG50 Review

Company: Casio

Type: Scientific/Graphing

Price: (about) $119

Battery: 4 AAAs

Memory: 60 KB RAM, 14 MB Flash

Colors: Can display up to 65,536 colors, graphing and text can be use up to 8 colors

I’m going to focus more on the new and updates in this review.

2017 fx-CG50 on the left, 2011 fx-CG10 on the right

Keyboard

The fx-CG50 is an update of the popular 2011 Casio Prizm (model fx-CG10 or fx-CG20). The fx-CG50 has an updated keyboard, in the style of the new fx-260 SOLAR and Casio FX-991 ES. As a result, the keys are easier to read, more consistent to the touch and size. In the previous keyboard (fx-CG10/20), the number keys were large but the function keys were very small.

The Screen

Like the previous fx-CG10/20, the diagonal of the screen is 3.17 inches. However, the screen of the fx-CG50 is brighter.

Processing Speed

Although I wasn’t able to find anything about the chip or its speed, the fx-CG50 seems to operate faster in accounts.

I tested a sample program:

For 1 → A To 1000

ClrText

Locate 2,1,A

On the fx-CG10, the program took 1 minute, 24.83 seconds to complete. With the fx-CG50, the program took just 34.87 seconds, a reduction of 58.89%.

General Features

fx-CG50 Menu selection screen

* Financial Solver: Time Value of Money, Days between Dates, Bonds

* Recursive, Polar, Function, Parametric, Inequality, and Conic Section Graphing

* General Function Solver

* Polynomial Solver: up to the 6^th degree, coefficients must be real, but roots can be complex numbers

* Simultaneous Equation Solver: up to 6 x 6 linear equations, can include complex numbers

* Number of Statistic Regressions (curve fitting): 12

Also textbook entry, calculus, and full complex number (yes that includes exponential, logarithms, and trigonometric functions of complex numbers – yes I’m happy about this!**). Base calculations include binary, octal, decimal, and hexadecimal integers.

** As of OS 3.10, trig functions no longer accept complex numbers. Why Casio why? (3/2/2018)

Additional modes include Geometry, Conversion, and Spreadsheet. 3D graphing is new to the fx-CG50.

Graphs can be used in one of 8 colors: black, blue, red, magenta, green, cyan, yellow, and white. This palette is the same of the SECAM palette shown on certain Atari 2600 machines. (Link: https://en.wikipedia.org/wiki/List_of_video_game_console_palettes#Atari_2600 )

3D Graphing

The 3D graphing mode offers one of four possible types: line, plane, sphere, and cylinder. Each of the types offer various formats to enter coefficients. Keep in mind these are the only four types of 3D graphs offered. The graph has full zoom features and it is pretty snappy with regards to rotation.

Physium

Physium is included with the fx-CG50. There are two features with the Physium: Periodic Table and Physical Constants.

Periodic Table: an underrated feature. You can display the entire table, or zoom in to a portion of the table. The atomic weight of each element can be stored in a variable (A through Z).

Physical Constants: Choose between 39 physical constants from five categories: Universal (speed of light, electric constant, Newton’s constant of gravitational, etc.), Electromagnetic constants, Atomic & Nuclear constants, Physico-Chemical constants (Avogardo constant, molar gas constant, etc), and three Adopted Values (Josephson constant, Klitzing constant, standard acceleration of gravity). Units are in SI.

Verdict

If you don’t have a Casio fx-CG10/20 and are interested in getting the updated version, go for it. I also think getting the update is worth it primarily for the faster processing speed, brighter screen, and much better keyboard as far as contrast on the labels and key size. Obviously Casio is very consistent with the programming language, so if you are upgrading from a previous non-color or three-color version, you should feel right at home with the fx-CG50. The one thing I wish the fx-CG50 had was more RAM instead of only the 60KB from fx-CG10. It’s not terrible, but given the TI-84 Plus CE has 128K RAM, Casio should have at least matched that amount.

Eddie

This blog is property of Edward Shore, 2017

Monday, June 12, 2017

HP Prime and Casio fx-9860GII/Prizm: Angular Distance Between Stars

HP Prime and Casio fx-9860GII/Prizm: Angular Distance Between Stars

Given the right ascension (α) and declination (δ) of two stars of the same epoch (J2000.0 is the most current), the distance between the stars are:

d = acos( sin δ1 * sin δ2 + cos δ1 * cos δ2 * cos (α1 – α2) )

The distance is usually given in decimal degrees.

Enter α in terms of hours, minutes, seconds (standard notation) and δ in terms of degrees, minutes, seconds (standard notation).

HP Prime Program: ANGSTAR

EXPORT ANGSTAR(α1,δ1,α2,δ2)

BEGIN

// 2017-06-08 EWS

// Angular Angle

// Degrees

HAngle:=1;

LOCAL d;

α1:=15*α1;

α2:=15*α2;

d:=ACOS(SIN(δ1)*SIN(δ2)+

COS(δ1)*COS(δ2)*COS(α1-α2));

RETURN →HMS(d);

END;

Casio fx-9860GII/Prizm Program: ANGSTAR

Deg

“RA 1: “?→A

“DEC1: “?→B

15A→A

“RA 2: “?→C

“DEC2: “?→D

15C→C

cos¯¹ (sin B * sin D + cos B * cos D * cos (A-C))→E

E>DMS

Example

Distance between Regulus (A) in Leo and Sadalmelik in Aquarius:

(data via Wikipedia)

Regulus: α = 10h8m23.11s, δ = +11°58’01.95”

https://en.wikipedia.org/wiki/Regulus

Sadamelik: α = 22h5m47.03593s, δ = -0°19’11.4568”

https://en.wikipedia.org/wiki/Alpha_Aquarii

Distance: 168°20’05.1793”

Source:

Meeus, Jean. Astronomical Algorithms William-Bell, Inc. Richmond, VA 1991. ISBN 0-943396-35-2

Please stay safe, happy, and sane. Happy computing,

Eddie

I hope to have the new Casio Prizm FX-CG50 soon for review as I ordered one last Friday.

This blog is property of Edward Shore, 2017.

Tuesday, December 6, 2016

TI-84 Plus and Casio Prizm: Area between Polynomials p(x) and q(x)

TI-84 Plus and Casio Prizm: Area between Polynomials p(x) and q(x)

The program POLYSURF calculates the area of a surfaces with:

* Side borders are straight vertical lines. The left border line begins at x = 0

* The top and the bottom are defined polynomials: p(x) for the top and q(x) for the bottom.

* There are n partitions in the shape, for all partition points, p(x) > q(x).

The program also draws the shape. If the number of partitions are 4 or less, an exact area is calculated. Otherwise, p(x) and q(x) are approximated by a quartic polynomial and an approximated area is calculated.

TI-84 Plus Program POLYSURF

"EWS 2016-12-06"

Disp "P(X) > Q(X)"

FnOff

PlotsOff

{0}→L₁

Input "P(0)=",P

{P}→L₂

Input "Q(0)=",Q

{Q}→L₃

Input "NO. OF PARTITIONS:",N

For(I,1,N)

ClrHome

Output(7,1,"POINT")

Output(7,8,I)

Output(8,1,"P(X)>Q(X)")

Input "X:",X

Input "P(X):",P

Input "Q(X):",Q

augment(L₁,{X})→L₁

augment(L₂,{P})→L₂

augment(L₃,{Q})→L₃

End

L₁(dim(L₁))→L

If N=1

Then

LinReg(ax+b) L₁,L₂,Y₁

LinReg(ax+b) L₁,L₃,Y₂

End

If N=2

Then

QuadReg L₁,L₂,Y₁

QuadReg L₁,L₃,Y₂

End

If N=3

Then

CubicReg L₁,L₂,Y₁

CubicReg L₁,L₃,Y₂

End

If N≥4

Then

QuartReg L₁,L₂,Y₁

QuartReg L₁,L₃,Y₂

End

FnOn 1,2

fnInt(Y₁-Y₂,X,0,L)→S

Disp "AREA=",S

Pause

ClrDraw

.5→Xmin

L+.5→Xmax

min(L₃)-.5→Ymin

max(L₂)+.5→Ymax

Shade(Y₂,Y₁,0,L)

Casio Prizm Program: POLYSURF

The character # can be found by exiting to the “main” program menu (TOP, BOTTOM, etc). Press F6 for CHAR, select #, and press [EXE].

Get the regressions by pressing [F4] (MENU), [F1] (STAT), [F6] twice (CALC, >) and selecting the regression. The statistic variables a, b, c, d, and e are calculated after regression calculation.

“EWS 2016-12-06”

“P(x)>Q(x)”

{0} → List 1

“P(0)=”? → P

{P} → List 2

“Q(0)=”? → Q

{Q} → List 3

“# PARTITIONS:”? → N

For 1 → I To N

“POINT”

I ◢

“X:”? → X

“P(X):”? → P

“Q(X):”? → Q

Augment(List 1, {X}) → List 1

Augment(List 2, {P}) → List 2

Augment(List 3, {Q}) → List 3

If N = 1

Then

LinearReg (ax+b) List 1, List 2

a → A

b → B

“Ax+B” → Y1

LinearReg (ax+b) List 1, List 3

a → F

b → G

“Fx+G” → Y2

IfEnd

If N = 2

Then

QuadReg List 1, List 2

a → A

b → B

c → C

“Ax^2+Bx+C” → Y1

QuadReg List 1, List 3

a → F

b → G

c → H

“Fx^2+Gx+H” → Y2

IfEnd

If N = 3

Then

CubicReg List 1, List 2

a → A

b → B

c → C

d → D

“Ax^3+Bx^2+Cx+D” → Y1

CubicReg List 1, List 3

a → F

b → G

c → H

d → I

“Fx^3+Gx^2+Hx+I” → Y2

IfEnd

If N ≥ 4

Then

QuartReg List 1, List 2

a → A

b → B

c → C

d → D

e → E

“Ax^4+Bx^3+Cx^2+Dx+E” → Y1

CubicReg List 1, List 3

a → F

b → G

c → H

d → I

e → J

“Fx^4+Gx^3+Hx^2+Ix+J” → Y2

IfEnd

List 1[Dim List 1] → L

∫(Y1-Y2, 0, L) → S

“AREA=”

S ◢

ClrGraph

ViewWindow -.5, L+.5, 1, Min(List 3)-.5, Max(List 2)+.5, 1

F-Line 0, List 2[1], 0, List 1[3]

Dim List 1 → Z

F-line List 1[Z], List 2[Z], List 1[Z], List 3[Z]

DrawGraph

Examples

Example 1

Data:

n	x	p(x)	q(x)
0	0	2	-2
1	1	5	-2
2	2	2	-2

Number of partitions, n = 2

Area = 12

Example 2

Data:

n	x	p(x)	q(x)
0	0.0	0.00	0.00
1	1.5	5.62	-0.64
2	2.5	3.83	1.38
3	3.5	1.25	0.76

Number of Partitions, n = 3

Area ≈ 13.16619792

Example 3

Data:

n	x	p(x)	q(x)
0	0.00	3.00	-3.00
1	0.50	2.54	-2.84
2	1.25	2.01	-3.00
3	1.60	2.36	-3.55
4	2.00	2.76	-1.98

Number of Partitions, n = 4

Area ≈ 10.77281698

This blog is property of Edward Shore, 2016

Sunday, November 6, 2016

Casio Prizm version 2.02.3210 Update (In Case You Missed it, Like Me)

Link: https://edu.casio.com/download_service/en/download/index.html

I found out that this version has been around since December 2015. This is a good reminder for me to check for updates more often!

Eddie

This blog is property of Edward Shore, 2016.

Friday, November 4, 2016

HP Prime and Casio Prizm: Orthogonal Matrix Test

HP Prime and Casio Prizm: Orthogonal Matrix Test

For the square matrix M, it is orthogonal when either of the following conditions are met:

(I) M * M^T = M^T * M = I

(II) M^-1 = M^T

The program presented on this blog entry will use the first test. Since matrices, unfortunately, cannot be directly compared on the Casio graphing calculators, a work around with two FOR loops is implemented.

HP Prime Program ORTHOG

EXPORT ORTHOG(m)

BEGIN

// 2016-11-01 EWS

// orthogonal test

LOCAL n,p,s;

s≔SIZE(m);

s≔s(1);

n≔TRN(m)*m;

p≔IDENMAT(s);

IF n==p THEN

RETURN 1;

ELSE

RETURN 0;

END;

Casio Prizm Program ORTH

1 → A

“MATRIX:”? → Mat Z

Dim Mat Z → List 26

List 26[1] → S

(Trn Mat Z * Mat Z) – Identity S → Mat Y

For 1 → R To S

For 1 → C To S

If Mat Y[R,C] ≠ 0

Then

0 → A

Break

IfEnd

Results: 0 for a non-orthogonal matrix, 1 for an orthogonal matrix

Example of an orthogonal matrix takes the form of a two dimension rotate matrix:

cos θ	-sin θ
sin θ	cos θ

For example, let θ = 0.2 rad.

This blog is property of Edward Shore, 2016.