Sunday, March 10, 2024

Fun with the TI-81 (March 2024 Edition)

Fun with the TI-81 (March 2024 Edition)






TI-81 SCATTER







Produces a scatter plot.


Size: 52 bytes


Code:


If Dim{x}=0

Disp “NO DATA”

If Dim{x}=0

Stop

ClrDraw

1→I

Lbl 0

PT-On({x}(I),{y}(I))

IS>(I,Dim{x})

Goto 0

DispGraph


Note: Dim{x} returns the number of data points in the statistics list {x}.

Keystrokes: [ VARS ], DIM, 7: Dim{x}



TI-81 ANGLES


Given three pints, the internal and external angle are calculated.





Size: 196 bytes


Code:

Deg

Disp “SIDE PT (S,T)”

Input S

Input T

Disp “CORNER (M,N)”

Input M

Input N

Disp “SIDE PT (U,V)”

Input U

Input V

(S-M)*(U-M)+(T-N)*(V-N)→D

√((S-M)^2+(T-N)^2)→A

√((U-M)^2+(V-M)^2)→B

cos^-1 (D/(A*B))→I

360-I→E

Disp “INTERNAL ANGLE”

Disp I

Disp “EXTERNAL ANGLE”

Disp E



Example:

(S,T) = (-4,-6)

(M,N) = (1,1)

(U,V) = (3,5)



INTERNAL ANGLE: 171.0273734

EXTERNAL ANGLE: 188.9726266


Source:

Cook, John D. “Ramanujan approximation for circumference of ellipse” John D. Cook Consulting. May 5, 2015. https://www.johndcook.com/blog/2013/05/05/ramanujan-circumference-ellipse/ Accessed January 24, 2024


TI-81 ELLIPSE

Given the length of the semi-axis, the program draws the ellipse, calculates the area, and approximates the circumference using Ramanujan formula.

Size: 195 bytes


Code:


Param

Rad

Disp “SEMI X-AXIS”

Input A

Disp “SEMI Y-AXIS”

Input B

(A-B)/(A+B)→L

π*(A+B)*(1+(3*L^2)/(10+√(4-3*L^2))→P

π*A*B→R

Disp “APPROX. CIR=”

Disp P

Disp “AREA=”

Disp R

Pause

All-Off

“A*cos T”→X_1T

“B*sin T”→Y_1T

X1T-On

-A-1→Xmin

A+1→Xmax

-B-1→Ymin

B+1→Ymax

0→Tmin

2π→Tmax

π/24→Tstep

DispGraph



Notes:

All-Off turns all the graphing equations off from graphing.

[ 2nd ] {Y-VARS}, OFF, 1: All-Off



XT1 and YT1 are the equation variables x1(t) and y1(t):

[ 2nd ] {Y-VARS}, Y, 5: X_1T and 6: Y_1T, respectively



Example:


SEMI X-AXIS? 2

SEMI Y-AXIS? 3



Results:

APPROX. CIRC= 15.86543959

AREA= 18.84955592






TI-81 RELATIVE

Calculate the consequences of reality when it comes to a length and mass of an object traveling near the speed of light, c = 299,792,458 m/s.


Size: 141 bytes


Code:

299792458→C

Disp “C=”

Disp C

Disp “M/S”

Pause

Disp “°/. OF C”

Input P

P*C/100→U

√(1-(U/C)^2)→V

Disp “LENGTH”

Input L

Disp “OBS LENGTH=”

L*V→K

Disp K

Pause

Disp “MASS”

Input M

Disp “OBS. MASS=”

M/V→N

Disp N


Enter the percentage of the speed of light (70%, 80%, 90%, etc.). Three characters are used to create the percent sign (%) (°, / , . )


Example:


92.5% of the speed of light

length: 40.8 m

mass: 6,700 kg


Results:

observed length = 15.50265784 m

observed mass = 17,633.10542 kg


Source:


Jackson, Mark D. The QuickStudy for Physics BarCharts Publishing Inc. Boca Raton, Florida. 2007. ISBN 13: 9781423202677. pp. 114-115

Eddie


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