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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