Saturday, March 18, 2023

TI-84 Plus CE: Tracing Polar Equations

TI-84 Plus CE:  Tracing Polar Equations



Traveling Around the Graphs


The programing BLINKING animates a dot around one of four polar equations:


1.  Ellipse


r = b / √(1 - ε^2 * cos^2 θ), where ε = √(a^2 - b^2)/a, a > b


2.  Cardioid


r = a + (1 + cos θ)


3.  3-Leaf Rose


r = a * cos(3 * θ)


4.  Log Spiral


r = a * e^(b * θ)



Notes:


The point alternates through blue (TI-84 Plus CE color 10), green (14), orange (15), and black (12).   The graph itself is light gray (21).  


r1 is the polar equation r1(θ).


Plotting points (not the polar graph) must be in cartesian coordinates (x,y).   




TI-84 Plus CE Program:  BLINKING


"2023-01-15 EWS"

Radian: Polar: FnOff

ZStandard

{10,14,15,12}→L6

Menu("PLOT","ELLIPSE",10,"CARDIOID",11,"3-LEAF ROSE",12,"LOG SPIRAL",13)


Lbl 10

Disp "A≥B"

Prompt A, B

√(A^2-B^2)/A→E

"B/√(1-E^2*cos(θ)^2)"→r1

Goto 20


Lbl 11

Prompt A

"A*(1+cos(θ))"→r1

Goto 20


Lbl 12

Prompt A

"A*cos(3*θ)"→r1

Goto 20


Lbl 13

Disp "A>0, B>0"

Prompt A,B

"A*e^(B*θ)"→r1

Goto 20


Lbl 20

Input "MAX? ",M

Input "NO. STEPS? ",S

M/S→N

FnOn 1

GraphColor(1,21)

0→P: r1(P)→Q

P>Rx(Q,P)→F: P>Ry(Q,P)→G

Pt-On(F,G,1,12)


For(K,1,S)

Wait 0.25

Pt-On(F,G,1,21)

remainder(K,4)+1→C

K*N→P: r1(P)→Q

P>Rx(Q,P)→F: P>Ry(Q,P)→G

Pt-On(F,G,1,L6(C))

End 


Disp "END"



Examples


In all examples, a = 3, b = 2, maximum = 4 * π, steps = 24


Ellipse





Cardioid




 

3-Leaf Rose





Log Spiral







Source


Harris, John W. and Horst Stocker.  Handbook of Mathematics and Computational Science  Springer:  New York.  2006.  ISBN 0-387-94746-9



Eddie


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