GeoGebra Script: Rotating circles
Check the video:
Version 1: Polar form
s = Slider(0.1, 1.5, 0.01)
t = Slider(0, 2pi, 0.01)
n = Slider(0, 50, 1)
Ln = 0...n
LR = Zip(s^k, k, Ln)
LP = Join({(0, 0)}, Zip((s^k * (1 - s); (k+1) * t), k, Ln))
LS = Zip(Sum(LP, k), k, Ln+1)
LC = Zip(Circle(P, r), P, LS, r, LR)
Task:
You may like to explore what happens when s>1!
Also, if you prefer, you can define the list
LP considering the cartesian form. That is
LP = Join( {(0,0)}, Zip((s^k * (1-s) * cos((k+1)t), s^k * (1-s) * sin((k+1)t)), k, Ln) )
It just a little bit longer, compared to the polar form.Demo: Polar form
Version 2: Using complex numbers
r = Slider(0.1, 1.5, 0.01)
t = Slider(0, 2pi, 0.01)
n = Slider(0, 50, 1)
Ln = 0...n
Z = r * exp(i * t)
LR = Zip(r^k, k, Ln)
LP = Zip((1/r - 1) Z^k, k, Ln)
LS = Zip((1-1/r, 0) + Sum(LP, k), k, Ln+1)
LC = Zip(Circle(P, R), P, LS, R, LR)
Task:
Explore what happens when r>1!
If you make a different version, let me know: https://x.com/jcponcemath
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Have ∞ fun!!!!
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