Cycloid
Author: Lenore Horner

The two circles are glued together and roll on the rim of the larger circle.

Click on the dot for the θ slider and then drag the slider or use the right arrow on your keyboard to roll the circles at a steady race.

Try adjusting the radii of the two circles.  Where is the surface the circles roll on?  What shapes to lights mounted at the edges of each circle (the green and blue dots) trace out?

r_1 = 2.5 (slider from 0 to 5, step 0.1)
A = (0, 2.5)
θ = 0 (slider from 0 to 15, step 0.1)
B: (x(A) + r_1 * θ, y(A))
c = Circle(B, r_1)
C: (x(B) - r_1 * sin(θ), y(B) - r_1 * cos(θ))
r_2 = 1 (slider from 0 to 5, step 0.1)
d = Circle(B, r_2)
D: (x(B) - r_2 * sin(θ), y(B) - r_2 * cos(θ))
E: (x(B), 0.0)
F: (x(B), y(B) - r_1 * cos(θ))
G = (0, 0)
u = Vector(G, E)
v = Vector(E, B)
w = Vector(B, F)
z = Vector(F, C)
a = Segment(B, C)