Epicycloids and Hypocycloids

Epi and Hypocycloids 001
Circle rolling inside a bigger circle, tracing out a rose curve. The random dots help to show the rotating plane centered on the contact point of 2 rolling curves. The significance is that the contact point to the tracing point is the normal of the curve, and this is true for any curve rolling on another curve.
Epi-_and_Hypocycloids.pdf