Roulette (Hypotrochogon) of a Polygon Rolling inside a Circle

This Demonstration shows the roulette drawn by a point attached to a regular polygon rolling without slipping inside a circle.

This roulette curve is a sequence of circular arcs traced by the polygon when rolling along the edge of the circle.

For generalized cyclogons [1] and generalized trochoidal curves [2], these roulettes can be considered as limiting cases of hypotrochogons with an infinite number of vertices of the base (stationary) polygon.