Rolling a Polygon on a Circle

This Demonstration simulates a regular polygon rolling without slipping around a stationary base circle of radius 1.
The roulette traced by a point attached to the polygon consists of two different curve types:
1. involute curve sections when an edge of the polygon rolls tangentially over the base circle.
2. circle arcs when a vertex of the polygon makes contact with the base circle.
Varying the circumradius of the rolling polygon changes the circumference ratio between the polygon and the base circle.
A closed curve can be obtained after one revolution around the base circle if the circumference of the -sided regular polygon equals .
By increasing the number of vertices of the polygon, the trace approaches an epitrochoid.

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