Rolling a Polygon on a Circle
Rolling a Polygon on a Circle
This Demonstration simulates a regular polygon that rolls without slipping around a base circle of radius 1.
The roulette traced by the centroid of the polygon is a discontinuous curve with a number of jump discontinuities [1] appearing when the vertices of the polygon touch the circle.
Varying the circumradius of the rolling polygon changes the circumference ratio between the polygon and the base circle. A "smooth" curve can be obtained after one revolution around the base circle if the circumradius of the -sided regular polygon equals . The snapshots saved in the bookmarks give several examples.
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