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.[more]
This roulette curve is a sequence of circular arcs traced by the polygon when rolling along the edge of the circle.
For generalized cyclogons  and generalized trochoidal curves , these roulettes can be considered as limiting cases of hypotrochogons with an infinite number of vertices of the base (stationary) polygon.[less]
 T. M. Apostol and M. A. Mnatsakanian, "Generalized Cyclogons," Math Horizons, 2002 pp. 25–28. www.mamikon.com/USArticles/GenCycloGons.pdf.
 T. M. Apostol and M. A. Mnatsakanian, "Area & Arc Length of Trochogonal Arches," Math Horizons, 2003 pp. 24–30. www.mamikon.com/USArticles/TrochoGons.pdf.