Roulette (Hypotrochogon) of a Polygon Rolling inside a Circle

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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.


Contributed by: Erik Mahieu (May 2017)
Open content licensed under CC BY-NC-SA




[1] T. M. Apostol and M. A. Mnatsakanian, "Generalized Cyclogons," Math Horizons, 2002 pp. 25–28.

[2] T. M. Apostol and M. A. Mnatsakanian, "Area & Arc Length of Trochogonal Arches," Math Horizons, 2003 pp. 24–30.

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