Roulette (Hypotrochogon) of a Circle Rolling inside a Regular Polygon

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


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 rolling polygon.

Use the button bar to select the right disk radius to get a closed trace with between 3 and 10 leaves.


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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