Roulette (Hypotrochogon) of a Circle Rolling inside a Regular Polygon
Roulette (Hypotrochogon) of a Circle Rolling inside a Regular Polygon
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.
The shape of these curves depends on the radius of the rolling disk. When the ratio between the circumferences of the polygon and the rolling disk is the integer , the traced curve is closed, with leaves.
m
m+1
Use the button bar to select the right disk radius to get a closed trace with between 3 and 10 leaves.