Roulette (Hypotrochogon) of a Polygon Rolling inside a Circle

number of vertices of polygon

n

3

4

5

6

7

8

radius of polygon circumcircle

r

0.366

pole offset from centroid

prolate hypotrochogon

pole at polygon centroid

pole at polygon vertex

number of traced sections

36

roll the polygon in the circle

ϕ

0.001

zoom control

2.5

show trace only

hide section markers

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.