Tracing a Cyclogon: Roulette of a Polygon Rolling along a Line

type of polygon

triangle

square

pentagon

hexagon

pole offset from thecentroid of the n-gon

rolling angle

0.

pole in center

pole at vertex

prolate cyclogon

This Demonstration traces the path of a point attached to a regular polygon rolling without slipping along a straight line. The point is called the pole or tracing point.

If the pole is a vertex of the polygon (Snapshot 1), the traced curve is called a cyclogon.

If the pole is inside the polygon, the curve is a curtate cyclogon (Snapshot 3). If outside the polygon, it is a prolate cyclogon (Snapshot 4).