# Epicycloid

- Author:
- Zoltán Kovács

An epicycloid is a plane curve produced by tracing the path of a chosen point of a circle which rolls without slipping around a fixed circle.

Roll point

*C*on the yellow circle and watch the trace of the point*F*. Change the sliders*a*and*b*. What is the sufficient and necessary condition to have a closed red curve? (The red curve is called*epicycloid*.)