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