# Epicycloid

**Epicycloid** is a plane curve produced by tracing the path of a chosen point of a circle (called *epicycle*) which rolls without slipping around a fixed circle. It is a particular kind of curve.

If the smaller circle has radius **r**, and the larger circle has radius **R = kr**, then the parametric equations for the **Epicycloid** can be given by either:

If **k** is an integer, then the curve is closed, and has **k** cusps, if **k** is a rational number (**k=p/q**), then the curve has **p** cusps, if **k** is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius **R + 2r**.

You can plot function online using the folowing script for **Epicycloid**:

# Example |