# Hypocycloid

**Hypocycloid** is a special kind of hypotrochoid. **Hypocycloid** is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.

If the smaller circle has radius **r**, and the larger circle has radius **R = kr**, then the parametric equations for the curve 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 then the curve has **p** cusps (where **k = p/q**), 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**.

A hypocycloid curve with 3 cusps is known as a deltoid, with 4 cusps is known as an astroid.

To draw function **Hypocycloid** use the folowing script:

# Example |