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**Parametric Cartesian equation: x = (***a - b*)cos(*t*) + *b*cos((*a/b* - 1)*t*), y = (*a - b*)sin(*t*) - *b*sin((*a/b* - 1)*t*)

This is a member of a set of four curves which are closely related. These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point *P* on a circle of radius *b* which rolls round a fixed circle of radius *a*.

For the hypocycloid, shown above in dodgy ASCII, the circle of radius *b* rolls on the inside of the circle of radius *a*. The point *P* is on the circumference of the circle of radius *b*. For the example *a* = 5 and *b* = 3.

**Special cases**

Also, the evolute of a hypocycloid is a similar hypocycloid.