# hypotrochoid

A hypotrochoid is a curve formed by the path of a point attached to a point *c*, which
is not on the circumference, of circle of
radius *b* that rolls around the inside of a larger circle of radius *a*. The parametric equations for a hypotrochoid can be written as:

*x* = (*a* - *b*) cos *t* + *c* cos(*a*/*b* -1)*t*,

*y* = (*a* - *b*) sin *t* - *c* sin(*a*/*b* -1)*t*.

The hypotrochoid is a generalized hypocycloid and comes in two varieties: a **prolate hypocycloid** if the
starting point is outside the circumference of the rolling circle and a **curtate hypocycloid** if the starting point is inside the
rolling circle. In the same family of curves as the hypotrochoid (and hypocycloid)
are the epicycloid and epitrochoid.