# epitrochoid

An epitrochoid is a curve traced out by a point that is a distance *c* from the center
of a circle of radius *b*, where *c* < *b*, that is rolling around the outside of another circle of radius *a*. It is described by the parametric equations

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

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

Closely related to the epitrochoid are the epicycloid, hypocycloid, and the hypotrochoid.
An example of an epitrochoid appears in Albrecht Dürer's
work *Instruction in Measurement with Compasses and Straightedge* (1525).