An epitrochoid is a roulette traced by a point attached to a circle of radius b rolling around the outside of a fixed circle of radius a, where the point is a distance h from the center of the exterior circle. In the differential geometry of curves, a roulette is the general concept behind cycloids, epicycloids, hypocycloids, and involutes. ... A circle, in Euclidean geometry, is the set of all points at a fixed distance, called the radius, from a fixed point, the centre. ... In classical geometry, a radius of a circle or sphere is any line segment with one endpoint on the circle (i. ...

The parametric equations for an epitrochoid are: Graph of a butterfly curve, a parametric equation discovered by Temple H. Fay In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters. ...

Special cases include the limaçon with a = b and the epicycloid with h = b In mathematics, limaçons, also known as limaçons of Pascal (pronounced with a soft c), are heart-shaped mathematical curves. ... In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called epicycle — which rolls around without slipping around a fixed circle. ...

See also: hypotrochoid A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. ...