Abstract
The epi- and hypo- cycloids are the track described by a point of a circle rolling on a stationary circle (base-circle). There are two parts in this thesis. The first part, we discuss the properties and applications of epi- and hopi- cycloids. The next part deals with the problems about the epicycloid-cardioid. We prove that a cardioid is the inverse of a parabola and show how a cardioid may be determined by ruler and compass without the knowledge of the base-circle.