Representations of Epitrochoids and Hypotrochoids
MetadataShow full item record
Representations of a given curve may consist of implicit or parametric equations, along with any envelopes that produce that curve. We will describe the diﬀerent methods of passing from one of these representations to another, then apply these methods with regards to epitrochoids and hypotrochoids. These are the families of curves that are produced by tracing the path of a point aﬃxed to a circle as it rolls around the inside or outside of a stationary circle. Epicycloids and hypocycloids are produced when the point aﬃxed to the moving circle is on the circumference. We will provide several conjectures and results on the representations of epitrochoids and hypotrochoids, with emphasis on epicycloids and hypocycloids, including their implicit representations and their construction as envelopes.