Wolfram Research
Wolfram Math World: Epicycloid
Shows how to graph them and also derives the polar equations from the parametric equation. The site then defines a few special Epiycloids. Includes a definition, formulas, graphs, video, and links to related topics.
Wolfram Research
Wolfram Math World: Cardioid
The site opens with a visual representation of how a Cardoid, a one-cusped epicycloid, is made. The site then shows the parametric, Cartesian, and polar equation for the special epicycloid. The last half of the page gives more equations...
Other
College of the Redwoods: The Epicycloid
This resource gives a brief description and history lesson. Shows you how to use epicycloids.
Other
College of the Redwoods: Nephroid
This resource describes what a nephroid is and what it looks like in graph form.
University of St. Andrews (UK)
University of St. Andrews: Curves: Epicycloid
Gives the parametric equation and a brief history.
University of St. Andrews (UK)
University of St. Andrews: Epicycloid
Very cool site. Allows you to zoom in/out and add evolutes, involutes, etc.
Wolfram Research
Wolfram Math World: Epicycloid1 Cusped
This is a brief page explaining the special epicycloid with one cusp. If you are not yet familiar with the epicycloid, there is a link to help you become familiar.
Wolfram Research
Wolfram Math World: Ranunculoid
It is shows a graph of a ranunculoid, a epicycloid with five cusps. Site is interactive and user-friendly, and includes good information for understanding.