The path traced out by a fixed point at a Radius , where is the Radius of a rolling Circle,
also sometimes called an Extended Cycloid. The prolate cycloid contains loops,
and has parametric equations

(1) | |||

(2) |

The Arc Length from is

(3) |

(4) |

(5) |

**References**

Wagon, S. *Mathematica in Action.* New York: W. H. Freeman, pp. 46-50, 1991.

© 1996-9

1999-05-26