First studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first pendulum clock in an attempt to force the pendulum to swing in the path of a Cycloid.

For a Circle with , the parametric equations of the circle
and their derivatives are given by

(1) |

(2) |

(3) |

(4) |

(5) |

(6) | |||

(7) |

The Arc Length, Curvature, and Tangential Angle are

(8) | |||

(9) | |||

(10) |

The Cesàro Equation is

(11) |

**References**

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, p. 83, 1993.

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 190-191, 1972.

MacTutor History of Mathematics Archive. ``Involute of a Circle.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Involute.html.

© 1996-9

1999-05-26