A curve named and studied by Newton in 1701 and contained in his classification of Cubic Curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor Archive).

The curve is given by the Cartesian equation

(1) |

(2) | |||

(3) |

The curve has a Maximum at and a Minimum at , where

(4) |

(5) |

(6) | |||

(7) |

**References**

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 111-112, 1972.

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

© 1996-9

1999-05-26