Let be a curve, let be a fixed point (the Pole), and let be a second fixed point. Let and be
points on a line through meeting at such that
. The Locus of and is called the
strophoid of with respect to the Pole and fixed point . Let be represented parametrically by
, and let and . Then the equation of the strophoid is

(1) | |||

(2) |

where

(3) |

(4) |

Curve | Pole | Fixed Point | Strophoid |

line | not on line | on line | oblique strophoid |

line | not on line | foot of Perpendicular origin to line | Right Strophoid |

Circle | center | on the circumference | Freeth's Nephroid |

**References**

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 51-53 and 205, 1972.

Lockwood, E. H. ``Strophoids.'' Ch. 16 in *A Book of Curves.* Cambridge, England: Cambridge University Press,
pp. 134-137, 1967.

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

Yates, R. C. ``Strophoid.'' *A Handbook on Curves and Their Properties.* Ann Arbor, MI: J. W. Edwards, pp. 217-220, 1952.

© 1996-9

1999-05-26