The devil's curve was studied by G. Cramer in 1750 and Lacroix in 1810 (MacTutor Archive). It appeared in *Nouvelles Annales*
in 1858. The Cartesian equation is

(1) |

(2) |

(3) |

(4) | |||

(5) |

A special case of the Devil's curve is the so-called Electric Motor Curve:

(6) |

**References**

Cundy, H. and Rollett, A. *Mathematical Models, 3rd ed.* Stradbroke, England: Tarquin Pub., p. 71, 1989.

Gray, A. *Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, p. 71, 1993.

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 151-152, 1972.

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

© 1996-9

1999-05-24