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Devil's Curve


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

\end{displaymath} (1)

equivalent to
\end{displaymath} (2)

the polar equation is
\end{displaymath} (3)

and the parametric equations are
$\displaystyle x$ $\textstyle =$ $\displaystyle \cos t\sqrt{a^2\sin^2 t-b^2\cos^2 t\over\sin^2 t-\cos^2 t}$ (4)
$\displaystyle y$ $\textstyle =$ $\displaystyle \sin t\sqrt{a^2\sin^2 t-b^2\cos^2 t\over\sin^2 t-\cos^2 t}.$ (5)

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


\end{displaymath} (6)

(Cundy and Rollett 1989).

See also Electric Motor Curve


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.''

© 1996-9 Eric W. Weisstein