Devil's Curve

The devil's curve was studied by G. Cramer in 1750 and Lacroix in 1810 (MacTutor Archive). It appeared in Nouvelles Annalesin 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.

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• Cauchy Criterion
• Cauchy Distribution
• Cauchy Equation
• Cauchy Functional Equation
• Cauchy-Hadamard Theorem
• Cauchy Inequality
• Cauchy Integral Formula
• Cauchy Integral Test
• Cauchy Integral Theorem
• Cauchy-Kovalevskaya Theorem
• Cauchy-Lagrange Identity
• Cauchy-Maclaurin Theorem
• Cauchy Mean Theorem
• Cauchy Principal Value
• Cauchy Problem
• Cauchy Ratio Test
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