Devil's curve

Devil's curve

Image: Jan Wassenaar. www.2dcurves.com.

The Devil's curve, also known as the Devil on Two Sticks, is a curve with the Cartesian equation


    y 4a 2y 2 = x 4b 2x 2


and the polar equation


    r 2(sin2θ – cos2θ) = a 2sin2θb 2cos2θ.


Early studies of it were carried out in 1750 by the Swiss mathematician Gabriel Cramer (1704–1752), who is most famous for his work on determinants, and in 1810 by Lacroix. For a = 25/24, the curve is called the electric motor curve.