# 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*^{ 4} – *a *^{2}*y *^{2} = *x *^{4} – *b*^{ 2}*x*^{ 2}

and the polar equation

*r*^{ 2}(sin^{2}*θ* – cos^{2}*θ*)
= *a*^{ 2}sin^{2}*θ* – *b*^{ 2}cos^{2}*θ*.

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