Devil's Curve

Cartesian equation:
y4x4+ay2+bx2=0y^{4} - x^{4} + a y^{2} + b x^{2} = 0
Polar equation
r=[(2524tan2(θ))/(1tan2(θ))]r = √[(25 - 24\tan^{2}( \theta ))/(1 - \tan^{2}( \theta ))]


The Devil's Curve was studied by Gabriel Cramer in 1750 and Lacroix in 1810. It appears in Nouvelles Annalesin 1858.

Cramer (1704-1752) was a Swiss mathematician. He became professor of mathematics at Geneva and wrote on work related to physics; also on geometry and the history of mathematics. He is best known for his work on determinants (1750) but also made contributions to the study of algebraic curves (1750).