Devil's Curve

Cartesian equation:
y4 - x4 + a y2 + b x2 = 0
Polar equation (Special case):
r = √[(25 - 24tan2(θ))/(1 - tan2(θ))]

Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute
Involute 1 Involute 2
Inverse curve wrt origin Inverse wrt another circle
Pedal curve wrt origin Pedal wrt another point
Negative pedal curve wrt origin Negative pedal wrt another point
Caustic wrt horizontal rays Caustic curve wrt another point

Click THIS LINK to experiment interactively with this curve and its associated curves.

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).

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JOC/EFR/BS January 1997

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