Devil's Curve

Cartesian equation: y^4-x^4+a y^2+b x^2 = 0

Polar equation: Special case: r = ((25-24tan^2(theta))/(1-tan^2(theta)))^1^/^2

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

Gabriel 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 February 1996