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Cartesian equation: y4 - x4 + ay2 + bx2 = 0
Parametric Cartesian equation: x = cost( (a2sin2t - b2cos2t)/(sin2t - cos2t) )1/2, y = sint( (a2sin2t - b2cos2t)/(sin2t - cos2t) )1/2
Polar equation: r2(sin2Θ - cos2Θ) = a2sin2Θ - b2cos2Θ
The Devil's Curve was studied by Cramer, a Swiss mathematician in 1750 and Lacroix in 1810. It also appears in Nouvelles Annales, a mathematics journal, in 1858.
The curve illustrated above corresponds to parameters a2 = 1 and b2 = 2.
A special case of the Devil's curve is the so-called "electric motor curve", where y2(y2 - 96) = x2(x2 - 100)
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