Devil's curve

Devil's curve for a = 0.8 and b = 1.

Devil's curve with a ranging from 0 to 1 and b = 1 (with the curve color going from blue to red).

In geometry, a Devil's curve is a curve defined in the Cartesian plane by an equation of the form

y²(y² − a²) = x²(x² − b²).

Devil's curves were studied heavily by Gabriel Cramer. The name comes from the shape it takes when graphed.

It seems that the devil in the name of the curve is from a juggling game called diabolo, which involves two sticks, a string, and a spinning prop in the likeness of the form of this curve. The confusion is the result of the Italian word diabolo meaning 'devil'.^[1]

References

1. ^ http://www.2dcurves.com/quartic/quarticd.html

External links

• MathWorld - Devil's Curve
• The MacTutor History of Mathematics (University of St. Andrews) - Devil's curve

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