## Lamé Curve

A curve with Cartesian equation

first discussed in 1818 by Lamé. If is a rational, then the curve is algebraic. However, for irrational , the curve is transcendental. For Even Integers , the curve becomes closer to a rectangle as increases. For Odd Integer values of , the curve looks like the Even case in the Positive quadrant but goes to infinity in both the second and fourth quadrants (MacTutor Archive). The Evolute of an Ellipse,

 Curve Astroid Superellipse 3 Witch of Agnesi

MacTutor History of Mathematics Archive. Lamé Curves.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Lame.html.