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 , thecurve is transcendental. For Even Integers , the curve becomes closer to a rectangle as increases. ForOdd Integer values of , the curve looks like the Even case in the Positive quadrant but goes to infinityin both the second and fourth quadrants (MacTutor Archive). The Evolute of an Ellipse,
| Curve |
 | Astroid |
 | Superellipse |
| 3 | Witch of Agnesi |
References
MacTutor History of Mathematics Archive. ``Lamé Curves.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Lame.html.
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