# Lamé curve

From Encyclopedia of Mathematics

A plane algebraic curve whose equation in rectangular Cartesian coordinates has the form

where , and are coprime numbers, and . The order of Lamé's curve is if and if . If , Lamé's curve is a straight line, if it is an ellipse, and if and it is an astroid. The Lamé curves are named after G. Lamé, who considered them in 1818.

#### References

[1] | A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) |

#### Comments

#### References

[a1] | K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962) |

[a2] | F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |

**How to Cite This Entry:**

Lamé curve.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Lam%C3%A9_curve&oldid=11566

This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article