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.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|[a1]||K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962)|
|[a2]||F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)|
Lamé curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lam%C3%A9_curve&oldid=22701