Difference between revisions of "Lamé curve"
From Encyclopedia of Mathematics
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Revision as of 18:53, 24 March 2012
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://encyclopediaofmath.org/index.php?title=Lam%C3%A9_curve&oldid=11566
Lamé curve. Encyclopedia of Mathematics. URL: http://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