Lamé curve

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

$$\left(\frac xa\right)^m+\left(\frac yb\right)^m=1,$$

where $m=p/q$, $p$ and $q$ are coprime numbers, $a>0$ and $b>0$. The order of Lamé's curve is $pq$ if $m>0$ and $2pq$ if $m<0$. If $m=1$, Lamé's curve is a straight line, if $m=2$ it is an ellipse, and if $m=2/3$ and $a=b$ 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)

References

[a1]	K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962)
[a2]	F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)