Curves studied by Lam� in 1818. Gabriel Lam� (1795-1870): French mathematician and engineer. Other names for�>2: super-ellipse, super-circle (if a = b), squircle (contraction of the words square and circle).

Cartesian equation of�:� ;� :� with a, b > 0 ,�;� Cartesian parametrization of� :�. Area delimited by� :� where� , i.e.� if�.

The Lam� curves� and� are defined by their Cartesian equation above.
For rational values of�, the curve�, the part of� located in the� quadrant, is a portion of an algebraic curve� of degree pq ?, and equation� ? (when p is even,� and� coincide); the same holds for the curves�.

Examples of curves with a = b:
�
�

	Lam� curve	associated algebraic curve�	figure: the Lam� curve in red, the associated algebraic curve in green.
1	square:�	line:�
2	�circle:�	ditto
3		Lam� cubic:�
1/2	union of 4 arcs of parabolas:�	parabola:�
2/3	astroid:�	ditto
- 1	union of 4 branches of rectangular hyperbolas:�	rectangular hyperbola:
-2	crosscurve:�	ditto

	Lam� curve�	associated algebraic curve�	figure: Lam� curve in red, the associated algebraic curve in green.
1	eight half-lines:�	line:�
2		rectangular hyperbola:�
1/2	union of 8 arcs of parabolas:�	parabola:�
2/3	and its symmetric image about y = x, of equation�	ditto; it is the union of two evolutes of hyperbola.
- 1	union of 8 branches of rectangular hyperbolas:�	rectangular hyperbola:
-2		bullet nose curve:�

When a = b =1 and a� = n is an integer,� is the Fermat curve.

See also the Lam� surfaces.

� Robert FERR�OL 2017