Gabriel Lamé (1795-1870): French engineer and mathematician. Other name: superellipsoid, quasi-ellipsoidal surface.

 

Cartesian equation of : . Cartesian parametrization: , . Volume of the associated ball: .

The Lamé surface  is the "sphere" with radius 1 associated to the norm ;
For rational values of , the surface , part of  intersected with the eighth of a space , is a portion of algebraic surface written  of degree ?? ; when p is even,  and  coincide.
Examples of Lamé surfaces with a = b = c:
 

	octahedral surface	plane
	sphere:	same sphere
		quartic surface
	astroidal surface	surface of degree 18

These surfaces can be generalized into the the n-dimensional hypersurfaces with equation  for which the volume of the associated ball is ; the case n = 2 is of course the Lamé curves.
 
 

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© Robert FERRÉOL  2021