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LAMÉ SURFACE


alpha = 1/2
alpha = 1

alpha = 3/2
alpha = 3



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

 
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 a , the surface , part of  intersected with the eighth of a space , is a portion of algebraic surface written  of degree pq ??, and equation ??; when p is even,  and  coincide.
Examples of Lamé surfaces with a = b = c:
 
a 
a = 1 octahedral surface plane 
a = 2 sphere same sphere
a = 1/2 quartic surface
a = 2/3 astroidal surface ditto

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  2017