next surface  previous surface  2D curves  3D curves  surfaces  fractals  polyhedra 
LAMÉ SURFACE





Gabriel Lamé (17951870): 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 ndimensional hypersurfaces with equation for which the volume of the associated ball is ; the case n = 2 is of course the Lamé curves.
next surface  previous surface  2D curves  3D curves  surfaces  fractals  polyhedra 
© Robert FERRÉOL 2017