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

BOUR SURFACE

Edmond Bour (1832 -1866): French mathematician.
Surface studied in 1861 by Bour.

 
Cartesian parametrization: (where   ).
Rational algebraic surface of degree 16.
First fundamental quadratic form: .
Surface element: .
Total curvature: .
Zero mean curvature (minimal surface).

The Bour surface is the minimal surface obtained by taking  in the Weierstrass parametrization of a minimal surface. It is a special case of generalized Enneper surface.
The projections on xOy of the lines r = constant are hypotrochoids with three branches. Compare to a sinusoidal half-cone: 

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

© Robert FERRÉOL  2017