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