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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 halfcone: 


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© Robert FERRÉOL
2017