Catalan's minimal surface - Alchetron, the free social encyclopedia

In differential geometry, Catalan's minimal surface is a minimal surface originally studied by Eugène Charles Catalan in 1855.

It has the special property of being the minimal surface that contains a cycloid as a geodesic. It is also swept out by a family of parabolae.

The surface has parametric equation:

x ( u , v ) = u − sin ⁡ ( u ) cosh ⁡ ( v ) y ( u , v ) = 1 − cos ⁡ ( u ) cosh ⁡ ( v ) z ( u , v ) = 4 sin ⁡ ( u / 2 ) sinh ⁡ ( v / 2 )

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