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Παρασκευή 31 Μαΐου 2024

Catalan's minimal surface

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 the mathematical characteristics exemplified by the following parametric equation:
x(u,v)=usin(u)cosh(v)y(u,v)=1cos(u)cosh(v)z(u,v)=4sin(u/2)sinh(v/2)