Catalan's Surface

This minimal surface was first studied by Eugène Charles Catalan in 1855. Catalan's surface has a cycloid as a geodesic and repeats infinitely often at every , where is an integer [1]. Another property is that its parametrization is isothermal. The angle reveals its associate surface [2].


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[1] U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal Surfaces, 2nd ed., New York: Springer, 2010.
[2] A. Gray, "Catalan's Minimal Surface," Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed., Boca Raton, FL: CRC Press, 1997 pp. 692–693.
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