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 . Another property is that its parametrization is isothermal. The angle reveals its associate surface .
 U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal Surfaces, 2nd ed., New York: Springer, 2010.
 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.
Wolfram Demonstrations Project
Published: June 24 2014