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.[2]
The surface has the mathematical characteristics exemplified by the following parametric equation:[3]
^Catalan, E. "Mémoire sur les surfaces dont les rayons de courbures en chaque point, sont égaux et les signes contraires." Comptes rendus de l'Académie des Sciences de Paris 41, 1019–1023, 1855.
^Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Minimal Surfaces, Volume 1. Springer 2010
^Gray, A. "Catalan's Minimal Surface." Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, Florida: CRC Press, pp. 692–693, 1997