Catalan's Surface
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].
2nπ
n
θ
References
References
[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.
External Links
External Links
Permanent Citation
Permanent Citation
Enrique Zeleny
"Catalan's Surface"
http://demonstrations.wolfram.com/CatalansSurface/
Wolfram Demonstrations Project
Published: June 24, 2014