Catalan's Surface

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u
12.56
v
2.
θ
0.
view
color
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
2nπ
, where
n
is an integer[1]. Another property is that its parametrization is isothermal. The angle
θ
reveals its associate surface[2].

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

Catalan's Surface (Wolfram MathWorld)
Cycloid (Wolfram MathWorld)
Geodesic (Wolfram MathWorld)
Minimal Surface (Wolfram MathWorld)
Isothermal Parameterization (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny
​
​"Catalan's Surface"​
​http://demonstrations.wolfram.com/CatalansSurface/​
​Wolfram Demonstrations Project​
​Published: June 24, 2014