Enneper's Minimal Surface
A self-intersecting Minimal Surface having zero Mean Curvature and nonconstant Gaussian Curvature.Enneper's minimal surface can be generated using the Enneper-Weierstraß Parameterization with
 |  |  | (1) |
 | |  | (2) |
Letting
and taking the Real Part give | |  | (3) |
 | |  | (4) |
 | |  | (5) |
where
and 
. Letting 
gives the figure above, with parametrization | |  | (6) |
| |  | (7) |
| |  | (8) |
(do Carmo 1986, Gray 1997, Nordstrand).See also Enneper-Weierstraß Parameterization
References
Dickson, S. ``Minimal Surfaces.'' Mathematica J. 1, 38-40, 1990. do Carmo, M. P. ``Enneper's Surface.'' §3.5C in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, p. 43, 1986. Enneper, A. ``Analytisch-geometrische Untersuchungen.'' Z. Math. Phys. 9, 96-125, 1864. Gray, A. ``Examples of Minimal Surfaces.'' §30.2 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 358 and 684-685, 1997. Maeder, R. The Mathematica Programmer. San Diego, CA: Academic Press, pp. 150-151, 1994. Nordstrand, T. ``Enneper's Minimal Surface.'' http://www.uib.no/people/nfytn/enntxt.htm.
Wolfram Research ``Mathematica Version 2.0 Graphics Gallery.''http://www.mathsource.com/cgi-bin/MathSource/Applications/Graphics/3D/0207-155.
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