Henneberg's Minimal Surface

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Henneberg's minimal surface (discovered by Lebrecht Henneberg in 1876) is a nonorientable surface (in fact, it contains a minimal Möbius band) defined over the unit disk, whose total curvature is [1]. As well as other interesting surfaces, it was found by solving the Björling problem [2, 3].

Contributed by: Enrique Zeleny (June 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The parameterization used here is

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References

[1] U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal Surfaces, 2nd ed., Heidelberg, NY: Springer, 2010.

[2] Wikipedia. "Björling Problem." (Dec 30, 2013) en.wikipedia.org/wiki/Bj% C3 % B6rling_problem.

[3] K.-W. Fung, "Minimal Surfaces as Isotropic Curves in : Associated Minimal Surfaces and the Björling's Problem," Bachelor's thesis, Department of Mathematics, Massachusetts Institute of Technology, 2004. ocw.mit.edu/courses/mathematics/18-994-seminar-in-geometry-fall-2004/projects/main1.pdf.



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