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Schwarz's Minimal Surface


A periodic minimal surface constructed by Schwarz using the following two principles:

1. If part of the boundary of a minimal surface is a straight line, then the reflection across the line, when added to the original surface, makes another minimal surface.

2. If a minimal surface meets a plane at right angles, then the mirror image of the plane, when added to the original surface, also makes a minimal surface.


See also

Minimal Surface

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References

GRAPE. "Schwarz's P-Surface and Deformation (Hermann Amandus Schwarz)." http://www-sfb256.iam.uni-bonn.de/grape/EXAMPLES/AMANDUS/schwarz.html.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 224-225, 1991.

Referenced on Wolfram|Alpha

Schwarz's Minimal Surface

Cite this as:

Weisstein, Eric W. "Schwarz's Minimal Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchwarzsMinimalSurface.html

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