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Scherk surface : ウィキペディア英語版 | Scherk surface
In mathematics, a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834;〔H.F. Scherk, Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen, Journal für die reine und angewandte Mathematik, Volume 13 (1835) pp. 185–208 ()〕 his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces (the first two were the catenoid and helicoid).〔http://www-history.mcs.st-andrews.ac.uk/Biographies/Scherk.html〕 The two surfaces are conjugates of each other. Scherk surfaces arise in the study of certain limiting minimal surface problems and in the study of harmonic diffeomorphisms of hyperbolic space. ==Scherk's first surface==
Scherk's first surface is asymptotic to two infinite families of parallel planes, orthogonal to each other, that meet near ''z'' = 0 in a checkerboard pattern of bridging arches. It contains an infinite number of straight vertical lines.
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