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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Henneberg surface ： ウィキペディア英語版 Henneberg surface In differential geometry, the Henneberg surface is a non-orientable minimal surface〔L. Henneberg, Über salche minimalfläche, welche eine vorgeschriebene ebene curve sur geodätishen line haben, Doctoral Dissertation, Eidgenössisches Polythechikum, Zürich, 1875〕 named after Lebrecht Henneberg.〔Lebrecht Henneberg from the German-language Wikipedia. Retrieved on September 25, 2012.〕 It has parametric equation :$\backslash begin$ x(u,v) &= 2\cos(v)\sinh(u) - (2/3)\cos(3v)\sinh(3u)\\ y(u,v) &= 2\sin(v)\sinh(u) + (2/3)\sin(3v)\sinh(3u)\\ z(u,v) &= 2\cos(2v)\cosh(2u) \end and can be expressed as an order-15 algebraic surface.〔Weisstein, Eric W. "Henneberg's Minimal Surface." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/HennebergsMinimalSurface.html〕 It can be viewed as an immersion of a punctured projective plane.〔Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Minimal Surfaces, Volume 1. Springer 2010〕 Up until 1981 it was the only known non-orientable minimal surface.〔M. Elisa G. G. de Oliveira, Some New Examples of Nonorientable Minimal Surfaces, Proceedings of the American Mathematical Society, Vol. 98, No. 4, Dec., 1986〕 The surface contains a semicubical parabola ("Neile's parabola") and can be derived from solving the corresponding Björling problem.〔L. Henneberg, Über diejenige minimalfläche, welche die Neil'sche Paralee zur ebenen geodätischen line hat, Vierteljschr Natuforsch, Ges. Zürich 21 (1876), 66–70.〕〔Kai-Wing Fung, Minimal Surfaces as Isotropic Curves in C3: Associated minimal surfaces and the Björling's problem. MIT BA Thesis. 2004 http://ocw.mit.edu/courses/mathematics/18-994-seminar-in-geometry-fall-2004/projects/main1.pdf〕 == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Henneberg surface」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.