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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 K-noid ： ウィキペディア英語版 K-noid In differential geometry, a ''k''-noid is a minimal surface with ''k'' catenoid openings. In particular, the 3-noid is often called trinoid. The first ''k''-noid minimal surfaces were described by Jorge and Meeks in 1983.〔L. P. Jorge and W. H. Meeks III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983)〕 The term ''k''-noid and trinoid is also sometimes used for constant mean curvature surfaces, especially branched versions of the unduloid ("triunduloids"). ''k''-noids are topologically equivalent to ''k''-punctured spheres (spheres with ''k'' points removed). ''k''-noids with symmetric openings can be generated using the Weierstrass–Enneper parameterization $f(z)\; =\; 1/(z^k-1)^2,\; g(z)\; =\; z^\backslash ,\backslash !$. This produces the explicit formula : $\backslash begin$ X(z) = \frac \Re \Bigg\ \Big) \Big(&(k-1)(z^k-1)_2F_1(1,-1/k;(k-1)/k;z^k)\\ & \end : $\backslash begin$ Y(z) = \frac \Re \Bigg\\Big) \Big(&(k-1)(z^k-1)_2F_1(1,-1/k;(k-1)/k;z^k) \\ & \end : $$ Z(z) =\Re \left \ \right\} where $\_2F\_1(a,b;c;z)$ is the Gaussian hypergeometric function. It is also possible to create k-noids with openings in different directions and sizes, k-noids corresponding to the platonic solids and k-noids with handles. ==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「K-noid」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.