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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 6-sphere coordinates ： ウィキペディア英語版 6-sphere coordinates In mathematics, 6-sphere coordinates are the coordinate system created by inverting the Cartesian coordinates across the unit sphere. They are so named because the loci where one coordinate is constant form spheres tangent to the origin from one of six sides (depending on which coordinate is held constant and whether its value is positive or negative). The three coordinates are :$u\; =\; \backslash frac,\backslash quad\; v\; =\; \backslash frac,\backslash quad\; w\; =\; \backslash frac.$ Since inversion is its own inverse, the equations for ''x'', ''y'', and ''z'' in terms of ''u'', ''v'', and ''w'' are similar: :$x\; =\; \backslash frac,\backslash quad\; y\; =\; \backslash frac,\backslash quad\; z\; =\; \backslash frac.$ This coordinate system is $R$-separable for the 3-variable Laplace equation. == References == * Moon, P. and Spencer, D. E. ''6-sphere Coordinates.'' Fig. 4.07 in ''Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed.'' New York: Springer-Verlag, pp. 122–123, 1988. * * (Six-Sphere Coordinates ) by Michael Schreiber, the Wolfram Demonstrations Project. 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「6-sphere coordinates」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.