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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 Spherical wedge ： ウィキペディア英語版 Spherical wedge In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's ''base''). The angle between the radii lying within the bounding semidisks is the dihedral ''angle of the wedge'' ''α''. If ''AB'' is a semidisk that forms a ball when completely revolved about the ''z''-axis, revolving ''AB'' only through a given ''α'' produces a spherical wedge of the same angle ''α''. Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon." A spherical wedge of ''α'' = π radians (180°) is called a ''hemisphere'', while a spherical wedge of ''α'' = 2π radians (360°) constitutes a complete ball. The volume of a spherical wedge can be intuitively related to the ''AB'' definition in that while the volume of a ball of radius ''r'' is given by $\backslash tfrac\; \backslash pi\; r^3$, the volume a spherical wedge of the same radius ''r'' is given by〔 :$V\; =\; \backslash frac\; \backslash cdot\; \backslash frac\; \backslash pi\; r^3\; =\; \backslash frac\; \backslash alpha\; r^3.$ Extrapolating the same principle and considering that the surface area of a sphere is given by $4\backslash pi\; r^2$, it can be seen that the surface area of the lune corresponding to the same wedge is given by :$A\; =\; \backslash frac\; \backslash cdot\; 4\; \backslash pi\; r^2\; =\; 2\; \backslash alpha\; r^2$ Hart (2009) states that the "volume of a spherical wedge is to the volume of the sphere as the number of degrees in the (of the wedge ) is to 360". Hence, and through derivation of the spherical wedge volume formula, it can be concluded that, if $V\_s$ is the volume of the sphere and $V\_w$ is the volume of a given spherical wedge, :$\backslash frac\; =\; \backslash frac$ Also, if ''S''''l'' is the area of a given wedge's lune, and ''S''''s'' is the area of the wedge's sphere, :$\backslash frac\; =\; \backslash frac$ == See also == *Spherical cap 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「Spherical wedge」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.