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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 Eutactic star ： ウィキペディア英語版 Eutactic star In Euclidean geometry, a eutactic star is a geometrical figure in a Euclidean space. A star is a figure consisting of any number of opposing pairs of vectors (or arms) issuing from a central origin. A star is eutactic if it is the orthogonal projection of a cross-polytope from a higher-dimensional space onto a subspace. Such stars were called "eutactic" – meaning "well-situated" or "well-arranged" – by because, for a common scalar multiple, their vectors are projections of an orthonormal basis. == Definition == A ''star'' is here defined as a set of 2''s'' vectors ''A'' = ±a1, ..., ±a''s'' issuing from a particular origin in a Euclidean space of dimension ''n'' ≤ ''s''. A star is eutactic if the a''i'' are the projections onto ''n'' dimensions of a set of mutually perpendicular equal vectors b1, ..., b''s'' issuing from a particular origin in Euclidean ''s''-dimensional space. The configuration of 2''s'' vectors in the ''s''-dimensional space ''B'' = ±b1, ... , ±b''s'' is known as a ''cross''. Given these definitions, a eutactic star is, concisely, a star produced by the orthogonal projection of a cross. An equivalent definition, first mentioned by Schläfli,〔 〕 stipulates that a star is eutactic if a constant ''ζ'' exists such that :$\backslash sum\_^s(\backslash mathbf\_k\; \backslash cdot\; \backslash mathbf)^2\; =\; \backslash zeta\; |\backslash mathbf|^2$ for every vector v. The existence of such a constant requires that the sum of the squares of the orthogonal projections of ''A'' on a line be equal in all directions. In general, :$\backslash zeta\; =\; \backslash sum\_^s\; |\backslash mathbf\_k|^2/n.$ A ''normalised'' eutactic star is a projected cross composed of unit vectors.〔〔(【引用サイトリンク】title=Eutactic Star – MathWorld )〕 Eutactic stars are often considered in ''n'' = 3 dimensions because of their connection with the study of regular polyhedra. 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「Eutactic star」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.