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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 Minkowski's theorem ： ウィキペディア英語版 Minkowski's theorem In mathematics, Minkowski's theorem is the statement that any convex set in R''n'' which is symmetric with respect to the origin and with volume greater than 2''n'' d(''L'') contains a non-zero lattice point. The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. ==Formulation== Suppose that ''L'' is a lattice of determinant d(''L'') in the ''n''-dimensional real vector space R''n'' and ''S'' is a convex subset of R''n'' that is symmetric with respect to the origin, meaning that if ''x'' is in ''S'' then −''x'' is also in ''S''. Minkowski's theorem states that if the volume of ''S'' is strictly greater than 2''n'' d(''L''), then ''S'' must contain at least one lattice point other than the origin.〔Since the set ''S'' is symmetric, it would then contain at least three lattice points: the origin 0 and a pair of points ±''x'', where ''x'' ∈ ''L'' \ 0.〕 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「Minkowski's theorem」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.