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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 Tarski's plank problem ： ウィキペディア英語版 Tarski's plank problem In mathematics, Tarski's plank problem is a question about coverings of convex regions in ''n''-dimensional Euclidean space by "planks": regions between two hyperplanes. Tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region. The question was answered affirmatively by . ==Statement== Given a convex body ''C'' in R''n'' and a hyperplane ''H'', the width of ''C'' parallel to ''H'', ''w''(''C'',''H''), is the distance between the two supporting hyperplanes of ''C'' that are parallel to ''H''. The smallest such distance (i.e. the infimum over all possible hyperplanes) is called the minimal width of ''C'', ''w''(''C''). The (closed) set of points ''P'' between two distinct, parallel hyperplanes in R''n'' is called a plank, and the distance between the two hyperplanes is called the width of the plank, ''w''(''P''). Tarski conjectured that if a convex body ''C'' of minimal width ''w''(''C'') was covered by a collection of planks, then the sum of the widths of those planks must be at least ''w''(''C''). That is, if ''P''1,…,''P''''m'' are planks such that :$C\backslash subseteq\; P\_1\backslash cup\backslash ldots\backslash cup\; P\_m\backslash subset\; \backslash R^n,$ then :$\backslash sum\_^m\; w(P\_i)\backslash geq\; w(C).$ Bang proved this is indeed the case. 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「Tarski's plank problem」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.