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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 Barbier's theorem ： ウィキペディア英語版 Barbier's theorem In geometry, Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape.〔.〕 This theorem was first published by Joseph-Émile Barbier in 1860.〔. See in particular pp. 283–285.〕 ==Examples== The most familiar examples of curves of constant width are the circle and the Reuleaux triangle. For a circle, the width is the same as the diameter; a circle of width ''w'' has perimeter π''w''. A Reuleaux triangle of width ''w'' consists of three arcs of circles of radius ''w''. Each of these arcs has central angle π/3, so the perimeter of the Reuleaux triangle of width ''w'' is equal to half the perimeter of a circle of radius ''w'' and therefore is equal to π''w''. A similar analysis of other simple examples such as Reuleaux polygons gives the same answer. 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「Barbier'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.