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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 Girth (geometry) ： ウィキペディア英語版 Girth (geometry) In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction.〔.〕〔.〕 For instance, the girth of a unit cube in a direction parallel to one of the three coordinate axes is four: it projects to a unit square, which has four as its perimeter. ==Surfaces of constant girth== The girth of a sphere in any direction equals the circumference of its equator, or of any of its great circles. More generally, if ''S'' is a surface of constant width ''w'', then every projection of ''S'' is a curve of constant width, with the same width ''w''. All curves of constant width have the same perimeter, the same value ''w'' as the circumference of a circle with that width (this is Barbier's theorem). Therefore, every surface of constant width is also a surface of constant girth: its girth in all directions is the same number ''w''. Hermann Minkowski proved, conversely, that every convex surface of constant girth is also a surface of constant width.〔〔 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「Girth (geometry)」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.