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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 Maekawa's theorem ： ウィキペディア英語版 Maekawa's theorem Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa. It relates to flat-foldable origami crease patterns and states that at every vertex, the numbers of valley and mountain folds always differ by two in either direction.〔.〕 The same result was also discovered by Jacques Justin.〔.〕 One consequence of Maekawa's theorem is that the total number of folds at each vertex must be an even number. This implies (via a form of planar graph duality between Eulerian graphs and bipartite graphs) that, for any flat-foldable crease pattern, it is always possible to color the regions between the creases with two colors, such that each crease separates regions of differing colors.〔. See in particular Theorem 3.1 and Corollary 3.2.〕 The same result can also be seen by considering which side of the sheet of paper is uppermost in each region of the folded shape. ==See also== *Kawasaki's theorem 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「Maekawa'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.