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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 De Bruijn's theorem ： ウィキペディア英語版 De Bruijn's theorem In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over. One of these results is now known as de Bruijn's theorem. According to this theorem, a "harmonic brick" (one in which each side length is a multiple of the next smaller side length) can only be packed into a box whose dimensions are multiples of the brick's dimensions.〔.〕 ==Example== De Bruijn was led to prove this result after his then-seven-year-old son, F. W. de Bruijn, was unable to pack bricks of dimension $\backslash scriptstyle\; 1\backslash times\; 2\backslash times\; 4$ into a $\backslash scriptstyle\; 6\backslash times\; 6\backslash times\; 6$ cube.〔.〕〔.〕 The cube has a volume equal to that of $\backslash scriptstyle\; 27$ bricks, but only $\backslash scriptstyle\; 26$ bricks may be packed into it; one way to see this is to partition the cube into $\backslash scriptstyle\; 27$ smaller cubes colored alternately black and white, and to observe that this coloring has more unit cells of one color than of the other, whereas with this coloring any placement of the $\backslash scriptstyle\; 1\backslash times\; 2\backslash times\; 4$ brick must have equal numbers of cells of each color.〔.〕 De Bruijn's theorem proves that a perfect packing with these dimensions is impossible, in a more general way that applies to many other dimensions of bricks and boxes. 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「De Bruijn'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.