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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 Hill tetrahedron ： ウィキペディア英語版 Hill tetrahedron In geometry, the Hill tetrahedra are a family of space-filling tetrahedra. They were discovered in 1896 by M. J. M. Hill, a professor of mathematics at the University College London, who showed that they are scissor-congruent to a cube. == Construction == For every $\backslash alpha\; \backslash in\; (0,2\backslash pi/3)$, let $v\_1,v\_2,v\_3\; \backslash in\; \backslash Bbb\; R^3$ be three unit vectors with angle $\backslash alpha$ between every two of them. Define the ''Hill tetrahedron'' $Q(\backslash alpha)$ as follows: :$Q(\backslash alpha)\; \backslash ,\; =\; \backslash ,\; \backslash .$ A special case $Q=Q(\backslash pi/2)$ is the tetrahedron having all sides right triangles with sides 1, $\backslash sqrt$ and $\backslash sqrt$. Ludwig Schläfli studied $Q$ as a special case of the orthoscheme, and H. S. M. Coxeter called it the characteristic tetrahedron of the cubic spacefilling. 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「Hill tetrahedron」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.