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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 Reeve tetrahedron ： ウィキペディア英語版 Reeve tetrahedron In geometry, the Reeve tetrahedron is a polyhedron, named after John Reeve, in $\backslash mathbb^3$ with vertices at $(0,\; 0,\; 0)$, $(1,\; 0,\; 0)$, $(0,\; 1,\; 0)$, and $(1,\; 1,\; r)$ where $r$ is a positive integer. Each vertex lies on a fundamental lattice point (a point in $\backslash mathbb^3$). No other fundamental lattice points lie on the surface or in the interior of the tetrahedron. In 1957 Reeve used this tetrahedron as a counterexample to show that there is no simple equivalent of Pick's theorem in $\backslash mathbb^3$ or higher-dimensional spaces.〔J. E. Reeve, "On the Volume of Lattice Polyhedra", ''Proceedings of the London Mathematical Society'', s3–7(1):378–395〕 This is seen by noticing that Reeve tetrahedra have the same number of interior and boundary points for any value of $r$, but different volumes. The Ehrhart polynomial of the Reeve tetrahedron $\backslash mathcal\_r$ of height $r$ is :$L(\backslash mathcal\_r,\; t)\; =\; \backslash fract^3\; +\; t^2\; +\; \backslash left(2\; -\; \backslash frac\backslash right)t\; +\; 1.$ Thus, for $r\; \backslash ge\; 13$, the Ehrhart polynomial of $\backslash mathcal\_r$ has a negative coefficient. == Notes == 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「Reeve 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.