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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 Circumcenter of mass ： ウィキペディア英語版 Circumcenter of mass In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass. More generally, the circumcenter of mass may be defined for simplicial polytopes and also in the spherical and hyperbolic geometries. In the special case when the polytope is a quadrilateral or hexagon, the circumcenter of mass has been called the "quasicircumcenter" and has been used to define an Euler line of a quadrilateral.〔.〕 The circumcenter of mass allows us to define an Euler line for simplicial polytopes. ==Definition in the plane== Let $P$ be an oriented polygon (with vertices counted countercyclically) in the plane with vertices $V\_1,V\_2,\backslash ldots,V\_n$ and let $O$ be an arbitrary point not lying on the sides (or their extensions). Consider the triangulation of $P$ by the oriented triangles $O\; V\_i\; V\_$ (the index $i$ is viewed modulo $n$). Associate with each of these triangles its circumcenter $C\_i$ with weight equal to its oriented area (positive if its sequence of vertices is countercyclical; negative otherwise). The circumcenter of mass of $P$ is the center of mass of these weighted circumcenters. The result is independent of the choice of point $O$. 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「Circumcenter of mass」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.