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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 mean width ： ウィキペディア英語版 mean width In geometry, the mean width is a measure of dimension length of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies. In $n$ dimensions, one has to consider $(n-1)$-dimensional hyperplanes perpendicular to a given direction $\backslash hat$ in $S^$, where $S^n$ is the n-sphere (the surface of a $(n+1)$-dimensional sphere). The "width" of a body in a given direction $\backslash hat$ is the distance between the closest pair of such planes, such that the body is entirely in between the two hyper planes (the planes only intersect with the boundary of the body). The mean width is the average of this "width" over all $\backslash hat$ in $S^$. More formally, define a compact body B as being equivalent to set of points in its interior plus the points on the boundary (here, points denote elements of $\backslash mathbb^n$). The support function of body B is defined as : $h\_B(n)=\backslash max\backslash$ where $n$ is a direction and $\backslash langle,\backslash rangle$ denotes the usual inner product on $\backslash mathbb^n$. The mean width is then : $b(B)=\backslash frac\}\; h\_B(\backslash hat)+h\_B(-\backslash hat),$ where $S\_$ is the $(n-1)$-dimensional volume of $S^$. Note, that the mean width can be defined for any body (that is compact), but it is most useful for convex bodies (that is bodies, whose corresponding set is a convex set). ==Mean widths of convex bodies in low dimensions== 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「mean width」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.