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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 Half-space (geometry) ： ウィキペディア英語版 Half-space (geometry) In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. More generally, a half-space is either of the two parts into which a hyperplane divides an affine space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane. A half-space can be either ''open'' or ''closed''. An open half-space is either of the two open sets produced by the subtraction of a hyperplane from the affine space. A closed half-space is the union of an open half-space and the hyperplane that defines it. If the space is two-dimensional, then a half-space is called a half-plane (open or closed). A half-space in a one-dimensional space is called a ray. A half-space may be specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane. A strict linear inequality specifies an open half-space: :$a\_1x\_1+a\_2x\_2+\backslash cdots+a\_nx\_n>b$ A non-strict one specifies a closed half-space: :$a\_1x\_1+a\_2x\_2+\backslash cdots+a\_nx\_n\backslash geq\; b$ Here, one assumes that not all of the real numbers ''a''1, ''a''2, ..., ''a''''n'' are zero. ==Properties== * A half-space is a convex set. * Any convex set can be described as the (possibly infinite) intersection of half-spaces. 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「Half-space (geometry)」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.