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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 Axiality (geometry) ： ウィキペディア英語版 Axiality (geometry) In the geometry of the Euclidean plane, axiality is a measure of how much axial symmetry a shape has. It is defined as the ratio of areas of the largest axially symmetric subset of the shape to the whole shape. Equivalently it is the largest fraction of the area of the shape that can be covered by a mirror reflection of the shape (with any orientation). A shape that is itself axially symmetric, such as an isosceles triangle, will have an axiality of exactly one, whereas an asymmetric shape, such as a scalene triangle, will have axiality less than one. ==Upper and lower bounds== showed that every convex set has axiality at least 2/3.〔. Erratum, .〕 This result improved a previous lower bound of 5/8 by .〔. As cited by .〕 The best upper bound known is given by a particular convex quadrilateral, found through a computer search, whose axiality is less than 0.816.〔.〕 For triangles and for centrally symmetric convex bodies, the axiality is always somewhat higher: every triangle, and every centrally symmetric convex body, has axiality at least $2(\backslash sqrt-1)\backslash approx\; 0.828$. In the set of obtuse triangles whose vertices have $x$-coordinates $0$, $\backslash sqrt\; 2$, and $1$, the axiality approaches $2(\backslash sqrt-1)$ in the limit as the $y$-coordinates approach zero, showing that the lower bound is as large as possible. It is also possible to construct a sequence of centrally symmetric parallelograms whose axiality has the same limit, again showing that the lower bound is tight.〔. As cited by .〕〔.〕 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「Axiality (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.