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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 Affine-regular polygon ： ウィキペディア英語版 Affine-regular polygon In geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation. Affine transformations include translations, uniform and non-uniform scaling, reflections, rotations, shears, and other similarities and some, but not all linear maps. All triangles are affine-regular. In other words, all triangles can be generated by applying affine transformations to an equilateral triangle. A quadrilateral is affine-regular if and only if it is a parallelogram, which includes rectangles and rhombuses as well as squares. In fact, affine-regular polygons may be considered a natural generalization of parallelograms.〔. See in particular p. 249.〕 Many properties of regular polygons are invariant under affine transformations, and affine-regular polygons share the same properties. For instance, an affine-regular quadrilateral can be equidissected into $m$ equal-area triangles if and only if $m$ is even, by affine invariance of equidissection and Monsky's theorem on equidissections of squares.〔.〕 More generally an $n$-gon with $n\; >\; 4$ may be equidissected into $m$ equal-area triangles if and only if $m$ is a multiple of $n$.〔.〕 ==References== 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「Affine-regular polygon」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.