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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 Configuration (geometry) ： ウィキペディア英語版 Configuration (geometry) In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.〔In the literature, the terms ''projective configuration'' and ''tactical configuration of type (1,1)'' are also used to describe configurations as defined here.〕 Although certain specific configurations had been studied earlier (for instance by Thomas Kirkman in 1849), the formal study of configurations was first introduced by Theodor Reye in 1876, in the second edition of his book ''Geometrie der Lage'', in the context of a discussion of Desargues' theorem. Ernst Steinitz wrote his dissertation on the subject in 1894, and they were popularized by Hilbert and Cohn-Vossen's 1932 book ''Anschauliche Geometrie'', reprinted in English . Configurations may be studied either as concrete sets of points and lines in a specific geometry, such as the Euclidean or projective planes (these are said to be ''realizable'' in that geometry), or as a type of abstract incidence geometry. In the latter case they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions: every two points of the incidence structure can be associated with at most one line, and every two lines can be associated with at most one point. That is, the girth of the corresponding bipartite graph (the Levi graph of the configuration) must be at least six. ==Notation== A configuration in the plane is denoted by (), where is the number of points, the number of lines, the number of lines per point, and the number of points per line. These numbers necessarily satisfy the equation :$p\backslash gamma\; =\; \backslash ell\backslash pi\backslash ,$ as this product is the number of point-line incidences (''flags''). Configurations having the same symbol, say (), need not be isomorphic as incidence structures. For instance, there exist three different (93 93) configurations: the Pappus configuration and two less notable configurations. In some configurations, and consequently, . These are called ''symmetric'' or ''balanced'' configurations and the notation is often condensed to avoid repetition. For example (93 93) abbreviates to (93). 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「Configuration (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.