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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 Non-Archimedean geometry ： ウィキペディア英語版 Non-Archimedean geometry In mathematics, non-Archimedean geometry〔Robin Hartshorne, ''Geometry: Euclid and beyond'' (2000), p. 158.〕 is any of a number of forms of geometry in which the axiom of Archimedes is negated. An example of such a geometry is the Dehn plane. Non-Archimedean geometries may, as the example indicates, have properties significantly different from Euclidean geometry. There are two senses in which the term may be used, referring to geometries over fields which violate one of the two senses of the Archimedean property (i.e. with respect to order or magnitude). == Geometry over a non-Archimedean ordered field == The first sense of the term is the geometry over a non-Archimedean ordered field, or a subset thereof. The aforementioned Dehn plane takes the self-product of the finite portion of a certain non-Archimedean ordered field based on the field of rational functions. In this geometry, there are significant differences from Euclidean geometry; in particular, there are infinitely many parallels to a straight line through a point—so the parallel postulate fails—but the sum of the angles of a triangle is still a straight angle. Intuitively, in such a space, the points on a line cannot be described by the real numbers or a subset thereof, and there exist segments of "infinite" or "infinitesimal" length. 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「Non-Archimedean 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.