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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 Intersection theorem ： ウィキペディア英語版 Intersection theorem In projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and possibly higher-dimensional objects and their incidences – together with a pair of objects and (for instance, a point and a line). The "theorem" states that, whenever a set of objects satisfies the incidences (''i.e.'' can be identified with the objects of the incidence structure in such a way that incidence is preserved), then the objects and must also be incident. An intersection theorem is not necessarily true in all projective geometries; it is a property that some geometries satisfy but others don't. For example, Desargues' theorem can be stated using the following incidence structure: *Points: $\backslash$ *Lines: $\backslash$ *Incidences (in addition to obvious ones such as $(A,AB)$): $\backslash$ The implication is then $(R,PQ)$—that point is incident with line . == Famous examples == Desargues' theorem holds in a projective plane if and only if is the projective plane over some division ring (skewfield} — $P=\backslash mathbb\_D$. The projective plane is then called ''desarguesian''. A theorem of Amitsur and Bergman states that, in the context of desarguesian projective planes, for every intersection theorem there is a rational identity such that the plane satisfies the intersection theorem if and only if the division ring satisfies the rational identity. *Pappus's hexagon theorem holds in a desarguesian projective plane $\backslash mathbb\_D$ if and only if is a field; it corresponds to the identity $\backslash forall\; a,b\backslash in\; D,\; \backslash quad\; a\backslash cdot\; b=b\backslash cdot\; a$. *Fano's axiom (which states a certain intersection does ''not'' happen) holds in $\backslash mathbb\_D$ if and only if has characteristic $\backslash neq\; 2$; it corresponds to the identity . 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「Intersection theorem」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.