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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 De Bruijn–Erdős theorem (incidence geometry) ： ウィキペディア英語版 De Bruijn–Erdős theorem (incidence geometry) In incidence geometry, the De Bruijn–Erdős theorem, originally published by , states a lower bound on the number of lines determined by ''n'' points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erdős is combinatorial, De Bruijn and Erdős noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester–Gallai theorem, by an induction on the number of points. ==Statement of the theorem== Let ''P'' be a configuration of ''n'' points in a projective plane, not all on a line. Let ''t'' be the number of lines determined by ''P''. Then, * ''t'' ≥ ''n'', and * if ''t'' = ''n'', any two lines have exactly one point of ''P'' in common. In this case, ''P'' is either a projective plane or ''P'' is a ''near pencil'', meaning that exactly ''n'' - 1 of the points are collinear. 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「De Bruijn–Erdős theorem (incidence 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.