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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 quadratic set ： ウィキペディア英語版 quadratic set In mathematics, a quadratic set is a set of points in a projective plane/space which bears the same essential incidence properties as a quadric (conic section in a projective plane, sphere or cone or hyperboloid in a projective space). == Definition of a quadratic set== Let be $\backslash mathfrak\; P=(,,\backslash in)$ a projective space. A non empty subset $$ of $$ is called quadratic set if :(QS1) Any line $g$ of $$ intersects $$ in at most 2 points or is contained in $$. :($g$ is called exterior, tangent and secant line if $|g\backslash cap\; |=0,\; \backslash \; |g\backslash cap\; |=1$ and $|g\backslash cap\; |=2$ respectively.) :(QS2) For any point $P\backslash in$ the union $\_P$ of all tangent lines through $P$ is a hyperplane or the entire space $$. A quadratic set $$ is called non degenerated if for any point $P$ set $\_P$ is a hyperplane. The following result is an astonishing statement for finite projective spaces. Theorem(BUEKENHOUT): Let be $\backslash mathfrak\; P\_n$ a ''finite'' projective space of dimension $n\backslash ge\; 3$ and $$ a non degenerated quadratic set which contains lines. Then: $\backslash mathfrak\; P\_n$ is pappian and $$ is a ''quadric'' with index $\backslash ge\; 2$. 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「quadratic set」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.