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平面上Clifford定理的一般证明

Proof of Clifford theorem on the plane
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摘要 Clifford定理作为几何学的一个最基本定理有着广泛的应用,读者通过该定理可以从整体上提高对几何学的认识。学习Clifford定理须从其证明入手,然而,目前很难找到一个通俗且完整的证明。文章利用实交比值引理给出了平面上Clifford定理的一般证明,这一方法对任意n条一般直线都适用。 Clifford theorem is one of the most important theorems in mathematics.A general picture in Geometry can be obtained by means of this theorem.Therefore,its proof becomes the key for understanding the Clifford theorem.However,we may not able to find a understandable proof cover the whole theorem.This paper gives a proof of Clifford theorem for n general lines in the plane by using the simple real cross ratio lemma.
作者 拉巴次仁
机构地区 西藏大学理学院
出处 《西藏大学学报(社会科学版)》 CSSCI 2010年第3期93-97,共5页 Journal of Tibet University
关键词 Clifford定理证明 实交比值引理 一般直线 Clifford Theorem Clifford Theorem Proof Real Cross Ratio Lemma General lines
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参考文献21

  • 1拉巴次仁.平面上的Clifford系列定理[J].西藏大学学报(社会科学版),2009,24(5):114-115. 被引量:1
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二级参考文献10

  • 1W.K.Clifford.Synthetic Proof of Miquel‘s Theorem[].Math-ematical Papers.1882
  • 2Lian-shin Hahn.Complex Numbers&Geometry[]..1994
  • 3Roger Fenn.Geometry[]..2003
  • 4J.W.CLAWSON.Ursinus College,A Chain of Circles As-sociated With The 5-Line[].American Journal of Mathematics.
  • 5M.Berger.Geometry1,2[]..1987
  • 6Hongbo Li,Ronghua Xu,Ningzhang.On Miquel’sFive-Circle Theorem[].Computer Algebra and Geometric Algebra with Applications.
  • 7Herbert W.Richmond.On a Chain of Theorems due toHomersham Cox[]..1941
  • 8H.W.Richmond.A hain of Theorems For Lines In Space[]..1941
  • 9H.W.Richmond.ANoteonthe"Morley-Pesci-deLongchamps"Chain of Theorems[]..1939
  • 10W.B.Carver.The failure of the Clifford chain[].American Journal of Mathematics.1920

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