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    蒋星耀. Descartes园定理的非欧推广[J]. 北京工业大学学报, 1982, 8(3): 18-21.
    引用本文: 蒋星耀. Descartes园定理的非欧推广[J]. 北京工业大学学报, 1982, 8(3): 18-21.
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    Jiang Xing-yao. An Extension of Descartes Circle Theorem in Non-Euclidean Spaces[J]. Journal of Beijing University of Technology, 1982, 8(3): 18-21.
    Citation: Jiang Xing-yao. An Extension of Descartes Circle Theorem in Non-Euclidean Spaces[J]. Journal of Beijing University of Technology, 1982, 8(3): 18-21.
    shu

    Descartes园定理的非欧推广

    An Extension of Descartes Circle Theorem in Non-Euclidean Spaces

      摘要
    • 摘要: 本文证明:如果在曲率为K的n维常曲率空间中n+2个球两两外切,用k1,k2……kn+2表示它们的主曲率,则下列关系成立:
      (???19880202???ki)2-n???19880202???ki2=2nK
      当K=0,n=2时,即得Descartes园定理的原始形式。

       

      Abstract: In this paper we have proved that if n+2 spheres in n-dimensional spaces with constant curvature K touch each other externally and if k1,k2,……kn+2 denote their principle curvatures, then the following relationhold.
      (???19880202???ki)2-n???19880202???ki2=2nK
      When K=0 and n=2, We get the original form of Descartes circle theorem.

       

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