【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……k_n（+2）表示它们的主曲率,则下列关系成立:（sum from i=1 to n+2 k_i）²-n sum from i=1 to n+2 k_i²=2nK当K=0,n=2时,即得Descartes园定理的原始形式。更多还原

【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 k 1,k 2,……kR+2 denote their principle curvatures, then the following relationhold.When K = 0 and n = 2, We get the original form of Descartes circle theorem.更多还原