An Extension of Descartes Circle Theorem in Non-Euclidean Spaces

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.

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.

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,……k_n+2 denote their principle curvatures, then the following relationhold.
(???19880202???k_i)²-n???19880202???k_i²=2nK
When K=0 and n=2, We get the original form of Descartes circle theorem.

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