Chinese Quarterly Journal of Mathematics ›› 2019, Vol. 34 ›› Issue (2): 204-208.doi: 10.13371/j.cnki.chin.q.j.m.2019.02.008

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Two Geometric Inequalities in Spherical Space

  

  1. Mingda middle school,Changsha,Hunan
  • Accepted:2015-04-19 Online:2019-06-30 Published:2020-10-06
  • About author:ZHOU Yong-guo(1962-), male, native of Yuangling, Hunan, High-school senior teacher, major research interests: elementary mathematics and high-dimentional geometric inequalities.

Abstract: In this paper, by using the theory and method of distance geometry, we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space. They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space. 

Key words: spherical space, simplex, volume, edge-length, height, inequality

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