J4 ›› 2011, Vol. 46 ›› Issue (2): 117-122.

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The stability of some inequalities for a simplex

YANG Shi-guo1, WANG Wen2, QIAN Di2, PAN Juan-juan2   

  1. 1. Department of Mathematics, Hefei Normal University,  Hefei 230061, Anhui, China;
    2. School of Mathematics Sciences, Anhui University, Hefei 230039, Anhui, China
  • Received:2009-12-24 Online:2011-02-16 Published:2011-03-30


Using the theory and method of distance geometry,  the problems of stability of some geometric inequalities for an n-dimensional simplex in the Euclidean space is studied. From the deviation regular metric of two simplexes, the stabilities of four important geometric inequalities of an n-dimensional simplex are proved, and the stability versions of these geometric inequalities for a simplex are given.

Key words:  simplex; circum-radius; in-radius; radius of escribed ball; stability

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