Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (6): 679-685.

• Articles • Previous Articles     Next Articles

MID-FACETS OF A SIMPLEX

LI Xiao-yan1,2, HE Bin-wu1,3, LENG Gang-song1   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China;
    2. Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China;
    3. Department of Mathematics, Hunan University of Science and Technology, Yueyang 414000, P. R. China
  • Received:2002-09-01 Revised:2003-11-25 Online:2004-06-18 Published:2004-06-18
  • Supported by:

    the National Natural Science Foundation of China(10271071)

Abstract: The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.

2010 MSC Number: 

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