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 edgelengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.
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Communicated by GUO Xing-ming
Foundation item: the National Natural Science Foundation of China (10271071)
Biography: LI Xiao-yan (1963≈), Associate Professor, Doctor
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Xiao-yan, L., Bin-wu, H. & Gang-song, L. Mid-facets of a simplex. Appl Math Mech 25, 679–685 (2004). https://doi.org/10.1007/BF02438211
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DOI: https://doi.org/10.1007/BF02438211