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| MID-FACETS OF A SIMPLEX | |
| 引用本文： | 李小燕,何斌吾,冷岗松. MID-FACETS OF A SIMPLEX[J]. 应用数学和力学(英文版), 2004, 25(6): 679-985. DOI: 10.1007/BF02438211 |
| 作者姓名： | 李小燕 何斌吾 冷岗松 |
| 作者单位： | [1]DepartmentofMathematics,ShanghaiUniversity,Shanghai200436,P.R.China [2]DepartmentofMathematics,HunanUniversityofScienceandTechnology,Yueyang414000,P.R.China |
| 基金项目： | theNationalNaturalScienceFoundationofChina (10 2 710 71) |
| 摘 要： | 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 us 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. |
| 关 键 词： | 单形 中值线 几何学 Grassmann代数 几何不等式 欧几里德空间 |
| 收稿时间： | 2002-09-01 |
Mid-facets of a simplex |
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| Li Xiao-yan,He Bin-wu,Leng Gang-song. Mid-facets of a simplex[J]. Applied Mathematics and Mechanics(English Edition), 2004, 25(6): 679-985. DOI: 10.1007/BF02438211 | |
| Authors: | Li Xiao-yan He Bin-wu Leng Gang-song |
| Affiliation: | 1. Department of Mathematics,Shanghai University,Shanghai 200436,P.R.China;Department of Mathematics,Hunan Normal University,Changsha 410081,P.R.China 2. Department of Mathematics,Shanghai University,Shanghai 200436,P.R.China;Department of Mathematics,Hunan University of Science and Technology,Yueyang 414000,P.R.China 3. Department of Mathematics,Shanghai University,Shanghai 200436,P.R.China; |
| 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. |
| Keywords: | simplex mid-facet median line Grassmann algebra geometric inequality |
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