1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向...1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向量,令则把θ<sub>?</sub>=arcsin|D<sub>?</sub>|定义为此单形的第 i 个界面对应的顶点角.从这个定义出发,Barto（?）建立了 n 维单形的正弦定理:展开更多
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 ...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.展开更多
文摘1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向量,令则把θ<sub>?</sub>=arcsin|D<sub>?</sub>|定义为此单形的第 i 个界面对应的顶点角.从这个定义出发,Barto（?）建立了 n 维单形的正弦定理:
文摘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.
