Research On Some Metric Properties Of A Simplex

In this thesis, by using theory of metric geometry and analytic method, some metric properties for an n-dimensional simplex in n-dimensional Euclidean space and relative some problems of geometric inequality are researched. Some geometric inequalities are established, and their applications are given.Chapter 1 briefly introduce development of the subject, especially concerning the study direction. And main results of the thesis are given.In the starting of chapter 2 and chapter 3, we introduce some concepts respectively which contain median, middle section, k-median, k-dimensional middle section and center section. And then, some classical theories are generalized from 2-dimension and 3-dimension to n-dimension in Euclidean space, we get some properties, geometric inequalities and their applications concerning k-dimensional middle section, middle sectional plane and incenter.Chapter 4 researches the relation between the points and the super-planes in E", and new formal n-dimensional Menelaus Theroy and n-dimensional Ceva Theroy are established.Chapter 5 researches the relation of profile area, high, circumradius and inradius, and establish n-dimensional Milosevic inequality. We research the relation of the circumradius and inradius involving a simplex and its Ceva simplex, and two correlation geometric inequalities are given.