Research About Some Geometric Inequalities For An N-dimensional Simplex In E～n

In this article, the problems of geometric inequality for an n-dimensional simplex in E~n are discussed by using convex geometry theory, method of distance geometry and analytic method. Some new geometric inequalities are established and some extensions are given.Altogether the full text divides four chapers.In the first chaper, the main content is the concise introduction about convex geometry research present situation and development history, some new sciences related to convex geometry are introduced. some basic concepts and some important conclusions about simplex are introduced as well.In the second chapter some geometric inequalities concerning an interior point of a simplex are studied, Simultaneously two new geometries inequalities are established.In the third chapter the main content is Neuberg-Pedoe inequality, One kind of n-dimensional Neuberg-Pedoe inequality is improved and two new inequalities are established.In the fourth chapter The content is mainly involved geometric inequalities about inscribed simplex, And in this chapter a kind of forms divisions to the Euler inequality is given.