Research On The Containment Measure Of Set Long-term Segment In A Special Kind Of Region

Integral geometry is a subject that investigating the natures of a graphic through a variety of integral,which is belonged to the category of differential geometry essentially. It originated in geometric probability research,The development has always been linked to geometric probability.The study of integral geometry start from Euclidean geometry of plane to three dimensional Euclidean space,extension to a high dimensional Euclidean and non-Euclidean space gradually,and then generaled to a homogeneous spaces that meet a certain conditions.In china,Wu Daren engaged in integral geometry more earlier than others.His first points in Euclidean space to the basic results of geometric.He extended the basic results of integral to the three-dimensional elliptic space at early.(Including the main formula) He also proved a series of inequalities of chord power integrals of convex bodies in the two-dimensional spaceand in the three-dimensional space.Chinese scholars have also received a number of other results.For example,Ren Delin had pushed the formula a fixed measure of long-term section within a convex body inndimensional Euclidean space and non-Euclidean space,and extended the inequality of chord power integrals toin the n-dimensional space,and generalized Buffon needle problem.This paper studies the problem is an important branch of integral geometry,discussed contain measure of set long-term segment in a special area,applied the concept of support function and restricted chord function,and the related theories of measure derivied the measure of such areas.And on this basis we get some results of the generalized Buffon problem,and then in this paper,on the basis of the classical isoperimetric inequality and the introduction of the concept of the mini annulus, according to the nature of the mini annulus,and in the situation of there has been the inequality of the mini annulus with the area and perimeter in the two-dimensional space.In this paper,we will rise the dimension to three-dimensional,in the three-dimensional space,the area rose to volume,perimeter to surface area.According to the discussion in the two-dimensional space we will get the inequality of the mini annulus with volume and surface area,and discussed the limiting case when the inequality established.Because the increase of dimension,the process becomes so complicated.this paper is divided into four chapters:The first chapter: Introduction:of the problem,introduces the background of the subject and the present research status at home and abroad,etc.The second chapter: Mainly study the contain measure of set long-term segment in a special area,calculate the contain measure using the formula of set long-term segment within a semi-circular. Also discussed the Buffon problem in this situation.Or to discussed the application problem of the contain measure in geometric probability in such situation.The third chapter: The main content of this chapter is on the basis of the inequality of the mini annulus and area and perimeter in the plane,to get the nequality of mini annulus and volume and area in the three-dimensional space.Because the increase of dimension,the process becomes so complicated. The fourth chapter: Development and prospect of papers...