Problems Relatived To Convex Bodies Of Illuminating Composition

In the middle of the20th century, Hadwiger had been presented the famousconjecture that the convex body was covered and illuminated——Hadwigerconjecture. More than half a century, Hadwiger conjecture had been aroused manymathematicians attention and research. Although, it had been solved about Hadwigerconjecture for2dimensional convex body. But, for3dimensional space and above,that we was know fewly and want to completely solve far away. So, If we want toresolve Hadwiger conjecture still need more efforts and more innovation.Because it is, this article will try to through study the quantity characteristics ofconvex body, will study the covering number of the convex body by the way ofindirect estimation and hope to contribute to the progress of Hadwiger conjecture.Firstly this article reviewed the Hadwiger conjecture the origin and itsequivalent firstly form and through studyed the number features of K toimplementing for indirect estimation.As the main content of this article, We introduced the concept of the convexbody of illumination composition. Then we considered the location of the convexbody about the convex body of illuminating composition, we introduced a newgeometric constant ι (K,m).After, we studied some simple properties about ι(K,m)and the invariance property of the nonsingular linear transformation. And usedthe ι (K,m). Hadwiger guess got another equivalent form.Finally, we calculate the value of ι (K,m)of some convex polyhedron and weestimate the value of the ι (K,m)about unit sphere of2dimensional Europeanspace...