The Common Reckon Method About Mean Distance Of Two Points Of A Convex Domain

Convex bodies are the research objects in the paper .This paper concerns the mean distance of two points of a convex domain.The definition of generalized support function: Letσbe the length of the chord obtained by intersecting the line G with a convex domain .If G∩(?)D≠φand G∩intD=φ,letσ=0.Forσ≥0,0≤φ≤2Ï€,define: p(σ,φ)= sup{p:m[G∩(intD)]=σ},Which is called the generalized support function of D .The definition of mean distance of two points of a convex domain:Let K be a bounded plane convex set ,the mean distance between the two points of K,is defined by E(r)= 1/(F²)∫_P1,P2∈KrdP₁∧dP₂, F the area of K, r is the distance between P₁ and P₂.The reckon method has not been provided by others.Generalized support function is a very important concept in plane convex sets, it play a crucial role in discuss kinematic measure of convex sets. This essay uses the generalized support function, providing a common method which reckons the mean distance of two points of a convex domain. And reckon the mean distance of two points in familiar convex sets as examples.