The Average Distance Betreen Two Points Of A Convex Set

Using the concept of generalized support functions, discussed the semicircle domain and an isosceles trapezoid domain these two kinds of symmetry is not very ideal of convex domain average distance between two points in the literature. Ever established category for convex domain, the average distance between two points of the universal formula, but did not give detailed derivation. After also appeared many specific results, but only some of the simpler, about symmetry good convex domain (e.g., square, triangle, rectangle, is round). This study semicircle domain and an isosceles trapezoid domain average distance between two points of relatively more difficult, embodies the regional classification, generalized support functions and maximum chord length function and the method of calculating the chord-power integrals and computing. In this paper, the discussion about an isosceles trapezoid domain method, for no general trapezoid also apply symmetry.General support function is planar convex domain of a very important concept in discussion.Convex domain, the average distance between two points of problem is integral geometry in a very important topic, it application in geometry problems has an important role. Convex domain, the average distance between two problems in a wide range of applications background.This paper generalized support function and convex domain chord-power integrals and the maximum chord length function the convex domain, the average distance between two points, and draw the calculation convex domain, the average distance between two points with the general formula: (?)(including F for convex set K area) Among them (?)And by using the formula and from the semicircle domain and an isosceles trapezoid domain, the average distance between two points.