Abstract
In the present paper, we discuss the measure of the point pairs whose distance are less than a distance r in a given area. By differentiating this measure with respect to r, we get the function f(r) which is called by distance distribution. Using formulae in Integral Geometry, we get an approximate polynomial for the distance distribution in an arbitrary convex region. The approximate expression consists of the area S and the perimeter L of the region and have good fitness to the numerical distributions of governmental districts in Tokyo.
