The use of the geometrical method of "hierarchical surface expansion" for revealing some average statistical regularities

The method that consists in representing a surface by an infinite hierarchy of nonintersecting circles land representing the surface area by an infini te series of sums) whose diameters are small compared to radii of curvature is proposed. As a simple example, the total cross-sectional area of a conv ex body is found-the area of its orthogonal projection (geometrical shadow) averaged over all three angular degrees of freedom of a solid body. This c ross-sectional area turned out to be equal to a quarter of the surface area of the body. For disperse systems, the method provides a direct procedure for finding some average statistical regularities of structural properties that are the same for monodisperse and polydisperse systems.