Radii of gyration and scattering functions of a torus and its derivatives

A torus is a simple body with cylindrical rotational symmetry. The radius of gyration and scattering function of a torus have been derived in cylindrical coordinates. Some derivatives of a torus (torus with elliptical cross section, tubular torus and two stacked tori) have been treated in the same manner as the torus. The radii of gyration are given by simple formulae and the scattering curves are easily obtained by numerical calculation using a personal computer.