On the Random Disorientation of two Cubes

Abstract

We are given two identical symmetrical bodies (e.g., cubes) with independent random orientations; then we can always, in several ways, turn one of these bodies about some axis through its centre of gravity, so as to bring it into the same orientation as the other body. The smallest angle of rotation needed will be called the disorientation, d, of the two bodies, and we shall be concerned with the distribution of d under these conditions.