On the distribution of distances between random points on a sphere

The theoretical distribution of distances between random points on the surface of a sphere is derived. The result is a cosine-exponential distribution of distances. This result may be applied in seismology, in order to compare the actual distribution of distances between earthquakes with the expected distribution on the assumption of random occurrence. This provides a criterion for detecting triggering effects at epicentral distances of 2 to 17 fault lengths.