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A number of authors have previously found the probability P n (r) that two points uniformly distributed in an n-dimensional sphere are separated by a distance r. This result greatly facilitates the calculation of self-energies of spherically symmetric matter distributions interacting by means of an arbitrary radially symmetric two-body potential. We present here the analogous results for P 2 (r;⑀) and P 3 (r;⑀) which respectively describe an ellipse and an ellipsoid whose major and minor axesdoi:10.1063/1.533249 fatcat:6lxti5j42zer5ovrsvmk45vc2a