  This technical note analyzes the properties of a random sequence of prolate
hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is
defined by a sample drawn randomly from the previous volume such that the
sample lies on the new surface (Fig. 1). Section 1 defines the prolate
hyperspheroid coordinate system and the resulting differential volume, Section
2 calculates the expected value of the new transverse diameter given a uniform
distribution over the existing prolate hyperspheroid, and Section 3 calculates
the convergence rate of this sequence. For clarity, the differential volume and
some of the identities used in the integration are verified in Appendix A
through a calculation of the volume of a general prolate hyperspheroid.
