On the Solid-Packing Constant for Circles

A solid packing of a circular disk U is a sequence of disjoint open circular subdisks Ul, U2, . whose total area equals that of U. The Mergelyan- Wesler theorem asserts that the sum of radii diverges; here numerical evidence is presented that the sum of ath powers of the radii diverges for every a < 1.306951. This is based on inscribing a particular sequence of 19660 disks, fitting a power law for the radii, and relating the exponent of the power law to the above constant. U 1. We shall be concerned here with solid packings of a closed circular disk U. Such a packing P consists of a sequence of open pairwise disjoint circular disks U1, U2, which are subsets of U; P is called solid if the areas of U and U n= Un are the same. Let r be the radius of U and rn that of Un so that the condition for a