On the Solid-Packing Constant for Circles

A solid packing of a circular disk $U$ is a sequence of disjoint open circular subdisks ${U_{1,}}{U_{2,}} \cdots$ whose total area equals that of $U$. The MergelyanWesler 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.