On the solid-packing constant for circles

Melzak, Z. A.

doi:10.1090/S0025-5718-1969-0244866-8

On the solid-packing constant for circles
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by Z. A. Melzak PDF

Math. Comp. 23 (1969), 169-172 Request permission

Abstract:

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.

References

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