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Mathematics of Computation

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On the solid-packing constant for circles


Author: Z. A. Melzak
Journal: Math. Comp. 23 (1969), 169-172
MSC: Primary 52.45
MathSciNet review: 0244866
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1969-0244866-8
Article copyright: © Copyright 1969 American Mathematical Society