On the solid-packing constant for circles
HTML articles powered by AMS MathViewer
- 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
- S. N. Mergelyan, Uniform approximations to functions of a complex variable, Amer. Math. Soc. Translation 1954 (1954), no. 101, 99. MR 0060015
- Oscar Wesler, An infinite packing theorem for spheres, Proc. Amer. Math. Soc. 11 (1960), 324–326. MR 112078, DOI 10.1090/S0002-9939-1960-0112078-8
- Z. A. Melzak, Infinite packings of disks, Canadian J. Math. 18 (1966), 838–852. MR 203594, DOI 10.4153/CJM-1966-084-8
- E. N. Gilbert, Randomly packed and solidly packed spheres, Canadian J. Math. 16 (1964), 286–298. MR 162183, DOI 10.4153/CJM-1964-028-8
- H. S. M. Coxeter, Introduction to geometry, John Wiley & Sons, Inc., New York-London, 1961. MR 0123930 S. Saks, Theory of the Integral, 2nd ed., Hafner, New York, 1958.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 169-172
- MSC: Primary 52.45
- DOI: https://doi.org/10.1090/S0025-5718-1969-0244866-8
- MathSciNet review: 0244866