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On the solid-packing constant for circles
| Content Provider | Semantic Scholar |
|---|---|
| Author | Melzak, Z. A. |
| Copyright Year | 1969 |
| Abstract | 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 |
| Starting Page | 169 |
| Ending Page | 172 |
| Page Count | 4 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0025-5718-1969-0244866-8 |
| Volume Number | 23 |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1969-23-105/S0025-5718-1969-0244866-8/S0025-5718-1969-0244866-8.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0025-5718-1969-0244866-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
