Thomas, P. B. ; Dhar, D. (1994) The Hausdorf dimension of the Apollonian packing of circles Journal of Physics A: Mathematical and General, 27 (7). pp. 2257-2268. ISSN 0305-4470
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Official URL: http://iopscience.iop.org/0305-4470/27/7/007
Related URL: http://dx.doi.org/10.1088/0305-4470/27/7/007
Abstract
We formulate the problem of determining the Hausdorf dimension, df, of the Apollonian packing of circles as an eigenvalue problem of a linear integral equation. We show that solving a finite-dimensional approximation to this infinite-order matrix equation and extrapolating the results provides a fast algorithm for obtaining high-precision numerical estimates for df. We find that df=1.305 686 729(10). This is consistent with the rigorously known bounds on df, and improves the precision of the existing estimate by three orders of magnitude.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Physics. |
| ID Code: | 82187 |
| Deposited On: | 10 Feb 2012 04:14 |
| Last Modified: | 10 Feb 2012 04:14 |
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