The sequence of radii of the Apollonian packing

Author:
David W. Boyd

Journal:
Math. Comp. **39** (1982), 249-254

MSC:
Primary 52A45

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658230-7

MathSciNet review:
658230

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Abstract: We consider the distribution function of the curvatures of the disks in the Apollonian packing of a curvilinear triangle. That is, counts the number of disks in the packing whose curvatures do not exceed *x*. We show that approaches the limit *S* as *x* tends to infinity, where *S* is the exponent of the packing. A numerical fit of a curve of the form to the values of for produces the estimate which is consistent with the known bounds .

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0658230-7

Article copyright:
© Copyright 1982
American Mathematical Society