# The disk-packing constant

@article{Boyd1971TheDC, title={The disk-packing constant}, author={David W. Boyd}, journal={aequationes mathematicae}, year={1971}, volume={7}, pages={182-193} }

- Published 1971
DOI:10.1007/bf01818512

The lower bound was subsequently improved by Wilker [8] to 1.059, and by the author [2] to 1.28467. An improved upper bound of 1.5403 . . . . (9+x/41)/10 was proved in [3], but the arguments there, although they apply to sphere packings in higher dimensions, are too general in nature to yield a significant improvement of this bound. In this paper, we present a method of attack which gives both upper and lower bounds. In fact, for any integer x, we obtain bounds 2 (K)<S</~(x) such that /z ( x… CONTINUE READING

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## N T ] 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory

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## N T ] 1 1 Se p 20 00 Apollonian Circle Packings : Number Theory

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## N T / 0 00 91 13 v 2 1 7 O ct 2 00 3 Apollonian Circle Packings : Number Theory

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## The sequence of radii of the Apollonian packing

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## Apollonian Circle Packings: Number Theory

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## Apollonian Circle Packings : Number

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