The disk covering problem asks for the smallest real number such that disks of radius can be arranged in such a way as to cover the unit disk. Dually, for a given radius ε, one wishes to find the smallest integer n such that n disks of radius ε can cover the unit disk.
The best solutions to date are as follows:
This is the best known layout strategy for r(9) and r(10):
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- Weisstein, Eric W. "Disk Covering Problem." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/DiskCoveringProblem.html
- Finch, S. R. "Circular Coverage Constants." §2.2 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 484–489, 2003.
- Illustrations of circles covering circles
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