Dilution assay
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.[1]
The best solutions to date are as follows:
| n | r(n) |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | |
| 4 | |
| 5 | 0.609382... |
| 6 | 0.555905... |
| 7 | |
| 8 | 0.445041... |
| 9 | 0.414213... |
| 10 | 0.394930... |
Method
This is the best known layout strategy for r(9) and r(10):
References
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External links
- 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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