Disk covering problem

The disk covering problem was proposed by C. T. Zahn in 1962.

Given an integer $n$, the problem asks for the smallest real number $r(n)$ such that $n$ disks of radius $r(n)$ can be arranged in such a way as to cover the unit disk.

The best solutions to date are as follows:

n	r(n)
1	1
2	1
3	$1/2*sqrt(3)$
4	$1/2*sqrt(2)$
5	0.609382...
6	0.555905...
7	$1/2$
8	0.445041...
9	0.414213... $1/2*sqrt(3)$
10	0.394930...

Method

This is the best know layout for r(9) and r(10):

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.