Covering density

Summary

The covering density of a covering of space by bodies measures, on average, how many times each point is covered. It is at least $1$, and the covering problem asks for the smallest possible value, the covering density of the body. It is the counterpart of the packing density, with overlaps allowed and gaps forbidden. For discs in the plane the optimum is $2\pi/\sqrt{27} \approx 1.2092$, given by the hexagonal lattice arrangement.