Covering the Plane with Congruent Copies of a Convex Body

@inproceedings{Kuperberg1989CoveringTP,
title={Covering the Plane with Congruent Copies of a Convex Body},
author={Wlodzimierz Kuperberg},
year={1989}
}

It is shown that every plane compact convex set /f with an interior point admits a covering of the plane with density smaller than or equal to 8(2\/3 — 3)/3 = 1.2376043 For comparison, the thinnest covering of the plane with congruent circles is of density 2n/\Z21 = 1.209199576... (see R. Kershner [3]), which shows that the covering density bound obtained here is close to the best possible. It is conjectured that the best possible is 2n/y/21. The coverings produced here are of the double… CONTINUE READING