Covering the Plane with Congruent Copies of a Convex Body

Content Provider	Semantic Scholar
Author	Kuperberg, Wlodzimierz
Copyright Year	1989
Abstract	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-lattice kind consisting of translates of K and translates of — K.
Starting Page	82
Ending Page	86
Page Count	5
File Format	PDF HTM / HTML
DOI	10.1112/blms/21.1.82
Alternate Webpage(s)	http://blms.oxfordjournals.org/cgi/reprint/21/1/82.pdf
Alternate Webpage(s)	https://doi.org/10.1112/blms%2F21.1.82
Volume Number	21
Language	English
Access Restriction	Open
Content Type	Text