Covering the Plane with Congruent Copies of a Convex Disk
نویسنده
چکیده
It is shown that there exists a number d 0 < 8(2 p 3?3)=3 = 1:237604::, such that every compact convex set K with an interior point admits a covering of the plane with density smaller than or equal to d 0. This improves on the previous result 9], which showed that a density of 8(2 p 3 ? 3)=3 can always be obtained. Since the thinnest covering of the plane with congruent circles is of density 2= p 27 = 1:20919. . ., we strengthen the case for the conjecture that the smallest such number d 0 is 2= p 27.
منابع مشابه
Covering the Plane with Congruent Copies of a Convex Body
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 ...
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