Covering the Plane with Translates of a Triangle
نویسندگان
چکیده
منابع مشابه
On covering by translates of a set
In this paper we study the minimal number τ(S,G) of translates of an arbitrary subset S of a group G needed to cover the group, and related notions of the efficiency of such coverings. We focus mainly on finite subsets in discrete groups, reviewing the classical results in this area, and generalizing them to a much broader context. For example, we show that while the worst-case efficiency when ...
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چکیده ندارد.
15 صفحه اولCovering the Plane with Convex Polygons
It is proved that for any centrally symmetric convex polygonal domain P and for any natural number r, there exists a constant k = k(P, r) such that any k-fold covering of the plane with translates of P can be split into r simple coverings.
متن کاملCovering 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 ...
متن کاملCovering the Plane with Congruent Copies of a Convex Disk
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=...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2009
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-009-9203-1