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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We compare the volumes of projections of convex bodies and the volumes of the projections of their sections, and, dually, those of sections of convex bodies and of sections of their circumscribed cylinders. For L ⊂ R a convex body, we take n random segments in L and consider their ‘Minkowski average’ D. For fixed n, the pth moments of V (D) (1 ≤ p < ∞) are minimized, for V (L) fixed, by the ell...
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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This is a somewhat expanded form of a four hours course given, with small variations, first at the educational workshop Probabilistic methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks later at the Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity, Kent, Ohio, August 13-20, 2008. The main part of these notes gives yet a...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.81.303