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How to build a barricade. (English) Zbl 0542.52010
Given a packing $$\mathcal C=\{C_i\mid i\in I\}$$ of congruent copies of a strictly convex planar set $$C$$ in a parallel strip $$S$$ of width $$w$$ and a straight line $$\ell$$, let $$| \ell \cap \mathcal C|$$ denote the sum of the lengths of the segments $$\ell \cap C_i$$ over all $$i\in I$$. It is proved that $\sup_{\mathcal C}\inf_{\ell}| \ell \cap {\mathcal C}| =(\delta(C)+o(1))w,$ where $$\delta (C)$$ is the density of the densest packing of congruent copies of $$C$$ in the plane. Some generalizations are also considered.
Reviewer: Peter Frankl

##### MSC:
 52C17 Packing and covering in $$n$$ dimensions (aspects of discrete geometry) 60D05 Geometric probability and stochastic geometry
##### Keywords:
densest packing; convex sets; independent random variables
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##### References:
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