How to build a barricade
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.
scientific article; zbMATH DE number 3861937