Pach, JanosTardos, Gabor2012-07-272012-07-272012-07-27201210.1016/j.jcta.2012.03.011https://infoscience.epfl.ch/handle/20.500.14299/84242WOS:000305820200001It is an old problem of Danzer and Rogers to decide whether it is possible to arrange 0(1/epsilon) points in the unit square so that every rectangle of area epsilon > 0 within the unit square contains at least one of them. We show that the answer to this question is in the negative if we slightly relax the notion of rectangles, as follows.enDanzer-Rogers problemPiercingQuasi-rectanglesEpsilon-netsWeak Epsilon-NetsPointsBoundstext::journal::journal article::research article