Abstract
An arrangement ofn halfplanes (or oriented lines) divides the plane into a certain number of convex cells. The weight of a cell is the number of halfplanes containing it, Presumably the sum of the weights of all cells of an arrangement ofn halfplanes attains its maximum if the halfplanes define an (almost) regularn-gon. We show that this is true at least for oddn.
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Linhart, J. On the total weight of arrangements of halfplanes. Geom Dedicata 46, 165–172 (1993). https://doi.org/10.1007/BF01264915
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DOI: https://doi.org/10.1007/BF01264915