Abstract
It is quite rare that a simple area optimization result bears somebody’s name. One of these statements, called Hajós’ Lemma, became particularly known, mainly because of its esthetic appearance and due to its application at solving the densest circle packing problem. Hajós considered a pair of concentric circles and wanted to find the minimum area polygon among those polygons which contain the smaller circle and whose vertices are outside of the larger circle. In this paper we state and prove two generalizations of Hajós’ Lemma. In the first version we allow the circles to be non concentric, in the second version we consider disc polygons instead of usual polygons.
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A. J. was supported by EFOP-3.6.1-16-2016-00003 founds, Consolidate long-term R and D and I processes at the University of Dunaujvaros.
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Bezdek, A., Joós, A. Area minimization of special polygons. Acta Math. Hungar. 160, 33–44 (2020). https://doi.org/10.1007/s10474-019-00957-y
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DOI: https://doi.org/10.1007/s10474-019-00957-y