Decompositions of a rectangle into non-congruent rectangles of equal area
Data de publicació2021-06
MetadadesMostra el registre d'unitat complet
In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called 'Mondrian art problem' that asks a similar question for dissections with rectangles of integer sides. Here, we generalize the Mondrian problem by allowing rectangles of real sides. In this case, we show that the minimum value of k for a rectangle to have a 'perfect Mondrian partition' (that is, with non-congruent equal-area rectangles) is seven. Moreover, we prove that such a partition is unique (up to symmetries) and that there exist exactly two proper perfect Mondrian partitions for k=8. Finally, we also prove that any square has a perfect Mondrian decomposition for k >= 7.
És part deDiscrete Mathematics, 2021, vol. 344, num. 6, p. 112389
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