Decompositions of a rectangle into non-congruent rectangles of equal area
Visualitza/Obre
Cita com:
hdl:2117/355588
Tipus de documentArticle
Data publicació2021-06
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
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 equalarea 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.
Descripció
© 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitacióDalfo, C. [et al.]. Decompositions of a rectangle into non-congruent rectangles of equal area. "Discrete mathematics", Juny 2021, vol. 344, núm. 6, p. 112389:1-112389:23.
ISSN0012-365X
Versió de l'editorhttps://www.sciencedirect.com/science/article/abs/pii/S0012365X21001023?via%3Dihub
Altres identificadorshttps://arxiv.org/pdf/2007.09643.pdf
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