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- W3043117569 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 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 $kge 7$." @default.
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- W3043117569 date "2020-07-19" @default.
- W3043117569 modified "2023-10-16" @default.
- W3043117569 title "Decompositions of a rectangle into non-congruent rectangles of equal area" @default.
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- W3043117569 doi "https://doi.org/10.48550/arxiv.2007.09643" @default.
- W3043117569 hasPublicationYear "2020" @default.
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