Decompositions of a rectangle into non-congruent rectangles of equal area
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. He...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/71007 |
| Acceso en línea: | https://doi.org/10.1016/j.disc.2021.112389 http://hdl.handle.net/10459.1/71007 |
| Access Level: | acceso abierto |
| Palabra clave: | Mondrian problem Non-congruent rectangles Dissection Digraph |
| Sumario: | 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. |
|---|