Abstract
Suppose that \(T(\alpha , \beta )\) is an obtuse triangle with base length 1 and with base angles measuring \(\alpha \) and \(\beta \) (where \(\alpha >90^{\circ }\)). Let S be a square with a side parallel to the base of \(T(\alpha , \beta )\) and let \(\{S_{i}\}\) be a collection of the homothetic copies of S. In this note a tight upper bound of the sum of the areas of squares from \(\{S_{i}\}\) that can be parallel packed into \(T(\alpha , \beta )\) is given. This result complements the previous upper bound obtained for \(\alpha \le 90^{\circ }\).
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Januszewski, J., Liu, X., Su, Z., Zielonka, Ł: Parallel packing squares into a triangle. Results Math. 77(1), 48 (2022)
Funding
This research was partially supported by National Natural Science Foundation of China (12271139), the NSF of Hebei Province (A2021205008), and the Science Foundation of Hebei Normal University (L2020Z01).
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Januszewski, J., Liu, X., Su, Z. et al. Parallel Packing Squares into an Obtuse Triangle. Results Math 78, 31 (2023). https://doi.org/10.1007/s00025-022-01803-4
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DOI: https://doi.org/10.1007/s00025-022-01803-4