Abstract
We show that squares of sides of length \( 1\), \(2^{-t}\), \(3^{-t}\), \(4^{-t}\),\(\ldots \) can be packed perfectly into a square, provided \( 1/2 < t \le 2/3\). Moreover, we prove that cubes of edges of length \( 1\), \(2^{-t}\), \(3^{-t}\), \(4^{-t}\), \( \ldots \) can be packed perfectly into a box, provided \( 2/3 < t \le 4/11\).
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Januszewski, J., Zielonka, Ł. A note on perfect packing of squares and cubes. Acta Math. Hungar. 163, 530–537 (2021). https://doi.org/10.1007/s10474-020-01114-6
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DOI: https://doi.org/10.1007/s10474-020-01114-6