A note on perfect packing of squares and cubes
type: Item
instance of: scholarly article
title: A note on perfect packing of squares and cubes
zbMATH Open document ID: 1474.52026
author: Janusz Januszewski
author: Łukasz Zielonka
published in: Acta Mathematica Hungarica
publication date: 2021-06-29T00:00:00Z
review text: A packing of squares into a rectangle is said to be perfect if its area equals to the sum of areas of the squares. Analogously, using volume, a perfect packing of cubes into a rectangular parallelotope is defined. The authors prove that the sequence of squares of sides of length \(1, 2^{-t}, 3^{-t}, \dots\) can be perfectly packed into a square provided \(2/3 < t \leq 4/11\). In order to show this, they modify a lemma of \textit{A. Joós} [``Perfect square packings'', Math. Rep., Buchar. (to appear)]. Moreover, the authors prove that the sequence of cubes of length \(1, 2^{-t}, 3^{-t}, \dots\) can be packed perfectly into a rectangular parallelotope if \(1/3 < t \leq 4/11\). This statement is obtained by a slight modification of the proof by \textit{A. Joós} [Acta Math. Hungar. 156, 375--384 (2018; Zbl 1413.05047)], who showed a bit weaker property.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52C15
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 7364764
zbMATH Keywords: cubes
zbMATH Keywords: perfect packing
zbMATH Keywords: square
MaRDI profile type: Publication
full work available at URL: s10474-020-01114-6
OpenAlex ID: W3129159089
cites work: On packing unequal squares
cites work: Perfect square packings
cites work: A note on three Moser's problems and two Paulhus' lemmas
cites work: Perfect packing of cubes
cites work: On packing of squares and cubes
cites work: An algorithm for packing squares
cites work: Perfect packings of squares using the stack-pack strategy
DOI: 10.1007/S10474-020-01114-6
description: scientific article; zbMATH DE number 7364764