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Parallel covering a rhombus with squares

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Abstract

Suppose that \(R^{\alpha }\) is a rhombus with side length 1 and with the acute angle \(\alpha \). Let \(\{S_{i}\}\) be a collection of squares. A tight lower bound of the sum of the areas of squares from \(\{S_{i}\}\) that permit a parallel covering of \(R^{\alpha }\) is given.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Number 12171362) and the Doctoral Research Project of Tianjin Normal University (Grant Number 52XB2112).

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Authors and Affiliations

  1. College of Mathematical Science, Tianjin Normal University, Tianjin, 300387, People’s Republic of China

    Chen-Yang Su

  2. College of Science, Tianjin University of Commerce, Tianjin, 300134, People’s Republic of China

    Xue Li

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  1. Chen-Yang Su
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  2. Xue Li
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Correspondence to Xue Li.

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Su, CY., Li, X. Parallel covering a rhombus with squares. Period Math Hung 88, 190–203 (2024). https://doi.org/10.1007/s10998-023-00547-0

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  • DOI: https://doi.org/10.1007/s10998-023-00547-0

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