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Cutting Polygons Composed of Equal Rectangles into Similar Rectangles

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Abstract

Assume that a polygon is composed of equal rectangles. We find all quadratic irrationalities \(r\) for which the polygon under study can be cut into similar rectangles with aspect ratio \(r\).

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References

  1. F. A. Sharov, “Rectangling a rectangle with a prescribed aspect ratios,” in Matem. Prosv., Ser. 3 (MTsNMO, Moscow, 2016), Vol. 20, pp. 200–214; English transl. in https://arxiv.org/abs/1604.00316.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, 101000, Russia

    I. V. Novikov

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  1. I. V. Novikov
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Correspondence to I. V. Novikov.

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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 736–743 https://doi.org/10.4213/mzm13262.

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Novikov, I.V. Cutting Polygons Composed of Equal Rectangles into Similar Rectangles. Math Notes 110, 726–731 (2021). https://doi.org/10.1134/S0001434621110092

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  • DOI: https://doi.org/10.1134/S0001434621110092

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