Covering of a rectangle by squares

2020/09/15 by Ozhegov, Fedor
#52C20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.07655

Abstract

We prove that one can cover the 1 × b rectangle by equal squares on both sides in one layer iff b = p ± √(p² - r²) , where p ≥ r ≥ 0 and p,q ∈ ℚ.

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• Perfectly packing a square by squares of nearly harmonic sidelength
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• Tiling a rectangle with the fewest squares
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