Abstract

How efficiently can a large square of side length x be packed with non-overlapping unit squares? In this note, we show that the uncovered area W(x) can be made as small as \(O(x^{3/5})\). This improves an earlier estimate which showed that \(W(x) = O\bigl (x^{({3+\sqrt{2}})/{7} }\log x\bigr )\).

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