Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfectly packing a square by squares of nearly harmonic sidelength   A well known open problem of Meir and Moser asks if the squares of sidelength
$1/n$ for $n \geq 2$ can be packed perfectly into a square of area
$\sum_{n=2}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}-1$. In this paper we show
that for any $1/2 < t < 1$, and any $n_0$ that is sufficiently large depending
on $t$, the squares of sidelength $n^{-t}$ for $n \geq n_0$ can be packed
perfectly into a square of area $\sum_{n=n_0}^\infty \frac{1}{n^{2t}}$. This
was previously known (if one packs a rectangle instead of a square) for $1/2 <
t \leq 2/3$ (in which case one can take $n_0=1$).

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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio