  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 $n_0=1$).

Metric Geometry