Különböző négyzetek pakolása téglalapba

Meir és Moser (1968) tette fel a kérdést, 
hogy az $1\over2$, $1\over3$, $1\over4$,
$\ldots$, oldalhosszú négyzetek milyen ${\pi^2\over6}-1 +epsilon$ területű
téglalapban helyezhetők el. Paulhaus (1997) megmutatta, hogy  $\epsilon\le
8.032653301\ldots\cdot10^{-10}$, amit javítunk $\epsilon\le
6.8684858\cdot10^{-10}$ becslésre.


On packing of unequal squares in a rectangle

Meir and Moser (1968) originally noted that since
$\sum\limits_{i =2}^\infty {1\over i^2}={\pi^2\over6}-1$ it is
reasonable to ask whether the set of squares with sides of length
$1\over2$, $1\over3$, $1\over4$, $\ldots$, which we will call the
reciprocal squares, can be packed in a rectangle of area
${\pi^2\over6}-1$. Failing that, find the smallest $\epsilon$ such
that the reciprocal squares can be packed in a rectangle $R$ of area
${\pi^2\over6}-1+\epsilon$. Paulhaus (1997) proved that $\epsilon\le
8.032653301\ldots\cdot10^{-10}$. We improve this and show that
$\epsilon\le 6.8684858\cdot10^{-10}$.