论文标题
包装$ 1.35 \ cdot 10^{11} $矩形到一个单位广场
Packing $1.35\cdot 10^{11}$ rectangles into a unit square
论文作者
论文摘要
众所周知，$ \ sum \ limits_ {i = 1}^{\ infty} \ frac {1} {i（i+1）} = 1 $。 1968年，Meir和Moser要求找到最小的$ε$，以使所有尺寸的矩形$ 1/i \ times 1/（i + 1）$，$ i = 1，2，\ ldots $，都可以包装到一个单位广场或区域矩形$ 1 +ε$中。在本文中，我们表明我们可以将第一个$ 1.35 \ cdot10^{11} $矩形包装到单元广场中，并从此包装中给出$ε$的估计。
It is known that $\sum\limits_{i=1}^{\infty} \frac{1}{i (i+1)} = 1$. In 1968, Meir and Moser asked for finding the smallest $ε$ such that all the rectangles of sizes $1/i \times 1/(i + 1)$ for $i = 1, 2, \ldots$, can be packed into a unit square or a rectangle of area $1 + ε$. In this paper, we show that we can pack the first $1.35\cdot10^{11}$ rectangles into the unit square and give an estimate for $ε$ from this packing.
