We provide, for any $r\in (0,1)$, lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius $1$ and $r$. The lower bounds are mostly folk, but the upper bounds improve the best previously known ones for any $r\in[0.11,0.74]$. For many values of $r$, this gives a fairly good idea of the exact maximum density. In particular, we get new intervals for $r$ which does not allow any packing more dense that the hexagonal packing of equal discs.

翻译：我们为欧元半径1美元和1美元圆盘最大密度包装的任何美元(0,1美元)提供低限和上限。低限多数是民间的,但上限改进了任何美元[0.11,0.74]美元已知的最佳值。对于许多美元值,这很好地说明了准确的最大密度。特别是,我们得到美元新间隔,不允许任何比等盘的六边包装更密集的包装。