A disc packing in the plane is compact if its contact graph is a triangulation. There are $9$ values of $r$ such that a compact packing by discs of radii $1$ and $r$ exists. We prove, for each of these $9$ values, that the maximal density over all the packings by discs of radii $1$ and $r$ is reached for a compact packing (we give it as well as its density).

中文翻译：

---

二元盘填料的密度：9 种紧凑填料

如果其接触图是三角剖分，则平面中的圆盘包装是紧凑的。存在 $9$ 的 $r$ 值，因此存在由半径为 $1$ 和 $r$ 的圆盘组成的紧凑包装。我们证明，对于这些 $9$ 值中的每一个，对于紧凑封装（我们给出它以及它的密度），半径为 $1$ 和 $r$ 的圆盘的所有填料都达到了最大密度。