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).

翻译：如果接触图是三角形,平面上的盘片包装是紧凑的,其价值为9美元,因此,光盘包装的金额为1美元和1美元。 我们证明,就每张9美元价值而言,光盘包装的最大密度为1美元和1美元(我们既提供其密度,也提供其密度)。