Circumscribe a disc with a regular hexagon, and circumscribe the hexagon with a circle. This gives what I call the hexagonally circumscribed circle of the original disc. It is a concentric circle whose radius is |
We shall need also another property of these circumscribed circles. Suppose two of them intersect, but that the discs themselves do not intersect. Then that intersection can only intersect the Voronoi cell of a third disc if the three discs are mutually touching in the configuration of discs in a hexagonal packing. For suppose In the diagram to the right, this means that the pointsin the yellow rhombus are never in the Voronoi cellof the third disc. | the hexagonally circumscribed circles. As a consequence, points in the yellow rhombus never lie inthe Voronoi cell of a third disc.Disc three is live. |