## Mergelyan-Wesler Theorem

Let be an infinite set of disjoint open Disks of radius such that the union is almost the unit Disk. Then

 (1)

Define
 (2)

Then there is a number such that diverges for and converges for . The above theorem gives
 (3)

There exists a constant which improves the inequality, and the best value known is
 (4)

References

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, pp. 36-37, 1983.

Mandelbrot, B. B. Fractals. San Francisco, CA: W. H. Freeman, p. 187, 1977.

Melzack, Z. A. On the Solid Packing Constant for Circles.'' Math. Comput. 23, 1969.