“Mergelyan-Wesler Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Mergelyan-Wesler Theorem

释义

Mergelyan-Wesler Theorem

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

(1)

Define

(2)

Then there is a number

such that

diverges for

and converges for

. The abovetheorem 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.

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