Five Disks Problem
Given five equal Disks placed symmetrically about a given center, what is the smallestRadius 
for which the Radius of the circular Area covered by the five disks is 1? The answer is
, where 
is the Golden Ratio, and the centers 
of the disks 
, ..., 5are located at
The Golden Ratio enters here through its connection with the regular Pentagon. If the requirement that thedisks be symmetrically placed is dropped (the general Disk Covering Problem), then the Radius for
disks can be reduced slightly to 0.609383... (Neville 1915).See also Arc, Disk Covering Problem, Flower of Life, Seed of Life
References
Ball, W. W. R. and Coxeter, H. S. M. ``The Five-Disc Problem.'' In Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 97-99, 1987. Neville, E. H. ``On the Solution of Numerical Functional Equations, Illustrated by an Account of a Popular Puzzle and of its Solution.'' Proc. London Math. Soc. 14, 308-326, 1915.
- Contour Integral
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