Given five equal disks placed symmetrically about a given center, what is the smallest radius 
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 
, ..., 5 are located at
![c_i=[1/phicos((2pii)/5); 1/phisin((2pii)/5)].](/images/equations/FiveDisksProblem/NumberedEquation1.svg) |
The golden ratio enters here through its connection with the regular pentagon. If the requirement that the
disks be symmetrically placed is dropped (the general disk
covering problem), then the radius for 
disks can be reduced slightly to 0.609383... (Neville 1915).
