Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The answer is r = ϕ - 1 = 1/ϕ = 0.618034..., where ϕ is the golden ratio, and the centers c_i of the disks i = 1, ..., 5 are located at c_i = [1/ϕ cos((2π i)/5) 1/ϕ sin((2π i)/5)]. 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 n = 5 disks can be reduced slightly to 0.609383....
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