five disks problem

Input interpretation

five disks problem

Illustration

Illustration

Definition

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)].
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Related terms

arc | circle covering | disk covering problem | flower of life | Miquel five circles theorem | seed of life

Subject classifications

MathWorld

combinatorial geometry | packing problems

MSC 2010

51E23
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