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Five Circles and the Golden Ratio

​
diameter of circles d
0.618
rotate pentagon
Place five circles of diameter
d
symmetrically about a given point. They intersect the unit circle at the vertices of a regular pentagon when
d=ϕ
or
d=1-ϕ=
1
ϕ
, where ϕ is the golden ratio, 1.61803….
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