Five Circles and the Golden Ratio


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


	Contributed by: Sándor Kabai

Five Disk Problem (Wolfram MathWorld)

Golden Ratio (Wolfram MathWorld)

"Five Circles and the Golden Ratio" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FiveCirclesAndTheGoldenRatio/

Contributed by: Sándor Kabai

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Golden Ratio
Plane Geometry
High School Algebra II and Trigonometry
High School Geometry
High School Mathematics

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Hexagons and the Golden Ratio
Geometric and Continued Fraction Expansion of the Golden Ratio
Golden Spiral
Pentagon Spirals
Golden Ratio by the Fibonacci Sequence
Golden Section
Fifteen Great Circles on a Sphere
Phone Numbers by Fibonacci Methods
The Base-Phi Number System
Graphs of Successive Digits of Pi, e, and Phi

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