# Nested Square Root Representation of the Golden Ratio

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One of the simplest possible formulas involving an infinite sequence of nested square roots is . From that, it can be easily seen that . The positive root of this quadratic equation is , which is none other than the golden ratio, known to Euclid and the ancient Greeks. This is also called the golden mean, golden section, and divine proportion. This is also equal to the limiting ratio of successive Fibonacci numbers: .

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

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