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The Golden Ratio (φ) holds many strange properties, some of which are as follows:

  • 1/φ + 1 = φ
  • (2φ-1)2 = 5
  • φ = √(1+φ) = √(1+√(1+√(1+√(1+φ)))) etc.
  • (φ+1)*(φ-1) = φ

It also appears in the Fibonacci Series - take two consecutive terms in the series, the larger the better, and divide the larger one by the smaller one - the larger numbers you choose for this, the closer the result will be to φ.

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Q: Why is golden ratio important in mathematics?
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