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The golden ratio φ = (1 + √5)/2 ≈ 1.6180340 is the unique number where the whole is to the longer part as the longer part is to the shorter. It satisfies φ² = φ + 1 and 1/φ = φ − 1.
Golden ratio
φ = (1 + √5) / 2, φ² = φ + 1
Golden section
(a + b) / b = b / a = φ
The longer part is 16.180340 and the whole is 26.180340.
Consecutive Fibonacci ratios converge to φ: 8/5 = 1.6, 13/8 = 1.625, 21/13 ≈ 1.6154, and so on.