The Golden Ratio φ

φ = (1+√5)/2 ≈ 1.6180339887…, the solution to x² = x + 1. It appears in the Fibonacci sequence: ratio Fₙ₊₁/Fₙ → φ. It also satisfies φ = √(1+√(1+√(1+…))) and φ = 1 + 1/(1+1/(1+…)). The golden ratio is often claimed to appear in art, architecture, and nature (spirals, leaf arrangements), though many claims are exaggerated. True occurrences: the regular pentagon’s diagonal to side ratio is φ; the golden spiral approximates many mollusc shells.