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The golden ratio (φ ≈ 1.6180339887) is a special mathematical ratio where (a+b)/a = a/b = φ. It appears in nature, art, architecture, and mathematics. A rectangle with side ratio φ:1 is a "golden rectangle," considered aesthetically pleasing.

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1. 1φ = (1 + √5) / 2 ≈ 1.6180339887
2. 2Each Fibonacci number / previous Fibonacci number → φ as numbers grow larger
3. 3Golden rectangle: if you remove a square from it, the remaining rectangle is another golden rectangle
4. 4φ² = φ + 1 and 1/φ = φ − 1

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