How to Calculate Golden Ratio
What is Golden Ratio?
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.
Step-by-Step Guide
- 1φ = (1 + √5) / 2 ≈ 1.6180339887
- 2Each Fibonacci number / previous Fibonacci number → φ as numbers grow larger
- 3Golden rectangle: if you remove a square from it, the remaining rectangle is another golden rectangle
- 4φ² = φ + 1 and 1/φ = φ − 1
Worked Examples
Input
Fibonacci sequence
Result
1, 1, 2, 3, 5, 8, 13, 21, 34...
21/13 = 1.615, 34/21 = 1.619, approaches φ
Input
Rectangle with width 100
Result
Golden height = 161.8
100 × φ = 161.8
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