φ = (1+√5)/2 ≈ 1.6180339887. Properties: φ² = φ+1, 1/φ = φ−1. Fibonacci: F(n+1)/F(n) → φ. Golden rectangle: width/height = φ. A golden rectangle can be divided into a square and another golden rectangle, infinitely.
How to Use
Enter a value:
- Input: Any positive number
- Output: Golden ratio pair
- Extra: Rectangle and verification
Properties of φ
- φ = (1+√5)/2 ≈ 1.61803
- φ² = φ + 1 ≈ 2.61803
- 1/φ = φ − 1 ≈ 0.61803
- φ = 1 + 1/φ (self-similar)
In Nature & Art
Spiral shells, flower petals, leaf arrangements, DNA, Parthenon façade, and Renaissance paintings all exhibit golden ratio proportions.
Step-by-Step Instructions
- 1Enter a value.
- 2See φ × value.
- 3Check golden rectangle.
- 4Verify two values.
- 5Explore constants.