The Golden Ratio φ
Watch Fibonacci squares unfold into the logarithmic spiral. Reveal steps, animate growth, and see why nature keeps returning to φ ≈ 1.618033…
φ from sequence
1.618
Fn / Fn−1 approaches φ
Definition. φ = (1 + √5) / 2, the positive root of x² = x + 1.
Fibonacci. Each term is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13…
Spiral. Quarter-circles through successive squares approximate the golden spiral.
Self-similarity. A golden rectangle minus a square leaves a smaller golden rectangle.