Fibonacci Calculator

Starting 1, 1, each Fibonacci number sums its two predecessors: 1, 1, 2, 3, 5, 8, 13… The sequence models branching growth — sunflower spirals, pinecone rows, and rabbit-population puzzles — anywhere the new generation adds to the old.

Consecutive ratios converge to the golden ratio φ = (1+√5)/2 ≈ 1.618 — by F(20)/F(19) the match is already eight digits deep. Binet's closed formula computes any term directly from powers of φ, no iteration required.