Fibonacci Sequence Generator
Generate Fibonacci numbers and see convergence to the golden ratio.
Golden ratio (φ)
1.6180339887
F(n+1) ÷ F(n) converges to φ as n → ∞
What is the Fibonacci sequence?
The Fibonacci sequence starts with 0 and 1. Each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … The sequence appears in nature (flower petal counts, spiral patterns in shells, leaf arrangements) and has deep connections to the golden ratio φ ≈ 1.618033988.
Frequently asked questions
What is the golden ratio?
The golden ratio φ = (1 + √5) ÷ 2 ≈ 1.618033… is an irrational number with the property that φ = 1 + 1/φ. It appears in architecture, art, and nature. The ratio of consecutive Fibonacci numbers F(n+1)/F(n) converges to φ as n increases.
Why does the tool use BigInt?
Fibonacci numbers grow exponentially. By the 50th term, the value exceeds JavaScript's safe integer range (2^53). The tool uses JavaScript BigInt to compute exact integer values without floating-point rounding errors.
