Math & Crypto
Fibonacci Sequence Explorer
Give a position (0-indexed) to get its Fibonacci number, see the growth curve, and compare to the golden ratio.
Sequence starts 0, 1, 1, 2, 3, 5, 8… where index 0 → 0. Built for quick intuition—values are computed in-browser.
API
Call /tools/fibonacci-sequence/?f=10 for JSON:
{"error":0,"position":10,"result":55}
Max position: 200.
Result
F(10) = 55
F(n+1)/F(n) ≈ 1.618
Golden ratio φ ≈ 1.6180339887…
Growth curve
Why the golden ratio shows up
As n grows, the ratio F(n+1)/F(n) approaches the golden ratio φ = (1 + √5) / 2. That’s why Fibonacci spirals and φ appear in nature, art, and even some trading heuristics. In cryptography, fast growth shows how quickly numbers explode—handy intuition for big-integer math.