Fibonacci Generator (first N)

Each term is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13. Leonardo of Pisa presented it in 1202 as a problem about breeding rabbits, but the pattern shows up far beyond that — in the arrangement of sunflower seeds, in plant branching, in shell spirals. The reason is that the ratio between consecutive terms converges to the golden ratio, which solves efficient packing problems.

Choose how many terms you want and the page generates the sequence. The implementation detail that matters: the numbers are computed with arbitrary-precision integers. The fiftieth term already exceeds 12 billion, and the seventy-ninth exceeds the largest integer a regular JavaScript number represents exactly — from there on, a naive implementation starts returning wrong values with no warning.

Watch out for an indexing trap: some people start counting at 0 and others at 1. This page starts at 0, which is the more common mathematical convention and the one making the closed formula work directly. If you are checking against another source and every value seems shifted by one position, that is almost always why.