The Fibonacci sequence \(F_n\) is defined by \(F_0 = 0\), \(F_1 = 1\), and \(F_n = F_{n-1} + F_{n-2}\). The first terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
The sequence appears throughout nature (sunflower seed spirals, pinecone scales, leaf arrangements) and in art and architecture. The ratio \(F_{n+1} / F_n\) converges to the golden ratio \(\varphi \approx 1.618\).
Named after Leonardo of Pisa (Fibonacci), who described the sequence in his 1202 Liber Abaci in the context of an idealized rabbit population. The only Fibonacci numbers that are also perfect squares are 0, 1, and 144.