The Fibonacci sequence · Pulse Beat
Start with 1 and 1. Each next number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
Start with 1 and 1. Each next number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
Divide each number by the one before: 2/1 = 2, 3/2 = 1.5, 5/3 ≈ 1.667, 8/5 = 1.6, 13/8 = 1.625, 21/13 ≈ 1.615. The ratios settle toward 1.618..., the golden ratio φ = (1 + √5) / 2.
Fibonacci numbers do turn up in nature: the spirals of a sunflower head or a pine cone often have counts that are neighbouring Fibonacci numbers, because growing at a golden-angle turn packs seeds efficiently. They do not explain everything people claim. Many "golden ratio" claims about art and the human face are exaggerated.
Leonardo of Pisa, called Fibonacci, introduced the sequence to Europe in 1202 in a problem about breeding rabbits.