Chapter V · nature's favourite number
Fibonacci
In 1202, Leonardo of Pisa — known today as Fibonacci — asked how many rabbits a single pair could produce in a year. The answer started a sequence that turned out to be written all over the natural world.
Fibonacci's rabbits breed on a simple rule: a pair matures in a month, then produces a new pair every month after that. Month by month the colony grows — 1, 1, 2, 3, 5, 8, 13, 21, 34… — each number the sum of the two before it. The puzzle came from his book Liber Abaci (1202), which also did something far more consequential: it taught Europe the Hindu–Arabic numerals we use today, in an arithmetic written for merchants.
Why does the sequence keep turning up in nature? Because it is the simplest way for growth to compound. A plant grows a new unit from an old one, which in turn grows a new unit — count the bumps on a pinecone, the scales of a pineapple, or the spirals of a sunflower, and you keep finding neighbouring Fibonacci numbers: 34 and 55, or 55 and 89.
The pattern behind it is a single angle. If a sunflower places each new seed at the same turn — about 137.5°, the golden angle — the seeds pack as tightly as possible, no two ever crowding the same radius. Count the spirals that emerge and they are always neighbouring Fibonacci numbers: the sequence isn't hiding in nature; it is the arithmetic of not getting in your own way.