Fibonacci and His Numbers

Leonardo of Pisa, known by the nickname Fibonacci, was an Italian mathematician who had studied arithmetic abroad and then wrote it up for a European audience unfamiliar with the number system he had learned there. His book, Liber Abaci, is remembered less for its arithmetic lessons than for a puzzle tucked inside it.

The puzzle asked how a population of rabbits would grow under a simple breeding rule: every mature pair produces a new pair each cycle, and every new pair becomes mature after a cycle of its own. Working the puzzle out by hand produces a running count of pairs, cycle after cycle, and that running count is the sequence now named after him.

The rule behind the sequence is plain once stated: each term is the sum of the pair of terms immediately before it. Start from the smallest matching seed values and the sequence builds itself forward, term after term, with no other input required.

What makes the sequence more than a counting exercise is what happens when neighboring terms are compared. Divide a later term by the term before it and the result drifts steadily toward the golden ratio, settling closer with every step further into the sequence. Fibonacci's rabbits, without meaning to, were marching toward the same proportion Euclid had already defined in geometry.

That is why this sequence is not just history here. The same progression of terms sets the spacing of the timeframe ladder this system climbs — the ladder is Fibonacci's sequence, put to work.