How does the Fibonacci sequence work?

Answer 1

The Fibonacci sequence is a series of integers where each number is the sum of the preceeding two numbers, and the first two numbers in the series is 0 and 1. The first 10 numbers in the series are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

Some definitions start the series at 1 and 1, omitting the 0.

The ratio of two sequential Fibonacci numbers, as the numbers get large, approaches phi, which is the golden mean, (1 + sqrt(5)) / 2, or about 1.61803. There are many, many other uses, as well as observations of the sequence in nature.

Fibonacci numbers get large very quickly, so generating more than a few of them requires an arbitrary decimal math library. In particular, the 47th number in the sequence is 2,971,215,073, which is the largest Fibonacci number that can be stored in a 32-bit unsigned binary integer, and the 93rd term is 12,200,160,415,121,876,738, which is the largest possible in 64-bit.