Fibonacci Sequence

The Fibonacci sequence is the sequence of integers in which each number is the sum of the two preceding ones, conventionally starting 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. Sequences of this kind had appeared earlier in Indian mathematics, in the study of Sanskrit poetic meters, but the sequence entered Western European mathematics through Leonardo of Pisa, known as Fibonacci, who introduced it in his 1202 book Liber Abaci as the solution to a hypothetical problem about the growth of a rabbit population. The ratio of consecutive Fibonacci numbers converges to the golden ratio as the sequence progresses, and Fibonacci numbers appear throughout number theory, combinatorics and the mathematical description of natural branching and spiral patterns.