Fibonacci number

In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation:

That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers also denoted as Fn, for n = 0, 1, … , are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418…

Sometimes this sequence is considered to start at F1 = 1, but it is more common to include F0 = 0. The Fibonacci numbers are named after Leonardo of Pisa, known as Fibonacci, although they had been described earlier in India.



A tiling with squares whose sides are successive Fibonacci numbers in length.


A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above.