Fibonacci numbers

A tiling with squares whose side lengths are successive Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13 and 21.

In mathematics, the Fibonacci numbers, commonly denoted <math>F_n</math>, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,

<math>F_0=0,\quad F_1= 1,</math>

and

<math>F_n=F_{n-1} + F_{n-2},</math>

for <math>n > 1</math>.

The beginning of the sequence is thus:

<math>0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots</math>

The ratio <math> \frac {F_n}{F_{n+1}} \ </math> approaches the golden ratio as <math>n</math> approaches infinity.

Resources:

• Golden spiral
• Fibonacci numbers