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]\displaystyle{ 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]\displaystyle{ F_0=0,\quad F_1= 1, }[/math]

and

[math]\displaystyle{ F_n=F_{n-1} + F_{n-2}, }[/math]

for [math]\displaystyle{ n \gt 1 }[/math].

The beginning of the sequence is thus:

[math]\displaystyle{ 0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots }[/math]

Resources:

• Golden spiral
• Fibonacci numbers