14 What is the Fibonacci Sequence?

A000045 – OEIS

The sequence is named after the Italian Leonardo Fibonacci, who used it to describe the growth of a rabbit population in 1202. However, the sequence was already known to both the Greeks and the Indians in ancient times.

Further research showed that the Fibonacci sequence also describes numerous other growth processes in nature. It seems that it is a kind of growth pattern in nature.

Another special feature is its connection with the golden ratio: the quotient of two consecutive Fibonacci numbers approximates the golden ratio.

The sequence is calculated with the formula

The first numbers 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,
317811,
514229,
832040,
1346269,
2178309,
3524578,
5702887,
9227465,
14930352,
24157817,
39088169,
63245986,
102334155