The mathematical forumla for the fibonacci numbers is:
f(0) = 0, f(1) = 1, f(n) = f(n-1)+f(n-2) for n>1
The first 50 fibonnacci numbers:
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1,597
2,584
4,181
6,765
10,946
17,711
28,657
46,368
75,025
121,393
196,418
317,811
514,229
832,040
1,346,269
2,178,309
3,524,578
5,702,887
9,227,465
14,930,352
24,157,817
39,088,169
63,245,986
102,334,155
165,580,141
267,914,296
433,494,437
701,408,733
1,134,903,170
1,836,311,903
2,971,215,073
4,807,526,976
7,778,742,049
12,586,269,025
...
The first 10,000 fibonacci numbers you can download
here (10MB).
As I portrayed Pi and prime-numbers
the fibonacci-numbers aren't that well known, also they display any
special significance at the first sight. But the numbers do appear in
nature:
Shell
Golden Mean
You find in the in the ratio of the fibonacci pairs an
approximation of the golden-mean:
1/1 = 1,
2/1 = 2,
3/2 = 1.5,
5/3 = 1.666...,
8/5 = 1.6,
13/8 = 1.625,
21/13 = 1.61538...
More examples follow ...
Especially the fibonacci-numbers with their strong connection
to nature you can look at them as a prayer build by the names
(invocation) of the names of the numbers making up the
sequence. As we address human with their names, the fibonacci-
numbers already manifested themselves in so many ways, that
when we invoke them we honor and acknowledge their presence
in all their manifestations.
One, One, Two, Three, Five, Eight, Thirteen, Twenty-One, . . .