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, . . .

The Fibonacci Series
Very good site about nature (especially flowers) and fibonacci
Finbonacci Numbers & Nature
More on the connection with nature
Fibonacci Numbers
More mathematical information

       
 
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