Fibonacci Series and Phyllotaxis © (2002) by nilum.com The following is my personal opinion. Any similarity with existing or previously existing persons, organizations or nation-states is purely accidentally. the calculations are supposed to be correct. Please verify yourself.

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The formula of phyllotaxis is the formula behind the emerging cristals, living cells, of life, cabbage, leafs, pine-cones, flowers, etc. nature everywhere shows us this sequence:

0+1 = 1
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13
8+13 = 21
13+21 = 34
21+34 = 55
34+55 = 89

to get the series, take the second operand of the sum and add the result of the last sum. the relation between the result of this sum and the previous sum will approach phi=1.618.... with growing precision. phi is an irrational number, which means, it has infinite decimal places behind the decimal point (like pi, 3.14...)

the relation phi between two numbers or objects' size is also called the divine section and is the basic fundation of beauty in art and architecture. it would not be a surprise if commercial products would not take advantage of that beauty. take a telefon card or a marlboro box and divide the length by width and most probably you get phi=1.618. if you don't get this number approximately, divide the diagonale ob the object by its length or width.

the fibonacci series also works for 1/phi. fibonacci has a number of beautiful mathematical properties in geometry and can be found in famous monuments like the angle of the egypthian pyramides, Stonehenge, churges and monasteries - although neither fractional nor irrational numbers were not known until the mid-ages.

to get phi, you can start with arbitrary two numbers and after only a few approximations, you always get 1.618.... as relation between two successive sums!

1000+1234 = 2234
1234+2234 = 4468
2234+4468 = 6702
4468+6702 = 11170
6702+11170= 17872

if you continue in the sequence, the value approaches phi.

try yourself. start with 1+1000 = 1001.

www.chalagam.com published four books about the devine section (nombre d'or in french). english translations of these books are in preparation.