Fibonacci numbers... the Nature's numbering system

The Fibonacci numbers appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

What are Fibonacci Numbers & Golden Ratio

In mathematics, the Fibonacci numbers are the following sequence of numbers:
0 1 1 2 3 5 8 13 21 34 55 89 ....
By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s.

If we take the ratio of two successive numbers in Fibonacci's series, (1, 1, 2, 3, 5, 8, 13, ..) and we divide each by the number before it, we will find the following series of numbers:
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...
It is easier to see what is happening if we plot the ratios on a graph:

The ratio seems to be settling down to a particular value, which we call the golden ratio or the golden number. It has a value of approximately 1•618034 , although we shall find an even more accurate value on The golden ratio 1•618034 is also called the golden section or the golden mean or just the golden number. It is often represented by a Greek letter Phi  . The closely related value which we write as phi with a small "p" is just the decimal part of Phi, namely 0•618034.

Fibonacci in Plants

Plants do not know about this sequence - they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144.
Why do these arrangements occur? In the case of leaf arrangement, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space.
In the seeming randomness of the natural world, we can find many instances of mathematical order involving the Fibonacci numbers themselves and the closely related "Golden" elements.
 
Fibonacci Petals
 
3 petals lily, iris
5 petals buttercup, wild rose, larkspur, columbine
8 petals delphiniums
13 petals ragwort, corn marigold, cineraria
21 petals aster, black-eyed susan, chicory
34 petals plantain, pytethrum
55, 89 petals michelmas daisies, the asteraceae family.