Who was Fibonacci?
Leonardo Pisano, was Italian mathematician born in Pisa during the The middle  Ages. He was renowned as one of the most talented mathematicians of his day. The name Fibonacci itself was a nickname given to Leonardo. It was derived from his grandfather’s name and means son of Bonaccio.
While most attribute the Fibonacci Sequence to Leonardo, he was not responsible   for discovering the sequence. In 1202 Leonardo published a book called,Liber  Abaci.In it he derived a method for calculating the growth of the rabbit population.
Suppose a newly-born pair of rabbits, one male, one female, are put in a field.Rabbits are able to mate at the age  of one month so that at the end of its   second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was…How many pairs will there be in one year?
At the end of the first month, they mate, but there is still one only 1 pair.
At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
At the end of the fourth month, the original female has produced yet another new pair, the female born two monthsago produces her first pair also, making 5 pairs.
This mathematical progression is now recognized as the Fibonacci Sequence.  Starting with zero and adding one,each new number in the sequence is the sum of the previous two numbers. In our example, 0+1 = 1, 1+1=2, 1+2=3,
2+3=5, and so on.
The sequence of numbers looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, to infinity. From this sequence.you can easily reason that at the end of one year there would be 233 pairs of rabbits.
This sequence has repeatedly appeared in popular culture from architecture to music to television. While the series is a powerful tool, the analysis of one number with the number up to four places to the right. The first three are shown below. While some are not exact, if you repeat this mathematical analysis through multiple sets of data, you will see.we arrive at some well known and fairly consistent ratios.
21/34   = 0.61764  ~  0.618                                34/21    =  1.61904  ~ 1.619
21/55   = 0.38181  ~  0.382                                55/21    =  2.61904  ~ 2.619
21/89   = 0.23595  ~  0.236                                89/21    =  4.23809  ~ 4.238
The dimensional properties adhering to the 1.618 ratio occur throughout nature and the ratio is most referred to as The Golden Ratio. The uncurling of a fern and the patterns found on various mollusk shells are commonly cited examples of this ratio.
This number, when added to 0.618, equals 1.
These ratios have been used for over a hundred years in the financial markets by the likes of W.D. Gann and Ralph Nelson Elliot. Up until the late 90s the tracking and use of these numbers were a manual process.  With the proliferation of real-time charting and data, software that automatically calculated and displayed these levels brought Fibonacci into the financial mainstream.