Fibonacci Number              0,1,1,2,3,5,8,13,21,34,55…Each number in the sequence is the sum of the two numbers that precede it.Here (0,1 )0 , 1 -> 0 + 1 = 1 generates sequence ( 0, 1, 1)Now 1 , 1 ->1+1 =2 generates sequence (0, 1, 1, 2)Now 1 , 2 ->1+2 = 3 generate sequence (0,1,1,2,3)2 , 3->2+3 = 5 generate sequence (0,1,1,2,3,5) and so on…It can be represented as:                                                                               Fn = Fn-1 + Fn-2                     Fibonacci Man Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa,Italy (see Pisa on Google Earth), the city with the famous Leaning Tower, about 1175 AD.well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic  (like our present numbers 0,1,2,3,4,5,6,7,8,9) through Europe in place of Roman NumeralsFascinating Facts           Fig: Number of petals in flowers following Fibonacci sequencePopulation of rabbit growth     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? 1.    At the end of the first month, they mate, but there is still one only 1 pair.2.    At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.3.    At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.4.    At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. Fig: Rabbits growth per month wise depicts Fibonacci numbers Mysterious Patterns         Fibonacci sequence table and its square valueLet X represent a Fibonacci number and Y represents square of Fibonacci number

 X 0 1 1 2 3 5 8 13 Y 0 1 1 4 9 25 64 169