Bits n Bytes - Fibonacci Series

Ever wondered how the Fibonacci series came into existence? Yes the same series all the students of computer science or electrical engineering have to encounter in the initial days of programming. I came across their history in a book on "XML Processing" by Elliotte Rusty Harold. I have added it here for your reading.

" .... as far as we know, the Fibonacci series was first discovered by Leonardo of Pisa around 1200 C.E. Leonardo was trying to answer the question, “Quot paria coniculorum in uno anno ex uno pario germinatur?”, or, in English, “How many pairs of rabbits are born in one year from one pair?” To solve his problem, Leonardo estimated that rabbits have a one month gestation period, and can first mate at the age of one month, so that each female rabbit has its first litter at two months. He made the simplifying assumption that each litter consisted of exactly one male and one female.

Leonardo begins with one pair of baby rabbits, a male and a female. At the end of the first month, these two have reached puberty and mate. There’s still one pair of rabbits. At the end of the second month, the female gives birth to a new pair of rabbits. There are now two pairs of rabbits, one pair of adults and one pair of babies. The adult pair mates again, so that they will produce one more pair at the end of the third month, at which point there are now three pairs of rabbits. One of these pairs has just been born, but the other two are old enough to mate, which, being rabbits, they do. At the end of the third month, two of the three pairs have babies producing five pairs of rabbits. Meanwhile all rabbits born in previous months mate, so that at the end of the fourth month there will be three more pairs of rabbits. Leonardo realized that the number of pairs at the end of each month was the sum of the number of pairs the preceding month and the number of pairs the month before that. The rabbits don’t simply double in population each month because it takes two months before a rabbit can have its first litter. Nonetheless, the numbers do grow only slightly more slowly than exponentially; and the process continues indefinitely, at least until you run out of rabbit food or the rabbits take over the world, whichever comes first. The number of pairs each month—1, 1, 2, 3, 5, 8, 13, ...— has come to be known as the Fibonacci series after Leonardo’s Latin nickname, Fibonacci (short for filius Bonacci, son of Bonacci)."