0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.
1 = 1+0
2 = 1+1
3 = 2+1
5 = 3+2
8 = 5+3
13= 8+5
21= 13+8
34= 21+13
55= 34+21
The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. His book, ‘Liber Abaci’ in 1202, introduced this sequence to Western European Mathematics. In one of the chapters of his book, Fibonacci posed a well known problem of rabbit population.Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: 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; rabbits never die and a mating pair 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?
To solve this problem we will consider the following steps:
- At the beginning of the experiment, there is one pair of rabbits
- At the end of the first month, the two rabbits have mated but have not given birth,therefore there is still 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 months ago produces her first pair also, making 5 pairs.
- At the end of fifth month, every pair that was alive two months ago gives birth. This makes three new pairs for a total of eight.
Continuing in this manner, to forecast the number of pairs of rabbits many months from now simply add together the number of pairs that were alive in the preceding two months.
Now, do you know of any series of numbers which begins with one and one and continues by adding the preceding two numbers to get the next? Of course you do. It's the Fibonacci series.
