Fibonacci Numbers

Fibonacci Numbers

Leonardo Fibonacci was an Italian mathematician born in the 12th century. He is known to have discovered the "Fibonacci numbers," which are a sequence of numbers where each successive number is the sum of the two previous numbers.

e.g. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

This sequence is often demonstrated on the rabbits example.

How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?

We can see that 1 pair will be produced the first month. 1 pair also will be produced in the second month, since the new pair produced in the first month is not yet mature, and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. 3 pairs will be produced in the fourth month, and in the fifth month 5 pairs.

This relationship can be rewritten as:

F(1) = 1
F(2) = 1
F(n) = F(n – 1) + F(n – 2)

These numbers possess a number of interrelationships, such as the fact that any given number is approximately 1.618 times the preceding number.


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