Fibonacci Sequence

Leonardo Fibonacci (see Figure 1.1) (Leonardo, the son of Bonaccio) lived around 1175–1250 A.D. He was born in medieval Pisa.  He had travelled to many parts of the Mediterranean region with her father as a boy.  During this period, he lived for a while in North Africa.  He encountered Eastern and Arabic mathematics during this time and became convinced that current European mathematical practices were inferior (Gosett, 2013).

Figure 1.1 Leonardo Fibonacci

In 12th century, the Leonardo Fibonacci questioned about the population growth of the rabbits (see Figure 1.2) under ideal circumstances, such as no predators to eat them or no dearth of food and water that would affect the growth rate.

 

Figure 1.2 Fibonacci’s Rabbit Problem

The answer of the question is the Fibonacci Sequence of Numbers, also known as Fibonacci Numbers that starts from 1 and each new number of the series is simply the sum of the previous two numbers.  So the second number of the series is also 1, the sum of the previous 1 and 0 of the series. The sequence of the number looks like the series bellow:

            Fibonacci numbers are said as one of the Nature's numbering systems because of its existence not only in the population growth of rabbits, but also everywhere in nature, from the leaf arrangements in plants to the structures in outer space.  The special proportional properties of the golden ratio have a close relationship with the Fibonacci sequence. Any number of the series divided by the contiguous previous number approximates 1.618. (Amir, 2011).