In the field of mathematics, Fibonacci numbers (alternatively called the Fibonacci Series or Fibonacci Sequence) are the numbers featured in the following integer series:  

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393 ……. and so on.  

This particular integer series was first discovered by Leonardo of Pisa, who was also known as Fibonacci. The Fibonacci numbers display a recurrence relation, a series of Fibonacci numbers is started with a 1 which is then followed by a 1, with the third number being calculated from the first two (1+1) and so on. So for example in the sequence above the fourth number (3) is calculated by adding the second and third number together (1+2).  Which is easy enough to understand.    

This Fibonacci numbers are then interpreted in a rather interesting way. If you begin measuring the ratios of each number next to one another you will get what are often called Fibonacci ratios. These ratios are the same numbers that often used in various forms of technical analysis. The ratios are as follows:  0.236, 0.382, 0.500, 0.618 and 0.764. These ratios are used in a number of different Fibonacci tools which are meant to help the trader predict changes in market direction.

Those who endorse Fibonacci ratios simply assert that you just need to understand how to use this magic ratios alongside technical analysis. With it being claimed Fibonacci ratios can be used to identify both support and resistance levels. Why are these ratios supposed to operate as both resistance and support levels? Well, there is no clear reason why this should be the case. However it has been asserted by some that we subconsciously seek out these so called golden ratios. A more plausible but hardly believable explanation may be that we are not psychologically comfortable with particularly long trends meaning that particular ratios or numbers often signal the end of trends.