# Fibonacci / Golden Ratio

Learn how to use a Fibonacci retracement to identify possible areas of support and resistance and decide when to open and close a position, or when to apply stops and limits to your trades.

## Origins of Fibonacci or the “Golden Ratio”

The Fibonacci Sequence or «Golden Ratio» is a powerful number that recurs in nature and can be used to explain relationships in geometry, art, architecture and astronomy. Represented by the Greek letter «Phi» and equal to approximately 1.618, it appears in many natural phenomena, from small strands of DNA to massive galaxies.

The ratio was first discovered by the Italian mathematician Leonardo Pisano Bogollo, who lived between 1170 and 1250. His nickname «Fibonacci» roughly translates to «Son of Bonacci».

The first two numbers in the Fibonacci sequence are 0 and 1, and then each subsequent number is the sum of the previous two. The relevance of the «Golden Ratio» to the Fibonacci sequence is that the further into the sequence you go, the closer the numbers increase by a ratio of 1.618.

In mathematical terms, the sequence *F _{n}* of Fibonacci numbers is defined by the recurrence relation, and can be written mathematically as a rule:

*F _{n = }F_{n-1 }+ F_{n-2}*

**Figures 1 & 2**: How the Fibonacci series develops and the first 15 numbers in the sequence

The Fibonacci sequence: |
---|

0 |

1 |

1 |

2 |

3 |

5 |

8 |

13 |

21 |

34 |

55 |

89 |

144 |

233 |

377 |

**Figures 3 & 4**: The Fibonacci sequence appears in naturally occurring phenomena such as Hurricane Sandy and the curvature of a seashell

## How is Fibonacci relevant to financial markets?

Fibonacci numbers can be used in several technical indicators. Some traders use the Fibonacci series to set up their moving average studies. Instead of using round number moving averages (20, 50, 90, 200), you can use Fibonacci numbers (21, 55, 89, 144) instead. It’s important to remember that, depending upon requirements, different moving averages will work for different traders and in different markets.

Fibonacci is more commonly used for the calculation of potential support and resistance levels in price retracements and projection levels. The key factor is that the quotient of the adjacent terms possesses the golden ratio of approximately 1.618, or its inverse 0.618.

Many traders will use combinations of Fibonacci techniques to obtain a more accurate forecast. For example, you might observe the intersecting points in a combination of Fibonacci fans and resistances.

*N.B. Fibonacci studies should not be used as primary indicators of timing on entry or exit of a position. They can be useful in establishing potential areas of support and resistance but should be used in conjunction with other indicators as a confirmation tool. *

## Calculating Fibonacci levels

- A number divided by the next highest number approximates 0.6180

(13/21=0.6190, 21/34=0.6176, 34/55=0.6181, 55/89=0.6179).

The approximation nears 0.6180 as the numbers increase.

This is **the basis for the 61.8% retracement**.

- A number divided by another two places higher approximates 0.3820

(13/34=0.382, 21/55=0.3818, 34/89=0.3820, 55/144=0.3819).

The approximation nears 0.3820 as the