Fibonacci Tutorial

First some background information…**Leonardo Fibonacci** was a noted Italian mathematician who was born around the year 1170. As a youth, Leonardo journeyed with his father, aiding him with his work, and it was during this period that he discovered the Hindu-Arabic numerical system.

Fibonacci numbers were formulated by Leonardo Fibonacci and they are simply a series of numbers with a certain characteristic – once you add the preceding two numbers you come up with the next number in the chronological sequence.

Here is an illustration:

The ratios originate from the series: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

The **golden ratio** 1·618034 is likewise called the golden section or the golden mean.

This series of numbers is gained by starting with 1 then 2 and then adding together 1 + 2 to come up with 3, the third number in the **Fibonacci series**. Then, adding together 2 + 3 to get 5 and so forth. The relationship between these Fibonacci numbers is what gives us the **Fibonacci retracements** and extensions in technical analysis. Beginning with the initial few numbers in the sequence, if you calculate the ratio of any number to the following higher number, you get .618. So take for example, 55 divided by 89 and you will get .618.

## How do I use this fibonacci information?

Forex currency pairs will frequently retrace a Fibonacci ratio percent of the preceding wave before continuing a trend. Fibonacci levels:0.236, 0.382, 0.618, 0.764. are the most common used with the the 50% level also popular (but not a **fib** level) as forex traders use this additional degree since the propensity of currency pairs to continue a trend after retracing half of the former move is high.

Also be aware of are the following primary derived ratios:

0.786 = square root of 0.618

0.886 = fourth root of 0.618

1.13 = inverse of 0.886 (1/0.886)

1.27 = inverse of 0.786 (1/0.786)

Currency traders utilise Fibonacci retracement levels as possible “support and resistance” zones. When clusters of these areas are found together they can be strong entry points if the market is resonating with the levels. You won’t really need to know how to calculate all of this. Your charting software will do all the work for you.

Modern chart platforms typically include a **Fibonacci retracement** and extension tool. We use Swing Highs and Swing Lows to calculate these areas which need to be obvious areas on a chart which other traders will identify. This helps with the self fulfilling prophecy element of this kind of entry when other market participants enter as and when we do.

## Fibonacci retracement chart

The chart below shows a move to the upside followed by a **retracement** to the 38.2% **Fibonacci** level. The other levels have been removed for clarity in this example. The retracement was added by pulling the **Fibonacci tool** from the low to the high on the chart. Some traders will trade using these levels exclusively. Anyone using this approach may potentially be better off if they look for confluence of multiple swings or utilising support and resistance inline with the retrace levels.

For example: The chart below shows how price has made a new high today. When we pull the fib we can now see the 38.2% is aligned with previous support. There is now a confluence of **Fibonacci retracement** and price structure at the level. This is a simplified look at the price action but is sufficient for this example scenario.

### Fibonacci extension chart

Fibonacci extensions (also called Fibonacci expansions) can be drawn on the chart as per the example below; they are used to look for potential support or resistance as price makes new highs or lows. Traders often use this tool as price makes new highs or lows with no price structure support to reference.