Leonardo Fibonacci (1170-1250) was an Italian mathematician, considered by many to be the most talented of the Middle Ages. He popularized a number series, which would later be named after him, as a model of the rabbit population growth generation by generation. But it will later be discovered that these number can be applied to a variety of other situations, including Forex trading.

The series starts with the numbers 0 and 1, and the next are the sum of the last two: so, putting it all together, the series starts with the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

The mathematical limit

or, in simpler terms, the ratio of an arbitrarily big number in the Fibonacci series and its successor, is 0.618, while the limit

or the ratio of a Fibonacci number and the one two places after it in the sequence, yields 0.382. Subtracting these two numbers gives 0.236, their average is 0.500, and their sum is 1.000. Finally, 1.000 − 0.236 = 0.764.

The numbers we just learned about — 0, 0.236, 0.382, 0.500, 0.618, 0.764 and 1.000 — are called the Fibonacci retracement levels. With calculations similar to those we made in the last section we could also obtain the ratios of 0, 0.382, 0.618, 1.000, 1.382 and 1.618, which are referred to as the Fibonacci extension levels.

Once you find the Highest High (HH) quickly followed by the Lowest Low (LL) and using them as the extremes to plot the Fibonacci retracement or extension levels on your trading platform, these ratios represent the levels, relative to the HH/LL range, at which the pair is more likely to find a support or resistance level, that is, levels at which the pair will revert its trend.

Retracement and extension levels are not the only application of these ratios in currency trading: in fact, there are many other tools relying on them. We will not have time here to discuss all of them, but it is still worth mentioning another commonly used tool: the Fibonacci fan, which uses the ratios to plot support/resistance levels, this time with the trend lines converging to a single point (hence the term "fan").

It has been speculated that although Fibonacci ratios can be very useful while trading, their effectiveness comes from its very widespread use among traders, which ends up influencing the market and the traders themselves, rather than because it is effective *per se*.

Although we do not have a definite answer to this matter, it is still worth pointing out that influencing a market, which involves movements worth several trillion dollars every day, certainly would not be something easy to achieve.

One way or another, knowing how to use these tools although not too easy at first, will really help you along in your trading experience.