Fibonacci Numerical Sequences

Online Forex trading often particularly appeals to those that are good at, or are in interested, maths and mathematical theory. Maths is a fundamental part of Forex trading and, although you don’t have to be a mathematical genius to be a successful Forex trader, you will need to certain mathematical calculations from time to time.

If you have a real interest in maths, then you will be delighted to know that the Forex market is full of interesting number sequences. Once such sequence that is particularly relevant to Forex trading is the Fibonacci sequence. In this article, we explain all about what the Fibonacci sequence is, how it appears in the world and how it appears in the Forex markets.

What is the Fibonacci Numerical Sequence?

The Fibonacci number sequence is a series of numbers, starting with 0 and 1, where each number is the sum of the previous numbers. It is a sequence that could go on infinitely, and begins as follows.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597 . . . . . . . .

Although this may seem like an insignificant series of numbers, it actually has great importance. It is named the Fibonacci sequence after Leonardo of Pisa (who was also known as Fibonacci, and Italian mathematician who was considered one of the greatest mathematicians of his time.

He described this sequence in his book Liber Abaci (Book of Calculation), which was published in 1202. The book was very well thought of in Europe at the time and had a major impact. At the time he was believed to be the first to discover this sequence, but it was subsequently learned that the sequence was known to Indian mathematicians as early as the 6th century.

Fibonacci Sequence in the World

The Fibonacci sequence has been referred to as nature’s numbering system. Fibonacci numbers appear everywhere in nature, such as the scales of a pineapple, the leaf arrangement in plants and the bracts on a pinecone. It is not necessary to understand the detail of how Fibonacci numbers appear in nature, but it is proven that this series of number can be related to many aspects of the natural world. In addition, the piano also follows a Fibonacci sequence in each octave.

The Golden Ratio

The Fibonacci sequence also has a correlation with the special ratio known as the golden ratio. The golden ratio, known for years to mathematicians and scientists appears in regularly in nature. Indeed, it is argued that virtually anything that has dimensional properties will, in some form, adhere to the golden ratio. In the Fibonacci sequence there are certain repeating ratios between the numbers that appear; notable .618 and 1.618. Again, it is not necessary to understand the detail, but it is also true that these ratios appear with regularity in the natural world.

The Fibonacci Sequence and The Golden Ratio in Forex Trading

The above information essentially makes the point that there are certain natural rules that govern the world. However, the same can be said for the Forex markets, and there are many traders that rely heavily on the Fibonacci sequence and the golden ratio in their trading. Specifically, these numbers are used in conjunction with technical analysis – that is to say that methods are used to plot points on charts that can help make more accurate forecasts. There is substantial evidence to suggest that the Fibonacci sequence and the golden ratio do appear regularly in the Forex markets and that Fibonacci studies combined with technical analysis can be a powerful trading tool.

The golden ratio is generally translated into percentages when combined with technical analysis – 38.2%, 50% and 61.8% - and there are four main methods for using Fibonacci studies in Forex trading. These are retracements, arcs, fans and time zones. A very basic overview of each of these methods follows.

Fibonacci Retracements - This is the use of horizontal lines on charts to indicate areas of resistance and support. After first locating the high and low of a chart depicting the price of any given currency, five lines would be added to the chart – at 38.2%, 50% and 61.8% as well as 0% and 100%. Following significant price movement – in either direction, the new support and resistance levels are often found on, or close to, these lines.

Fibonacci Arcs - This is similar to Fibonnaci Retracements, but involves drawing three curved lines (creating arcs) at 38.2%, 50% and 61.8% after finding the high and low on a chart. These curved lines will then, in theory, depict the support and resistance levels.

Fibonacci Fans - These are diagonal lines that are drawn from the left most point of a chart and passing through the 38.2%, 50%, and 61.8% points. These lines will then indicate areas of support and resistance.

Fibonacci Time Zones - Time zones are vertical lines which are spaced across a chart in increments in accordance with the Fibonacci sequence (ie. 1, 1, 2, 3, 5, 8 etc.) to create segments. These segments depict areas where significant price movements can be expected.


The use of Fibonacci studies and technical analysis is far more complex that can be described in one article. In essence, although not specifically useful for deciding when to enter or exit a position, they can be very useful in forecasting an estimation for areas of support and resistance. It is difficult to doubt that the Fibonacci sequence and the golden ratio have their place in Forex trading, and many successful Forex traders certainly use them. As with most theories, the important to thing is to study them, put them to the test and incorporate them, if suitable, into your own trading strategies.