Number theory – Technical Forex Analysis

Fibonacci numbers

The Fibonacci numbers are a sequence of number ratios which are used to pick out repetitive sequence of events on the forex charts. They were first described by Leonardo Fibonacci. The number sequences are generated by adding a number to a previous number to get the third number and continuing this process to get a sequence of numbers in the following order:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on

If we look at this number sequence we can see that the number 1 which is the third in the series, is derived by adding the previous 0 and 1. The number 55 is derived by adding 21 and 34 which are the prior two numbers. Same goes for adding 55 and 89 to get 144. This is the addition sequence.

Subsequently, if we move down the number sequence after the first few numbers, dividing a number by the number immediately after it produces a Fibonacci ratio of 61.8% or 0.618. Dividing a number by the alternate number before it produces another Fibonacci ratio of 38.2%. For instance, 89 divided by 144 is 61.8% ratio or 0.618, while 55 divided by 144 is 0.3819 or 0.382 approximately, which is the 38.2 Fibonacci ratio.

Fibonacci ratios can be used to detect areas of price retracement or areas of price extension. They therefore find applications on the Fibonacci arcs, retracement/extension tools, time zone indicators as well as Gartley patterns. Even the 1-2-3 reversal pattern in forex is based on Fibonacci ratios.

The popular Fibonacci retracement ratios are:
• 0.236 (23.6%)
• 0.382 (38.2%)
• 0.5 (50%)
• 0.618 (61.8%)
• 0.764 (76.4%)
• (100%)

The Fibonacci extension ratios are
• (100%)
• 1.382 (138.2%)
• 1.618 (161.8%)

Application of Fibonacci Numbers

The Fibonacci numbers are mostly used in detecting price retracement and extension levels. This gives rise to several applications of the Fibonacci indicators.

a) Fibonacci Retracement as a Forex Entry Tool

Retracements are a normal occurrence in forex. They represent areas where traders who got in early on a trend have decided to take profit. However, profit taking will continue until a certain point when market players decide that an opportunity to further profit from a re-entry has presented itself. The point is: where does a retracement end for the trend to continue on its run once more? This is where the Fibonacci retracement tool comes in. The tool shows several retracement levels when traced from the highest to lowest price points (downtrend) or from the lowest to the highest price point on the chart (uptrend). Combining the Fibonacci indicator with another indicator will identify which retracement level can be used for price re-entry.


b) Fibonacci extension tool as a Take Profit Tool

After making a retracement entry such as is shown above, the next question is: how far will prices go before the trend ends? The Fibonacci extension tool can be used to answer this question. The tool is plotted on the chart to follow the retracement tool’s trace, but the difference is that the trace is extended to the retracement point as shown below:

This throws up the Fibonacci extension levels (61.8% and 100% in the chart above). The trader can use one of these areas as the Take Profit area.

This strategy only works well on a previous Fibo retracement area, and is also not fool proof. It requires a lot of practice to perfect and should be rehearsed thoroughly on a demo account.

Gann numbers

W.D. Gann was a stock and a commodity trader working in the ’50s, who reputedly made over $50 million in the markets. He made his fortune using methods that he developed for trading instruments based on relationships between price movement and time, known as time/price equivalents. There is no easy explanation for Gann’s methods, but in essence he used angles in charts to determine support and resistance areas, and to predict the times of future trend changes. He also used lines in charts to predict support and resistance areas.

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