Fibonacci Trading Concept

Fibonacci

Leonardo Pisano Bogollo (c. 1170-c. 1250), also known as Leonardo Fibonacci, was an Italian mathematician and is considered by many to have been one of the most talented western mathematicians of the Middle Ages. As a boy he studied the Hindu-Arabic numeral system, which was easier to use than Roman numerals.

In 1202, he published his findings in his book Liber Abaci, and introduced the number sequence that was known to Indian mathematicians as early as the 6th century. Later it became known as the Fibonacci sequence. In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. Thus the sequence begins:

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

At first glance it seems an innocuous sequence, but as we will see, it holds quite extraordinary properties. By dividing one number in the sequence by the next, the results shown in Figure 4.1 occur.

Note that the first few numbers begin with common fractions:

1 1/2 2/3 3/5

However, after 10 numbers we can see that the result remains at 61.80%.

By dividing one number in the sequence by the preceding number we have a similar development which sees the result remaining at 161.8% (as shown in Figure 4.2).

This is the golden ratio, which is found in nature and in classical architecture, including the Egyptian pyramids and some Greek structures such as the Acropolis and Parthenon.

This can be developed further by dividing numbers two apart, three apart, and so on in the sequence (as shown in Figure 4.3).

Figure 4.3 Fibonacci Ratios above 100%

Thus a series of ratios can be generated both below and above 100% (also as shown in Figure 4.3).

For ratios above 100%, the results are as shown in Figure 4.3.

These generate ratios of 161.8%, 261.8%, 423.6%, 685.4%, 1,109%, and 1,794.4%. 

For ratios less than 100% the following are generated:

5.6%, 9%, 14.6%, 23.6%, 33.3%, 38.2%, 50%, 61.8%, 66.6%, 76.4%, 85.4%, 91%, and 94.4%

A further interesting feature of Fibonacci ratios is that when dividing or multiplying one ratio by another, the result will be another Fibonacci ratio (as shown in Figure 4.5).

Figure 4.5 Multiplying and Dividing Ratios

The higher grid provides the results when ratios are multiplied by each other while the lower grid provides the results from dividing one ratio by another.

Before moving on to how these can be applied to the Wave Principle, I would like to just cover the ratios provided by harmonic ratios.