Leonardo Fibonacci (1170-1250) is an Italian mathematician, founder of “the Fibonacci sequence” of numbers, where each number is the sum of the previous two:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 etc.
There are several manifestations of the so called “Golden Ratio”, which can be found through the Fibonacci sequence:
5/8≈0,618; 8/13≈0,618; 13/21≈0,618; 21/34≈0,618; etc.
8/5≈1,618; 13/8≈1,618; 21/13≈1,618; 34/21≈1,618; etc.
13/5≈2,618; 21/8≈2,618; 34/13≈2,618; 55/21≈2,618; etc.
5/13≈0,382; 8/21≈0,382; 13/34≈0,382; 21/55≈0,382; etc.
The Golden Ratio can be very helpful on the financial markets when we compare one wave to another in a wave pattern. For example if we compare the length of wave 3 to the length of wave 1 in an impulse, or if we measure the depth of the corrective waves 2 and 4 in relation to waves 1 and 3.
Wave 2 and wave B often retrace 61.8% of wave 1 and wave A respectively.
Example:
Wave 4 often retraces around 38.2% of wave 3. Wave 3 is often 1.618 or 2.618 times the length of wave 1. Examples:
However, ratio analysis does not provide firm rules, only some very useful guidelines.