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Leonardo Fibonacci and The Golden Ratio

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.




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.

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