Chart analysis based on Fibonacci numbers

From this article you will learn the history of Fibonacci numbers and, in particular, their role in chart analysis of the Forex market.

Leonardo Fibonacci (Leonardo Pisano) – was a famous Italian mathematician who lived in XIII century. He gained acceptance as an outstanding person after publication of his work "Liber Abaci". The book was issued in 1202, the second revised edition – in 1228, which remained till our time.  Fibonacci introduced Hindu-Arabic number system to Europeans. It greatly contributed to such branches of science as physics, maths, astronomy, biology etc. Fibonacci sequence allows to interpret various natural phenomenon and forms, whereas "golden ration", according to Johannes Kepler, is one of the treasuries of geometry.

Fibonacci row represents a certain sequence of numbers from 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…, to the infinity. This row has following regularities:

• Each subsequent number of the row represents the sum of two previous numbers.
• Ratio of subsequent number to the previous tends to 1,618.
• Ratio of previous number to the subsequent tends to 0,618.
• Ratio of subsequent number to the previous number next by one tends to 2,618.
• Ratio of previous number to the subsequent number next by one tends 0,382.

Selecting proportions this way, we will get Fibonacci numbers: 4.235, 2.618, 1.618, 0.618, 0.382, 0.236

Sequence of Fibonacci numbers tend to a certain constant ratio. It is impossible to express this ratio precisely because it is irrational (the number with infinite sub-sequence of decits in fractional part). Therefore it is accepted to reduce fractional part and refer to the ratio to 0,618 (1,618).

Medieval maths called that proportion "The Divine Proportion", modern name is the "golden ration".

Relation of Fibonacci numbers with financial markets

For a long time many analysts and traders applied proportions of Leonardo Fibonacci to charts. Application of golden ratio in technical analysis is mainly connected with Elliot's name. In wave theory the length of momentum and correction waves is calculated through coefficients, whereas the very number of waves corresponds to one of Fibonacci coefficients.

Apart from Fibonacci Expansion and Fibonacci Retracement, other analytical and forecast methods are distinguished: Fibonacci Fan, Fibonacci Arcs and Fibonacci Time Zones.