Fibonacci (1170-1240), an italian merchant, became famous in europe because he was also a brilliant mathematician. One of his greatest achievements was to introduce Arbic numerals as a substitute for roman Numerals.

He developed the Fibonacci summation Series, which runs as follows:

1,1,2,3,5,8,13,21,34,55,89,144,…………………………….

The mathematical series tends asymptotically toward a contant ratio.

this is an irrational ratio, however; it has a never-ending, unpredictable sequence of decimal values stringing after it and can never be expressed exactly. if each number, as part of the series, is divided by its preceding values (e.g., 13/8 or 21/13), the operation results in a ratio that oscillates around the irrational figure 1.61803398875….., being higher than the ratio one time and lower the next.

We will never know, into infinity, the precise ratio. for the sake of brevity, we refer to the fibonacci ratio as 1.618 and ask the reader to keep the margin of error in mind.

This ratio had begun to gather special names even before luca pacioli (1445-1514), another medieval mathematician, called it “divine proportion.” Among its contemporary names are “Golden Section” and Golden mean.” Johannes kepler (1571-1630), a German astronomer, referred to the fibonacci ratio as one of the jewels in geometry. Algebraically, it is generally designated by the Greek letter PHI;

And it is not only PHI that is interesting to scientists (and traders also). if we divide any number of the Fibonacci summation series by the number that follows it (e.g. , 8/13 or 13/21), the series asymptotically gets closer to the ratio PHI’ with

PHI’= 0.618

this is a remarkable phenomenon- and a useful one when designing trading tools. Because the original ratio PHI is irrational, the reciprocal value PHI’ to the ratio PHI necessarily is also an irrational figure, which means that again there is a slight margin of error when calculating 0.618 in an approximated, shortened way.

we have discovered a series of plain numbers that can be applied to science by Fibonacci. before we try to use the Fibonacci summation series to develop trading tools, it is helpful to consider its relevance in nature. it is then only a small step to reach conclusions about the relevance of the Fibonacci summation in international market movements, whether in currencies or commodities, stocks, or derivatives. Humans subconsciously seek the divine proportion, which is nothing but a constant and timeless striving to create a comfortable standard of living.

### The Fibonacci summation series in nature and geometry

This is not just a numbers game, however; it is the most important mathematical representation of natural phenomena ever discovered. Generally speaking, the Fibonacci summation series is nature’s law, and it is a part of the aesthetics found in any perfect shape or curve.

Fibonacci discovered how nature’s law related to the summation series when he proposed that the progeny of a single pair of rabbits increased in a repeatable patterns.

Introduction Of the Fibonacci Trading Tools

Corrections

In General, for corrections with Fibonacci-related trading tools, an impulse wave that defines a major market trend upward or downward will have a corrective wave before the next impulse Wave reaches new territory. This occurs in both bull market and bear market conditions. Analysis would be easy if we could detect a single general pattern of corrections. The problem is that there can be many more price patterns than impulse waves in the commodities, futures, stock index futures, stocks, or currency markets. Markets move sideways for a longer period than an impulse wave appears.

Corrections are closely related to the Fibonacci ratios through the swing size and the volatility of a product. which ratio to choose depends on the product and the time intervals selected. weekly data might need different ratios from daily or intraday data. the safest way to find the best ratio for products and time spans is to test them on historical data with a computer.

the most common approach to working with corrections in research and practical trading is to relate the size of a correction to a percentage of a prior impulse wave.

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