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Leonardo Pisano is better known by his nickname Fibonacci. Born in 1170 in Italy and died their in 1250. He was educated in North Africa where his father, Guilielmo, held a diplomatic post.

Fibonacci was educated in mathematics in Bugia and traveled widely with his father. During his travels he came to recognize the enormous advantages of the mathematical systems used in the various countries. Fibonacci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe with his book Liber Abaci (1202). In addition to the use of Arab numerals, known as algorism, problems related to linear equations were discussed. It is probable that many of the problems analyzed by Fibonacci in Liber Abaci were similar to those appearing in Arab sources. The book went on to be widely copied and imitated.

The second sector of Liber Abaci contained a large collection of problems aimed at merchants. The problems focused on: (a) the price of goods; (b) how to calculate profit or loss on transactions; and (c) how to convert between the various currencies in use in Mediterranean countries – a problem that originated in China.

The Numberical Sequence of Fibonacci

A problem in the third section of Liber Abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence for which Fibonacci is best remembered today- the resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... (Fibonacci omitted the first term in Liber abaci). This sequence, in which each number is the sum of the two preceding numbers, has proved extremely fruitful and appears in many different areas of mathematics and science. This series possesses very interesting properties between which we are going to emphasize the existing relation between and among the numbers that compose it:

If we divide the numbers that are consecutive in the series as follows: 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, etc., the calculated result tends to the number 0.618.
If we divide the not consecutive numbers of the series as follows: 1/2 1/3, 2/5, 3/8, 5/13, 8/21, etc., the calculated result tends to the number 0.382.
If we calculate the reason of any number of the series to the lowest following number as follows: 21/13, 13/8, 8/5 etc., the result tends to 1.618, which it is the inverse one of 0.618.

The Most Important Ratio

The following will establish a series of priorities between the ratios and explain as, they must be in use.

The most relevant ratios is 0.382, 0.618 and 0.5. These ratios will be applied to calculate the regressions and possible evolutions of the movements of prices in percentage terms. Furthermore, many systems of graphs possess the ratios 23.6 % and 76.4 %. The first one comes from the difference between 38.2 and 50 % for 2. (n X 2=) while 76.4 % comes from the subtraction of the previous value to 100 % of possible alteration.

Dynamics in The Process of Evolution and Regression

Thus we have obtained a set of ratios that already were known and used before Fibonacci by the former Greeks and Egyptians. Concepts derived from these ratios known as the "golden proportion" were applied in constructions as Gizeh's pyramid or the Partenón. It is also known that golden proportion exists in the measures of the human body; for example, the average ear (hearing), or corporal appendices. The extremities have 3 extensions: (1) arm; (2) forearm; and (3) hand with 5 fingers that in turn have 3 extensions. Interesting truth?

The Market is A Dynamic and Social Phenomenon

In the same way, social behavior evolved. The type, geographical location of villages, and their uses and customs etc. are all linked to these principals. They have an evolutionary modality that measured graphically observes the form of a logarithmic spiral that has one ratio of growth and regression based on the "golden reason." Examples of manifestation of this spiral are seen in the shells, the caparison of the snail, the form of the galaxy. Therefore, it is believed that the stock market, besides representing an example of the behavior of the human mass, is a manifestation of the phenomenon of natural growth that characterizes any human progress.

The market is also a social behavior and as such a measurable phenomenon. The particularity is that the more dynamic the market object of analysis is as well as the size of the participants the better it will be to apply the measurement and forecast (prediction) of Fibonacci's ratios. Because of it we invite to use the technologies (skills) of Fibonacci to explore the Forex Market. The Forex Market is the best exponent of the mentioned characteristics.

Application: From the theory to the practice

The Fibonacci ratios and his lines of analysis are applied to:

Early discovery of possible bosses of setback or alteration of the directional movement of prices.
Measure of the aims of the above mentioned alterations.
Aims or zones of trading.
Points of revenue to the market.
Dynamic supports and resistances.
It helps to the placement of the stop–loss.

The Market is A Dynamic and Social Phenomenon

Application: From the theory to the practice

The Fibonacci ratios and his lines of analysis are applied to:

Early discovery of possible bosses of setback or alteration of the directional movement of prices.
Measure of the aims of the above mentioned alterations.
Aims or zones of trading.
Points of revenue to the market.
Dynamic supports and resistances.
It helps to the placement of the stop–loss.

In order that they serve the lines of Fibonacci

We are going to show these ratios as they are going to take direct application as tools of analysis at the moment of determining percentages of alteration against the principal trend or extensions in favor of it.

Let's suppose that we have a rally of prices to the rise, which measures from the minimum up to the maximum 100 points. We observe that there is in process a pattern of reversion, but we want to be necessary which will be the zone that this movement opposite to the trend was reaching.

The first zone’s target will be 38.2 percent of those 100 points, that is to say in the zone of a price of 62. This point will be taken as a minimum of probable reactions to the market. If it was not like that and the price continues to fall our next aim is in 50 percent of alteration zone for a price of 50. This point again will be interpreted as a minimum of reaction, that is to say a price that should be supported. Undoubtedly the most probable aim is 61.8 %, let's not forget that it is the “golden reason”. It is equivalent in our example to the zone of price of 32, concern of our virtual rally of 100 points.

The market will respect the zones determined by the lines planned depending on the ratios and in the above mentioned zones you will observe as the price will stop as if the market was doubting of penetrating the prices established hereby. Then, if the market respects the ratios, your trading plan cannot ignore this information.

Modalities

Attending to the devices of analyses that apply Fibonacci ratios are (1) the retracement analysis; (2) the speed lines; and (3) the arches.

The retracement is defined as the reoutline points to establish as we said it, static prices aims or zones of trading. Only it needs that to isolate the movement from beginning up to the detection a pattern of reversion, plans the lines of reoutline and places your positions on the similar market the above mentioned lines they are penetrated observing attentively also evolution in the minor graphs to that the original analysis was realized since we will be able to detect in early form alterations and this way to place our market transactions in exact points.

The speed lines are defined as those lines give us unlike previous supports - and resistances dynamical, since they extend towards the future in the shape of diagonal a graphical projection. The above mentioned lines will serve as guide of the movement and you see one damaged they propose us an aim (lens) of prices that one finds in the close line of speed. These aims are dynamical since the speed lines will change the point of the support and resistance as it passes the time of measurement.

The arches besides the dynamical properties of aims of prices offer to us the possibility of measuring the temporary cycles since the above mentioned arches related in the scale of the axis of time allow to the being to project and to be predicted by it. In that moment will touch the price the arched line.

The process would be the following: One vertical line are placed in periods corresponding to the series. That is to say, vertical lines are placed in the periods of 5, 8, 13, 21, 34, 55, 89, etc. With this one lines relate to the lines of the arches and these crosses will give us forecasts (predictions) with a degree of important accuracy.

With Fibonacci's arches it joins changeable time. Not only it is a question of identifying the zones of support and resistance, but when they are going to produce these. It is suitable to use together the all lines and Fibonacci's arches. The strongest signs are produced when both types of curves coincide.

W.D Gann- The Numbers and Gann’s Geometry

Mr. Gann was known as a prolific businessman and for the theoretical and practical contributions to Technical Analysis- his concept of price in relation with the time was the only and insuperable. Though his mathematical and geometric theories are complex once understood they are useful and help to predict behaviors of the market. It has been said of him: "... We have seen him to pass in one 16th consecutive orders in the same action, eight of which turned out to be operations done exactly in the support or resistance of the above mentioned wave and we it can verify. A record like that of operations does not have precedent in the history of Wall Street (Ticker and Investment Digest, Volume 55 Number 2, December, 1909, page 54.)

The Geometry

Many people claim that Gann's theories are big series of discoveries that do not guard any relation, though this is not real. Gann believed that it fixes the variables in the technical analysis (price, range of fluctuation and time), they could be analyzed to the same time. His symbol a circle with a square and a triangle inside, they summarize his technologies of analysis.

Gann discovered that the supports and the resistances of the prices could be calculated taking the roof of market and to divide it by four and by three - in other words in his fourth and third party divides. The square and the triangle inside the circle show us this concept. The points of resistance are calculated acting of similar form with the ranges of fluctuation and the lapses of time.

Angles: The Sustainability of the 45º Angle

He taught his pupils to observe soils and roofs every 30 days, using the degrees of the angles of his symbol as help, verifying that 90-, 180-, 270-and 360-, which do not stop to be the sum of the angles of a square or 120-, and 240-, that of the triangle, are used as tool of forecast (prediction), expressed in days. But actually to the cycles that more importance was giving Gann it was to the cycles of 144 and 360 days and his respective divisions in a quarter and a third.

Gann affirms that on a market with a definite trend, the lines of trend planned possess certain angles; likewise, a change in the trend takes place (is produced) when they give themselves three temporary movements in opposition to the principal movement (for example, three days of falls after a marked up). The most important angle for Gann is of 45º (known also as line 1x1, because relation between the price and the time one expresses to one. Therefore, we will say that a trend can be inverted temporarily or definitively, depending on that the above mentioned correlation between price and time is kept or not. Major all that is the angle that dominates a raise, major is the force of the movement.

Speed lines

It is a device used to establish dynamical aims (lenses), supports and resistance and plan bearing in mind the division of an angle of 90 degrees in 8 angle combinations to which there is awarded a speed and the percentage one of possible setback.

This way, for Gann the most significant percentages of setback from a maximum or a minimum are 12.5 % (1/8), 25 % (2/8), 37.50 % (3/8), 50 % (4/8), 62.50 % (5/8), 75 % (6/8), 87.50 % (7/8) and 100 % (8/8) of the previous movement. Gann attributed a particular importance to the setbacks of 50 %, of 37.50 % and of 62.50 %; three alterations characterize respectively the most balanced alteration, the minimal alteration and the maximum alteration of the movement.

It is a device used to establish dynamical aims(lenses), supports and resistance and plan taking the division of an angle of 90 degrees in 8 angle combination, with a speed and the percentage one of possible setback.

Now, for Gann, more significant percentages of setback from a maximum or a minimum are 12.5 % (1/8), 25 % (2/8), 37.50 % (3/8), 50 % (4/8), 62.50 % (5/8), 75% (6/8), 87.50% (7/8) and 100% (8/8) from previous movement. Gann gave main importance to 50%, 37,50% and 62.50% retracements; This three alterations are the most balanced alteration, the minimal alteration and the maximum alteration of the movement.

Application: The square

He realized on the historical letter of the prices of the value under examination a distribution inside a rectangle that was creating from the historical minimum that grown-up in the shape of logarithmic spiral. On the above mentioned letter he was planning the angles of 45,90,180,270 and 360 degrees and was locating the possible temporary aims of price inside the square in favor or in opposition to the logarithmic spiral bearing in mind the current price. This nowadays allows us to know which are the possible aims y/maximums or minimums of reaction of the market.

Relation between Fibonacci and Gann:

Both theories take mathematical relations as a sustenance between the prices.
Respect of the speed lines of one and another device, empirically we have observed that the angle of Sustentation of the Line directive 45º degrees coincides with regressions of 38.2 and of 61.8 % with the same rally when the extension impulse of the prices has had a volatile development. Angle 1/8 for example.
A natural level of great importance in Gann's theory is the number 144 (number of Fibonacci) and his multiple ones.
Fibonacci's setbacks of 38.2, 50 and 61.2 coincide almost exactly with the proposed ones for Gann of the setbacks of 50 %, of 37,50 % and of 62.50 %.
The application of both theories in the practice relates price and time.

(Adrian Aquaro is a Principal of www.tcollegeweb.com and is an expert in the area of Technical Analysis.)

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