Fibonacci numbers

Fibonacci numbers! Doesn't that sound a lot like an enormous chapter in high school mathematics' book? If that's what you think then you are absolutely right. We are indeed talking about those kinds of numbers. Fibonacci numbers are a sequence of numbers formed as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… etc

The sequence begins with 0 and 1.  Then keep adding the last two numbers to get the next. Meaning that:

0+1=1

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13

well, you have got the picture now!

Why this sequence is called Fibonacci? The sequence of numbers was discovered by Leonardo de Pisa, also known as Fibonacci. He lived in 12^th century and was lucky enough to be the one to discover this amazing mathematical sequence. Off the topic Fibonacci numbers can be found EVERYWHERE! Scary enough these numbers represent the natural proportions of things in our enormous universe. And since forex is a part of the universe – Fibonacci numbers are applied here as well in search of a simple proportional solution for trading profits!

Speaking of trading, lets get to the main issue here – forex. You don't have to learn how to calculate any of this by yourself. The forex broker of your choice will provide you with software that calculates everything for you. 

Now here is the mystery – with major ratios calculated from Fibonacci numbers forex traders can actually predict a behavior of trend and countertrend movements in forex market. Spooky!!! 

Here is a set of numbers to remember: 38%, 50% and 62%  

If you take these percentages and apply them to the trending price you will notice not only a certain amount ofretracement, but also where new high and low could go. These marks are very important to forex traders since they are support and resistance areas where the price will either hesitate for a while or will reverse. 

Before grabbing the charts there is one more thing you have to know. The primary trends move all together in 5 waves. First there are 3 forward waves, and then there are 2 backward waves. Now countertrends move differently – 3 waves at a time. First there are 2 forward waves, followed by 1 backward wave.  

Now you are officially eligible to get some charts to "play" with and test your knowledge. Once you figure out how to place the marks correctly (every trading platform is different), you will definitely notice Fibonacci ratios in the price movements as it changes the position from support to resistance and back to support. Then you will realize that looking at certain time frames the trends tend to have similar proportionality. Wow!!

Whether on a hourly or a daily chart the Fibonacci lines that you draw are relevant until the price action has either confirmed or rejected them. Lets say if the price retraces to 38% line and then suddenly reverses again back to its original path crossing over the 0% line then you can for sure say that the cycle is over.    

Fibonacci Spiral

 The Fibonacci Spiral is a geometric spiral whose growth is regulated by the Fibonacci Series. Its sudden, almost exponential growth parallels the rapid growth of the series itself.

 The spiral itself is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. This is illustrated below.

Fibonacci rectangle

Another interesting occurrence of Fibonacci numbers in nature is the relationship to proportional squares. Taking an example, we draw a series of squares starting with the size of the first numbers in the Fibonacci sequence.

Continuing to draw squares with a size equal to the next Fibonacci number in the sequence we end up with a picture of squares all placed together to from a larger rectangle. The following steps illustrate this concept:

1. Start with two squares of size 1 and 1 (the first numbers in the Fibonacci sequence)

2. Add a square of size 2 on top of these two squares, then add a square of size three to the right side of this square. The shape which is produced by the group of squares is known as the Fibonacci rectangle.

3. The process continues with a square representing the size of the next Fibonacci number being added to the Fibonacci rectangle, the new square will reside on the next clockwise face of the rectangle. This process continues indefinitely. The following picture shows the Fibonacci rectangle produced up to the 13 number.

 

The Fibonacci Spiral in nature

When a circle is drawn in each square in the Fibonacci rectangle so that a quarter circle appears in each square it produces a spiral. This is shown in the picture above on the right.

This spiral formation occurs in many places in nature. You may have seen this shape in various sea shells.

Fibonacci quotes

Fibonacci quotes - Fibonacci quotes are derived applications of Fibonacci mathematical theories. One of them questions about the number of rabbits that can be bred from a single pair in a year. Differentiating into specifics, the quote says that a man owns a pair of rabbits enclosed inside a walled structure. They can breed every month a pair and start breeding in the second month after their month.

Fibonacci Golden Rule

Fibonacci Golden Rule - The golden ratio has been a subject of extensive study for mathematicians and naturalists, and is accurately affiliated with the Fibonacci sequence. As the definition goes, Fibonacci sequence is the result of an explicit addition of its two preceding terms. Golden ratio, on the contrary, being derived from the formula: Fn=((Phin-(1-Phi)n)/Sqrt[5]; is the limit of the proportions obtained by dividing the preceding two terms. As the Fibonacci sequence progress rightwards, the ratio of the preceding two terms inches amazingly near to the golden ratio.

Fibonacci functions

Fibonacci functions - Fibonacci functions are represented as Fn = Fn-1 + Fn-2; where F denotes a function followed by a subscripted symbolization of its iteration. They can be alternately elucidated as 'a generalized form of Fibonacci numbers'. However, for reporting the magnitude for the nth term, adding the numbers iteratively may produce an uphill task (especially in cases where n is very large). Therefore, a special function has been devised to resolve this impediment, given by: an = [ Phin - (phi)n]/Sqrt[5]; where Phi = (1+Sqrt[5])/2.

Fibonacci biography and history facts

Mathematical contributions of Fibonacci

Fibonacci introduced the arithmetic system of Hindu-Arabic fundamentals in Europe for the very first time. Its still the positional systems which are continued to be used till today. It contains ten digits and zero and a decimal point.

Fibonacci had written a book - Liber abbaci, the book on abacus or calculating, which explains the different logical methods for doing the arithmetic in the logical and decimal system. This book was completed by 1202 and simultaneously Fibonacci tried his level best to persuade and convince the other mathematicians to apply the system. This book is written in Latin and meticulously explains the different methods for addition, subtraction, multiplication and division. There are many different problems to further explain the process.

The Fibonacci numbers

The Fibonacci number series includes the consecutive addition of first two numbers to give the third one. For example, 0+1=1, 1+1=2, 2+1=3 and so on. So the Fibonacci numbers are 0, 1,2,3,5,8,13, 21, and 43 and so on. Amazingly, these Fibonacci numbers have their role in Forex trade and currency marketing. They aid in the charting of curves, rectangles and triangles through which the forecasting of the forex market is done.

Contributions

The important contribution of Fibonacci in the number theory is one of the most important incorporations in the domain of arithmetic and calculations. He conferred the following benefits.

1. Implementation of square root notation.
2. Introduction of bars in the fractions. Earlier, the numerator used to have quotations around it.

Later it was discovered that the Fibonacci numbers and the respective series were not only limited to the arithmetic but it also played a pivotal role in economics, commerce and trading sectors too.

Fibonacci Forex trading

The concept of Fibonacci forex trading has been used by millions of forex traders all around the world. These numbers forecast the coming oscillation in the forex charts. Though, at the same time, the prediction made cannot be proclaimed as flawless and straight hitting to the mark, the closeness it gets to is quite amazing. Thus, this has also led to the emergence of the Fibonacci price points. Thus, the Fibonacci levels are very elementary and fundamental concepts which need to be grasped before delving into the risky environment of forex trading.

Algorithm of Fibonacci analysis

Fibonacci analysis and algorithm: Technical analysis is one of the most pivotal tools for forecasting the different twists and turns of the forex trading. Resistance and support levels in the bar charts of the forex trading are the most important components which have to be scrutinized through the technical analysis. These levels are very important to know regarding the entry and exit spots of the forex market. For this respective utility, the Forex traders are also using the "retracement" levels involving the Fibonacci percentages. 38.2% and 62.8% are the two most important retracement levels in the Fibonacci percentages.

Retracement technique: the algorithmic sequence in Forex trading

Most of the times, the retracement track is planned by the forex traders with respect to the initial and peak price of the currencies. At the same time, there are other retracement percentages which are used for the technical analysis like 33%, 50% and 75%. For example, if the initial value of any price trend was zero and later it reached to its peak of 100 but eventually, it lowered to 50, its retracement would be 50%. The same concept is applicable in other calculations are well. In the same manner, if the market price is witnessing a downtrend, the "correction" can be applied in it.

Fibonacci numbers and their application in forex market

The Fibonacci numbers were introduced by Leonardo da Pisa, a renowned mathematician of the 13th century. The Fibonacci sequence was invented by him, a series which later became to be applicable to various realms of arithmetic, economics, commerce and even forex trading. The Fibonacci sequence is as follows like 0, 1,2,3,5,8,13 and so on to infinity. The addition of the first two members given the third consecutive number and there on, the process continues. This sequence aids in the forecasting of the forex market, the oscillations in the exchange rates and the currency conversions. Moreover, since forex is all about history repeating itself time and again, the sequence aids in grasping the fundamentals of forex trading.

The Golden ratio

Later, more calculations were made and it became evident that the sequence also follows a certain fixed ration. For example, when the particular number was in ratio with its just next higher number in the sequence, the value came out to be 0.618 while on the other hand, if the number was in ratio with the previous lower number, the ratio came out to be 1.618. Eventually, these two ratio values were known as the Golden mean or the Golden ratio. It was also later realized that the application of the Golden ratio and the Fibonacci numbers in the technical analysis was very beneficial as it also reflected the human behavior and human nature. This is because the Fibonacci numbers and the golden ratio are applicable to everything from architecture to human body, music, biology and art. Most of the forex traders who have been adopting this technique feel that the entire concept is applicable because trading is related to both science and art. They believe that after a lot of meticulous and close scrutiny of the forex market, it becomes clear that both the price movements and patterns of human behavior are interlinked and the Fibonacci technique have relations to both the patterns.

Risk and greed tolerance are applicable to the forex trade and guide the outputs of the trade. Most of the traders, whether long term or short term undergo the risking and greed tolerance levels. In this case, if an average it calculated, it becomes evident that what the current perspectives of the traders are. In the same manner, the Fibonacci sequence reveals through the cost of the pricing instruments that how many traders have reached or are reaching the tolerance levels.

With the application of the Fibonacci techniques, it also becomes easier to predict the various turning points which would crop up in the forex trading.