# Understanding Fibonacci Numbers and Their Value as a Research Tool

## What Are Fibonacci Numbers?

Fibonacci studies are popular trading tools. Understanding how they are used and to what extent they can be trusted is important to any trader who wants to benefit from the ancient mathematician's scientific legacy. While it's no secret that some traders unquestionably rely on Fibonacci tools to make major trading decisions, others see the Fibonacci studies as exotic scientific baubles, toyed with by so many traders that they may even influence the market. In this article, we examine how the Fibonacci studies may influence the market situation by winning the hearts and minds of traders.

### Key Takeaways:

• Fibonacci studies are popular trading tools used by investors to make trading decisions.
• Leonardo Pisano Fibonacci applied the ancient Indian system of nine symbols and other mathematical skills to develop Fibonacci numbers and lines.
• Some consider that the Fibonacci tools can successfully predict market behavior in 70% of cases while others consider the method too time-consuming and complex.

## Understanding The Famous Italian

It was during his travels with his father that the Italian Leonardo Pisano Fibonacci picked up the ancient Indian system of nine symbols and other mathematical skills that would lead to the development of Fibonacci numbers and lines.

One of the Italian's works, Liber Abaci (1202), contained some practical tasks that were related to merchant trade, price calculations, and other problems that needed to be solved as a matter of their everyday activities.

An attempt to solve a sum about the propagation ability of rabbits gave birth to the system of numbers that Fibonacci is known for today. A sequence in which each number is the sum of the two numbers that precede it seems to be nature's underlying principle behind life's many events and phenomena.

Leonardo Fibonacci also applied his life-inspired theory in conjunction with geometrical constructions. It is this marriage of concepts that continue to be used by traders to help them cash in on their investments.

### The Enigmatic Legacy

Let us first look more closely at what the Fibonacci numbers are. The Fibonacci sequence is as follows:

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

This sequence moves toward a certain constant, irrational ratio. In other words, it represents a number with an endless, unpredictable sequence of decimal numbers, which cannot be expressed precisely. For the sake of brevity, let's quote it as 1.618. At present, the sequence is often referred to as the golden section or golden average. In algebra, it is commonly indicated by the Greek letter Phi (Phi = 1.618).

The asymptotic behavior of the sequence and the fading fluctuations of its ratio around the irrational Phi number can be better understood if the relations between several first members of the sequence are shown. The following example illustrates the relationship of the second member toward the first one, the relationship of the third member toward the second one, and so on:

1:1 = 1.0000, which is less than phi for 0.6180

2:1 = 2.0000, which is more than phi for 0.3820

3:2 = 1.5000, which is less than phi for 0.1180

5:3 = 1.6667, which is more than phi for 0.0486

8:5 = 1.6000, which is less than phi 0.0180

As the Fibonacci sequence moves on, each new member will divide the next one, coming closer and closer to the unreachable phi. Fluctuations of the ratio around the value 1.618 for a lesser or greater value can also be seen when using the Elliott wave theory.

In many cases, it is believed that humans subconsciously seek out the golden ratio. For example, traders are psychologically uncomfortable with excessively long trends. Chart analysis has a lot in common with nature, where things that are based on the golden section are beautiful and shapely, and things that do not look ugly and seem suspicious and unnatural. This, in small part, helps to explain why, when the distance from the golden section becomes excessively long, the feeling of an improperly long trend arises.

There are five types of trading tools that are based on Fibonacci's discovery: arcs, fans, retracements, extensions, and time zones. The lines created by these Fibonacci studies are believed to signal changes in trends as the prices draw near them.

### How It Works

It is a popular opinion that when correctly applied, the Fibonacci tools can successfully predict market behavior in 70% of cases, particularly when a specific price is predicted. Others consider computations for multiple retracements too time-consuming and difficult to use. Perhaps the greatest disadvantage of the Fibonacci method is the complexity of the results for reading and the ensuing inability of many traders to really understand them. In other words, traders should not rely on the Fibonacci levels as compulsory support and resistance levels. In fact, they may actually be levels of psychological comfort as well as another way to look at a chart. The Fibonacci levels, therefore, are a sort of a frame through which traders look at their charts. This frame neither predicts nor contributes anything, but it does influence the trading decisions of thousands of traders.

However, Fibonacci studies do not provide a magic solution for traders. Rather, they were created by the human mind in an attempt to dispel uncertainty. Therefore, they should not serve as the basis for trading decisions. Most often, Fibonacci studies work when no real market-driving forces are present in the market. It is obvious that the levels of psychological comfort and the "frame" which they make up, and through which the majority of traders look at their charts, are by no means the determining factors in those situations when more important reasons for the prices' growth or reduction exist.

When used by a vast number of traders, the Fibonacci studies themselves may become a major factor influencing the market. Most of the time, the Fibonacci studies work due to the cascade effect, which arises because of the huge number of traders artificially creating support and resistance levels.

The market is a complex system and the realization of the true nature of Fibonacci studies as a self-fulfilling prophecy will help you use the tools more efficiently. How? Very simple: it will help to avoid any perilous over-reliance on those tools.

## Special Considerations

The Fibonacci method should only be used in a combination with other methods, and the results derived should be considered just another point in favor of a decision if they coincide with the results produced by the other methods in the combination.

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. Laurence Sigler. “Fibonacci's Liber Abaci,” Page v. Springer New York, 2012.

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