**Fibonacci studies** encompass a series of technical analysis tools based on Fibonacci numbers and ratios representing **geometric laws of nature **and** human behavior**, applied to financial markets.

Fibonacci numbers and Fibonacci ratios are used by a wide range of traders to spot potential turning points in the market.

## Fibonacci Series

The Fibonacci series was introduced by an Italian mathematician, Leonardo Pisano Bogollo who was also known as Fibonacci (son of Bonacci), in his 1202 manuscript

*Liber Abaci.*

The series is derived by finding the sum of the two preceding numbers in the series, with 0 and 1 being the seed numbers, or starting point, in the series.

With 0 and 1 being the first two seed numbers, the third number in the series is the sum of 0 and 1 (0 + 1), which is 1.

The fourth number in the series is the sum of the second and third numbers in the series, namely, 1 + 1, and so forth.

The first few numbers in the series thus are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... ∞

## Fibonacci Ratios

As the numbers in the series increase towards infinity,

**mathematical relationships**, expressed as ratios, appear between the numbers.

For example, the ratio between consecutive numbers tends to oscillate closer and closer towards **1.618034**, which is known as the **golden ratio** or the **golden section** or the **golden mean** and is denoted by the upper-case Greek letter Phi Φ in mathematics. This ratio is reached by dividing a number in the summation series by the number that precedes it: 233 ÷ 144 = 1.618055

The inverse of this ratio is **0.618034**, which is denoted by the lower-case Greek letter phi φ in mathematics. This ratio is reached by dividing a number in the summation series by the number that succeeds it: 144 ÷ 233 = 0.618025

In general, these ratios are **used to predict levels of support and resistance** through relationships between Fibonacci numbers. These are the most used Fibonacci ratios:

**0.618**(61.8%): A Fibonacci number divided by the number that follows is approximately 0.618.**0.382**(38.2%): A Fibonacci number divided by the number occupying two later positions is approximately 0.3820.**0.2360**(23.60%): A Fibonacci number divided by the number occupying three later positions is approximately 0.2360.**0.764**(76.4%): Obtained by adding the difference of 38.2% and 23.6% to 61.8%, that is, 76.4% = 61.8% + (38.2% – 23.6%).**0.5**(50%): Half the progress of the main trend. It’s the average between 38.2% and 61.8%.**0.0**(0%): Beginning of a market movement.**1.9**(100%): End of a market movement.

To understand Fibonacci studies, it’s necessary to remember the concept of support and resistance.

**Support**: The troughs (or lows). These are the points at which the buying interest is**strong enough to overcome the selling pressure**. As a result, the decline is suspended and the price rises again.**Resistance**: The peaks (or highs). These represent a price level or area above the market where**the selling pressure exceeds the buying pressure**.