# What are Fibonacci numbers?

The Fibonacci sequence is named after Leonardo of Pisa who was known as Fibonacci (a contraction of *filius Bonacci*, "son of Bonaccio). He is considered one of the greatest mathematicians of the middle ages. His book *Liber Abaci*, published in 1202 introduced the Fibonacci sequence to the west.

The sequence is as follows:

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

There are a number of interesting things to note.

Each Fibonacci number is obtained by adding the previous two Fibonacci numbers together. For example, 144 added to 89 equals 233. Each number measures 1.618 the previous number, and .618 of the next number (the larger the Fibonacci number the closer the relationship is to the exact 0.618 and 1.618.).

0.618 and 1.618 are known as Fibonacci ratios.

Each number is related to the number two places away (e.g. 21 and 55, or 144 and 377) by the ratios 0.382 and 2.618. Subtracting 0.618 from 1 equals 0.382.

1.618 is also known as the Golden Ratio or the Golden Mean in mathematics and the arts. A ratio that occurs in nature and that is also pleasing to the eye. Many artists and architects have proportioned their works to approximate the golden ratio. You can find a great deal of additional information by googling the Golden Ratio or the Golden Mean

How does this relate to markets? Well, technicians have long observed that market movements often approximate Fibonacci numbers in extent (either numerical or percentage) and often in time; or are related to prior movements by Fibonacci ratios.

Fibonacci and Elliott Wave go hand in hand.

Suffice to say, Wave 3 Technical Trading incorporates Fibonacci and Elliott Wave into its methodology.