The Fibonacci numbers sequence and the golden ratio have fascinated mathematicians for hundreds of years.

While Fibonacci numbers have many applications, they have received considerable interest from traders due to their uncanny accuracy in spotting market turning points in advance.

You can use Fibonacci numbers as a predictive tool and when used correctly they can enhance a your analysis of the market, helping you to increase profits and decrease risk.

The History of Fibonacci Numbers

The Fibonacci number sequence first appeared as the solution to a problem in the Liber Abaci, a book written by Leonardo Fibonacci in 1202 to introduce the Hindu-Arabic numerals used today to a Europe still using Roman numerals.

The original problem in the Liber Abaci posed the question: How many pairs of rabbits can be generated from a single pair, if each month each mature pair brings forth a new pair, which, from the second month, becomes productive.

The Fibonacci number Sequence

The resulting Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, are the result of the following equation.

If Fn is the nth Fibonacci number, then successive terms are formed by addition of the previous two terms, as Fn+1 = Fn + Fn-1, F1 = 1, F2 =

The ratio of any number to the next larger number is 62%, which is a popular Fibonacci retracement number. The inverse of 62% is 38%, and this 38% is likewise a Fibonacci retracement number.

Fibonacci Numbers and the Golden Ratio

Fibonacci numbers are found to have many relationships to the Golden Ratio F = (1 + /5)/2, a constant of nature which was of constant interest to the ancient Greeks, appearing in both Greek art and architecture.

Fibonacci Numbers and Market Analysis

Changes in stock prices are not simply a tug of war between supply and demand but also reflect human opinions, valuations, and expectations.

A study carried out by mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi, with 61.8% positive and 38.2% negative and that Fibonacci numbers are rooted in a trader