| The Fibonacci numbers sequence and the golden ratio | | | | Fibonacci Numbers and Market Analysis |
| have fascinated mathematicians for hundreds of | | | | Changes in stock prices are not simply a tug of war |
| years. | | | | between supply and demand but also reflect human |
| While Fibonacci numbers have many applications, they | | | | opinions, valuations, and expectations. |
| have received considerable interest from traders due | | | | A study carried out by mathematical psychologist |
| to their uncanny accuracy in spotting market turning | | | | Vladimir Lefebvre demonstrated that humans exhibit |
| points in advance. | | | | positive and negative evaluations of the opinions they |
| You can use Fibonacci numbers as a predictive tool | | | | hold in a ratio that approaches phi, with 61.8% positive |
| and when used correctly they can enhance a your | | | | and 38.2% negative and that Fibonacci numbers are |
| analysis of the market, helping you to increase profits | | | | rooted in a trader's psychology. |
| and decrease risk. | | | | Predicting Market Movements with Fibonacci Numbers |
| The History of Fibonacci Numbers | | | | Research shows markets as being perfectly |
| The Fibonacci number sequence first appeared as the | | | | patterned, explaining that humans, being part of nature, |
| solution to a problem in the Liber Abaci, a book written | | | | create perfect geometric relationships in their |
| by Leonardo Fibonacci in 1202 to introduce the | | | | behaviours, even if they don't realize it themselves. |
| Hindu-Arabic numerals used today to a Europe still | | | | The Golden Mean is the number 0.618. In Both Greek |
| using Roman numerals. | | | | and Egyptian cultures, this number was highly |
| The original problem in the Liber Abaci posed the | | | | significant. They believed that the number had |
| question: How many pairs of rabbits can be generated | | | | important implications in many areas of science and |
| from a single pair, if each month each mature pair | | | | art. This dimension was utilised in the construction of |
| brings forth a new pair, which, from the second month, | | | | many buildings - including the pyramids. |
| becomes productive. | | | | The Golden Mean appears frequently enough in the |
| The Fibonacci number Sequence | | | | timing of highs and lows and price resistance points |
| The resulting Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, | | | | that adding this tool to technical analysis of the |
| 55, 89, are the result of the following equation. | | | | markets can help to identify key turning points. |
| If Fn is the nth Fibonacci number, then successive | | | | W. D.Gann and Fibonacci Numbers |
| terms are formed by addition of the previous two | | | | Gann was a stock and commodity trader who |
| terms, as Fn+1 = Fn + Fn-1, F1 = 1, F2 = | | | | reputedly made over $50 million trading the markets. |
| The ratio of any number to the next larger number is | | | | Gann made his fortune using methods which he |
| 62%, which is a popular Fibonacci retracement number. | | | | developed for trading instruments based on |
| The inverse of 62% is 38%, and this 38% is likewise a | | | | relationships between price movement and time and |
| Fibonacci retracement number. | | | | his work was heavily influenced by Fibonacci numbers. |
| Fibonacci Numbers and the Golden Ratio | | | | Gann divided price action into eighths and thirds. This |
| Fibonacci numbers are found to have many | | | | yields numbers such as 1/3, 3/8, 1/2, 5/8, and 2/3. In |
| relationships to the Golden Ratio F = (1 + /5)/2, a | | | | percentage terms, these fractions are 33.3%, 37.5%, |
| constant of nature which was of constant interest to | | | | 50%, 62.5%, and 66.7%. These five ratios are |
| the ancient Greeks, appearing in both Greek art and | | | | commonly used retracement values. Gann placed |
| architecture. | | | | strong significance on 50% retracements. |