Fibonacci numbers are named after Leonardo Fibonacci, a twelfth century Italian mathematician, who discovered the unique properties of a particular number sequence; apparently from studying the dimensions of the Great Pyramid at Gizeh in Egypt.
|1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.|
|Each number in the sequence is the sum of the previous two numbers:
1 + 1 = 2,
1 + 2 = 3,
2 + 3 = 5,
and so on....
As we progress along the sequence, the ratio of each number to its preceding number approaches closer and closer to the golden ratio: approximately 1.618. The golden ratio, often represented by the Greek letter Φ (Phi), is calculated as:
( 1 + √ 5 ) / 2
Each number is also approximately 0.618 of its successor. This reciprocal number, known as φ (phi), is calculated as:
( √ 5 - 1 ) / 2
Where √ 5 is the square root of 5.
|Fibonacci Golden Ratio and its Reciprocal|
|Each number divided by its predecessor approaches 1.618||Each number divided by its successor approaches 0.618|
Fibonacci numbers occur throughout nature:
- the arrangement of petals in most flowers
- the arrangement of leaves on most plants
- sea-shell spirals
- the arrangement of seeds on sunflowers, pine cones and many other plant species.
While the Fibonacci number sequence may be prevalent in nature, it is not a universal law. There are many exceptions.
Four ratios are normally plotted:
- 0.618 (or 61.8 per cent), the reciprocal of the golden ratio, is the most important;
- 0.50 (or 50 per cent) - the second number divided by the third (1 divided by 2);
- 0.382 (or 38.2 per cent) - the reciprocal of the golden ratio squared (i.e. 89 / 233);
- 0.236 (or 23.6 per cent) - the reciprocal of the golden ratio cubed (i.e. 55 / 233).
Fibonacci ratios regularly occur in stock market cycles and in the determination of support and resistance levels. Some traders attach almost mystical significance to them, but I have yet to find any statistical support for this.
The weakest of the Fibonacci ratios is 0.50. In fact some maintain that 0.50 is not really a Fibonacci ratio at all because it has no connection to the golden ratio. Nevertheless, it is probably the most prevalent: the first line of support in a rally is the previous peak -- which often equates to a 50% retracement.