Leonardo Fibonacci of Pisa was the most important mathematician of the Middle Ages. In 1202, he wrote a landmark book on arithmetic, which popularized the decimal and Hindu-Arabic numbering system that we use today. In that book he referred to an additive numeric sequence derived from the growth of a population of rabbits.
The Fibonacci sequence begins with 1 and 1 (two love-struck rabbits), and then progresses by adding each number to the one before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. However, what is important to us as Elliott wave students is not so much the numbers themselves as the ratios between them.
As the sequence progresses, the ratios between adjacent numbers approach closer and closer 0.618 – or its inverse, 1.618 (depending on which of two adjacent numbers you divide by). In fact, you can start the sequence with any two numbers, and the ratios will rapidly approach .618. Try these examples with a calculator.
Phi (.618034…) is an important, irrational number called the Golden Ratio. This ratio exists throughout nature – in demographic trends, the DNA helix, plants, in the structure of the human brain and in spiral structures from seashells to galaxies.
R.N. Elliott – the discoverer of the Wave Principle – also observed (without a computer) that this growth pattern found throughout the universe also shows up in stock market chart patterns. To Elliott, this could only mean that, "man's collectively expressed emotions are keyed to this mathematical law of nature."
Elliott was the first person to use Fibonacci analysis in markets. He had two main observations about Fibonacci relationships within waves:
- Corrective waves tend to retrace a Fibonacci proportion of impulse waves, most often 38%, 50% and 62%.
- Impulse waves of the same degree within a larger impulse sequence tend to be related to each other in Fibonacci proportion – as this chart shows:
Fascinating? You bet. Needless to say, proper use of this knowledge can be a powerful addition to your arsenal of market analysis tools.
And you're in luck, because on March 17 and 19, Elliott Wave International's Senior Tutorial Instructor Wayne Gorman will show practical tips on how to use Fibonacci in trading in his LIVE webinar titled,
Get more details now. (Register for this LIVE event before March 15, and you also get a free copy of Bob Prechter's "coolest book," Beautiful Pictures.)