# Fibonacci Numbers

Up to now, our review of Elliott Waves has only covered the wave form in itself. But there is more to the Elliott Wave Theory than simply describing the shapes and repetitions of the waves observed in the price.

The theory also includes ratios which can be applied to both price and time. These ratios are derived from the Fibonacci sequence of numbers, discovered in the 13th century, and related to many natural observations. Leonardo Fibonacci at that time noticed that in nature there were certain recurring patterns that could be identified mathematically, now known as the Fibonacci sequence of numbers. The Fibonacci sequence is easily generated by adding together the two previous numbers to make the next, so the beginning of it is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and so on to infinity.

Fibonacci

The applicability of the Fibonacci sequence in many diverse areas is astonishing. For instance, you can see the numbers in the spiral patterns of the head of a sunflower; in seashells; in ferns; and in many other natural areas. In fact once you start looking for them, you will see the ratios and numbers in many areas of nature. If you are so inclined, there is plenty of information on the Internet about these other relationships.

One of the features of the number sequence is that the ratio between two adjacent numbers tends towards 0.618 or taken the other way towards 1.618, which is the inverse of 0.618, known as the golden ratio or golden mean. This ratio is also a natural part of the Elliot Wave Theory which Robert Prechter outlines superbly in his book The Elliott Wave Principle, the bible on Ralph Elliott’s price-behaviour theories of the 1930s. Elliott believed that man’s behaviour conformed to these numbers, including when he traded on the stock market. The Fibonacci sequence provides the basis for the wave principle, even though many applications include 0.50 with the sequence fractions simply because it seems to work too.

Some people tend to find Elliott quite complicated but in actual fact it’s quite simple.

In fact, the ratio between alternate numbers tends towards 2.618, or the inverse 0.382. Elliot stated in his book ‘Nature’s Law’ that his wave principle was based on the Fibonacci sequence, and you can see that Fibonacci numbers count the number of waves as you increasingly subdivide the form. But further than that, here are some rules of thumb based on Fibonacci numbers.

- the target for the length of wave 3 is wave 1 multiplied by 1.618
- the target for the top of wave 5 is wave 1 multiplied by 1.618 then doubled, added to the top and bottom of wave 1 to give maximum and minimum targets
- for a normal correction, wave A and wave C are usually equal, and wave C is wave A multiplied by 0.618 below the bottom of A
- for a flat correction, the length of wave C is about 1.618 times the length of wave A
- for a symmetrical triangle, each successive wave is about 0.618 times the previous length

Fibonacci are similar in workings to the daily pivots and is considered a reliable trading tool for trading any timeframe chart. It is particularly useful for extreme price movements for the trading day. Fibonacci are in fact related to patterns in nature and everything; imagine trading on the natural rhythm of life, as opposed to treating trading as a zero-sum game where everyone else is out to get you!

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