Fibonacci review

The Fibonacci ratios are named after Leonardo of Pisa, an Italian mathematician who introduced the Hindu- Arabic number series that would eventually bear his name to Western Europe in his work titled Liber Abaci (Book of Calculations) approximately eight centuries ago.

The Fibonacci sequence is a number series for which every new number is the sum of the previous two numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 etc. One of the primary properties of the series is that as it progresses, the ratio of any number and its preceding number comes increasingly closer to 0.618 — e.g., 55/89 = 61797, 377/233 = .61803, and so on.

The Fibonacci ratio is found in, among other things, the geometry of the logarithmic spiral found throughout nature (in a snail’s shell, etc.).

The ratio of the length of the arc to its diameter is 1.618, which is the inverse of 0.618.

Another natural form that exhibits Fibonacci proportions is the double helix of the DNA molecule.

Fibonacci ratios are used by both classic technical analysts and Elliott Wave practitioners. For example, Elliott Wave adherents often project future price targets by measuring the most recent trend and multiplying by a Fibonacci ratio.

Here’s a summary of some of the Fibonacci series’ interesting numerical relationships:

• The sum of any two consecutive numbers in the series equals the next number.

• After the first four numbers, the ratio between two consecutive ascending numbers approaches 0.618, which is a common retracement percent used by traders.

• As the numbers rise, the ratio between two consecutive descending numbers approaches 1.618, which is the inverse of 0.618.

• The ratio between every other number in ascending order (e.g., 55 and 144) approaches 0.382, while the inverse approaches 2.618.