LEONARDO FIBONACCI

Leonardo Fibonacci was a brilliant Italian mathematician who lived during the late 1100's and early 1200's. He introduced or discovered many important new ideas, but one of his most famous is a natural mathematical series. The Fibonacci series is the sum of the two previous numbers. Starting with one and two, the next number in the series is the sum of one and two:

          1+2=3

The next number is the sum of 2 plus 3:

          2+3=5

The series continues:

          3+5=8

          5 + 8 = 13

and so on and is written as:

        1, 2, 3, 5, 8, 13, 21, 34, 55, . . .

and continues indefinitely.

Fibonacci believed the numbers in the series had special importance. He visited the great pyramid of Gizeh in Egypt, and noted many of the dimensions. He believed the ancient cultures may have maintained a significance with this series of numbers because certain dimensions in the great pyramid corresponded with the series.

The ratio of two consecutive numbers in the Fibonacci series approaches 0.618 as shown in the following calculations:

1/2 = 0.5

2/3 = 0.667

3/5 = 0.6

5/8 = 0.625

8/13 = 0.615

The ratio 0.618 is called the golden mean and had special significance with the ancient Greek and Egyptian cultures. They believed the number had important implications in many areas of science and art. Many buildings, including the pyramid, were built with this dimension in mind. The golden mean has been, and still is an important reference level in the arts, such as painting.

Many occurrences in nature seem to exhibit either the Fibonacci series or the golden mean. For example, certain flowers such as daisies increase the number of their petals in a Fibonacci sequence. Certain animal shapes and dimensions in galaxies exhibit the golden.

The Fibonacci series is an interesting mathematical idea, but what does it have to do with trading? Many studies, such as the Elliott Wave theory, are based on some of the concepts of the Fibonacci series.

PERCENTAGE RETRACEMENTS

Percentage retracements refer to the market reacting from a high or low by a certain percentage. The more popular retracements include the 25%, 33%, 38%, and 50% retracement levels which are derived from the importance of the common fractions 1/4, 1/3, 3/8, and 1/2. The 3/8 is an important fraction because of its relationship with the golden mean. Recall from the Fibonacci section the golden mean 0.62 is considered an important number. The 38% retracement Is derived by subtracting 1 from the golden mean or 1 - 0.62 = 038.

These percentage levels, when measured from the high of a move, should act as a support level when the market retraces from the high. The percentage levels, when measured from the low of a move, should act as a resistance level when the market retraces from the low.