Leonardo Fibonacci lived in the thirteenth century. His work on the relationship of mathematics and nature has been applied in physics, astronomy and engineering. Many famous market analysts believe that Fibonacci principles apply equally as well to markets and market psychology.

The Fibonacci number sequence is created by adding the last two numbers in the sequence to create the next number (i.e., 1,1,2,3,5,8,13,21,34,55,89,144Š). The first three numbers in the sequence are normally dropped for analysis purposes. The number sequence creates some interesting mathematical relationships. The most commonly used are: the ratio of any number to its next higher number which approaches a constant value of .618 (e.g. 34/55 = .618, 55/89 = .618); the ratios of alternate numbers which approach a constant .382 (e.g. 21/55 = 382, 34/89 = .382). For those that are mathematically inclined, .382 is also the inverse of .618 (i.e., 1- .618 = .382).

The number series and its ratios are used to create four indicators; ratios or retracements, time lines, arcs and fan lines.

Time lines are vertical lines drawn at fibonacci intervals from the significant high or low of the current trend. The first line is drawn five days after the significant high or low which is circled. In theory, future turning points are likely coincide near these time lines.

Fibonacci Ratios are horizontal lines drawn using the ratios .786, .618, .5, .382 and .146, from the same high or low point. These lines are often useful in identifying retracement points when you have missed entry or exit.

Fibonacci Fan lines are drawn using the same high or low point. An invisible vertical line is drawn through the second extreme value. This vertical line is then divided into three using the fibonacci ratios. Three trend lines are then drawn connecting the first significant point and each of the dividing points on the invisible line.

Arcs combine time and price to display expected containment of price action over time. Circles are used to identify the significant high and low used for these indicators.