## 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 ƒ). 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 indicatorsŠ

## 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 should coincide near these time lines. Note how the significant low was made exactly 55 days after the significant high..

## Fibonacci Ratios are horizontal lines drawn using the ratios .618, .5 and .382, from the same high or low point. These lines are often useful in identifying retracement points when you have missed entry. In our example, Soy Beans found resistance at the 50% ratio on the 89th day after the significant high was made.

Fibonacci time lines and ratios chart

## Fibonacci Fan lines are drawn using the ratios .618, .5 and .382, from the same high or low point. An invisible vertical line is drawn through the second extreme value..i.Fibonacci:fan lines;.i.Fibonacci:arcs; 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. Note how prices found support, after the significant high at the outer arc.

Many analysts use arcs and fan lines together expecting significant

support or resistance to occur where these lines cross.