The Fibonacci sequence is a commonly used concept used generally in tandem with Fibonacci retracements. When most people think about how to use a Fibonacci ratio, they quickly ponder a potential correction once a market has made a move. Fortunately, there are other techniques that may be used that are constructed using the same Fibonacci concept. The most actively employed are Fibonacci arcs and Fibonacci Fans.

**Fibonacci Sequence**

The Fibonacci sequence was initially introduced by Leonardo Pisano Bogolla, who was an Italian mathematician from the city of Pisa. The sequence of number’s that begins with zero, and then 1, creates a new number by adding the sum of the two prior numbers.

The sequence continues to infinity and contains many unique mathematical properties. Once of those properties is that a number in the sequence that is divided by the previous number generates a ratio that is 1.618. For example, 13/8 is 1.618. A number that is divided by the next highest number in the sequence equals 0.618. For example, 21/34 = 0.618 and 8/13 = 0.618. Another unique ratio that is created is that any number divided by another number two places higher is 0.3820. For example, 5/13 = 0.382.

The ratios that are generated through the Fibonacci sequence are used as retracement to help market participants determine future levels that can be used to either enter a trade, stop out of a trade or even target a take profit level. The 1.618 level is a 61.8% retracement figure while the 0.382 is the 38.2% retracement level. These ratios are also known as the golden ratio and is found throughout nature.

**Fibonacci Arcs**

Fibonacci Arcs are semi-circles that are generated by extending from a line that forms the basis between two or more points. There are multiple arcs in a Fibonacci arc drawing and the first arc and third arc are based on the Fibonacci ratios of 38.2% and 61.8%. The second or middle arc is set at 50% and is taken from Dow theory. After an advance of a security, the Fibonacci arcs are created by measuring the base line that extends from trough to peak. The radius of the arc are measured using the 38.2%, 50%, and 61.8% Fibonacci levels. The arc that is create marks support and resistance levels, where price might correct after an advance. After a drop in the price of a security, the Fibonacci arc are used to estimate resistance for a counter trend move.

Similar to evaluating a Fibonacci retracement the first step in evaluating a Fibonacci arc is to pick the peak and trough of move of an asset. You would then draw the line from trough to peak for an advance and the reverse for a decline.

The example above shows Gold with a Base Line from peak to trough. The radius for the first Fibonacci Arc measures 38.2% of the Base Line. The radius for the second Fibonacci Arc is in the middle of the Base Line (50%). The radius for the third Fibonacci Arc measures 61.8% of the Base Line. Three half circles are drawn based on these radii.

Fibonacci Arcs are interesting as they add time to the retracement scenario. The Fibonacci Retracements Tool is based on a vertical line from trough to peak or from top to bottom. It is only concerned with the change in price. In contrast, a Base Line after an advance extends from trough to peak at an angle that is dependent on elapsed time. The slope and length of the line depend on changes in both price and time.

Similar to retracements, arcs are used as retracement tools as well as target tools that may be used to find a take profit level. If the market retraces after an advance it is deemed a correction that will eventually find support above the beginning of the advance. As with Fibonacci retracements, arcs are not stand alone tools and are best used in tandem with other tools that help designate support and resistance such as moving averages and trend lines.

**Fibonacci Fan Lines**

Fibonacci Fan lines are trend lines that are generated based on Fibonacci retracement points. Fan lines extend up from a bottom in a security prices through retracement based on the increase in price from the trough to the peak. These fan lines may then be used to estimate support and resistance areas as well as target zone where the market might reverse.

Once a pullback starts, you may use the Fibonacci fan line to find a target. The fan lines provide chartists with key levels to watch as prices correct. After a decline, the Fibonacci Fan lines may be drawn to identify potential resistance or reversal areas. Once the bounce starts, the fan lines provide chartists with key levels to watch as prices bounce.

Fibonacci Fans, similar to retracements and arcs are used to identify potential support, resistance or reversal points. These metrics assume the move is corrective in nature and that the market will bounce and target these levels. Fibonacci Fan lines allow users to anticipate the ending points for these counter-trend moves. The key is to use Fibonacci fans as well as Fibonacci arcs with other technical analysis tools such as moving averages and trend lines to enhance your technical analysis tool box.