The Fibonacci studies were developed by Leonardo Fibonacci, an Italian mathematician born in the late twelfth century, when he was studying the Great Pyramid of Gizeh in Egypt.

Fibonacci numbers are a number series in which each successive number is the sum of the previous two numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. Any given number in the series is approximately 1.618 times the preceding number and any given number is approximately 0.618 times the following number.

There are four popular Fibonacci studies: arcs, fans, retracements, and time zones. All of these studies use the Fibonacci numbers to forecast support and resistance levels.

Arcs
Fibonacci Arcs are displayed by first drawing a trend line between two points, usually one significant high and one significant low. Three arcs will then appear, with the second point being the center point, so that the arcs will intersect the trend line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%. These arcs will act as support and resistance levels for future price movements.

Fans
Fibonacci Fans are displayed by first drawing a trend line between two points, usually one significant high and one significant low. An invisible vertical line will then be drawn through the second point. Three trend lines will then be drawn from the first point so that they intersect the invisible vertical line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%. These three trend lines will then fan out and the lines will then act as support and resistance for future price movements.

Retracements
Fibonacci Retracements are displayed by first drawing a trend line between two points, usually one significant high and one significant low. For ProSticks, a series of 7 horizontal lines are drawn intersecting the trend line at the Fibonacci levels of 0.0%, 38.2%, 50.0%, 61.8%, 100.0%, 161.8%, and 200.0%. After a rally or sell-off, prices will tend to retrace, or give back, a portion of the original move. As the prices move, support and resistance levels, more often than not, will appear at or near the Fibonacci levels.

Associated with Fibonacci Retracements is Fibonacci Projection. The Projection study simply takes the retracement levels found in a Fibonacci Retracement calculation and projects it to any other point in time.

Time Zones
Fibonacci Time Zones are a set of vertical lines spaced at the Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc. As the price traverses through the timeline, tops and bottoms, or significant support or resistance, tend to appear at or near the Fibonacci intervals.

Associated with Fibonacci Time Zones is Fibonacci Ruler. Instead of using the Fibonacci numbers as intervals, the intervals are calculated with the Fibonacci levels of 38.2%, 50.0%, 61.8%, 100.0%, 161.8%, and 200.0%.