Fibonacci, not so much the man but the math, is pretty fascinating on its own apart from trading.
To see how each number in the Fibonacci Sequence relates to each other in some set ratio (ie.618, 1.382, etc.) and then connect these ratios to objects of nature is absolutely fascinating. Within minutes of starting to learn about Fibonacci numbers, you are drawn into a world of plant proportions and architecture of pyramids and other monuments.
The connection of the Fibonacci numbers and all things nature is also found in the world of trading itself.
When I started trading the markets back in the mid-80's, my focus was like that of many new traders. The analysis of choice was fundamentals. Listen to the news, recommendations from friends and talking heads, or glace at the supply / demand numbers. But then something wonderful happened at the start of the 1990's. I discovered (for myself) Fibonacci and its basic application to price and time analysis. From then on I focused on Technical Analysis and never listened to another talking head (or friend) on what to buy or sell ever again.
The applications of Fibonacci to trading are many. Most traders who use Technical Analysis are familiar with the basic use of Fibonacci in chart analysis. Here are some basic examples:
Solving for Support or Resistance – After prices have trended for a number of days / weeks / months in a certain direction, from either a significant bottom to a top, or from a significant top to a bottom, it is called a "range". The trader identifies the range, then multiplies that range by the Fibonacci ratios of .382 and 618 for example. The results are deducted from the top price (if the range is from bottom to top) or added to the bottom price (if the range is from top to bottom) in order to get support or resistance price levels, respectively. Often additional ratios are included in this calculation.
Solving for time – A basic but fascinating approach to using Fibonacci is to count the days / weeks / months between previous tops peaks and bottoms and multiply the count by the Fibonacci ratios. The result is count from the last top or bottom forward in time where another top or bottom is then expected to happen.
Moving from the basics of Fibonacci and chart analysis are more advanced (or mostly unknown) applications for the ratios.
There are the use of Fibonacci spirals, for example, which produce both time and price results.
There are the combined use of Fibonacci ratios along with time / price squaring results.
The techniques and methods one can use to exploit the markets using Fibonacci are numerous!
Within my charting software I often use what is called Fibonacci Fan Lines. The application here is something like that mentioned above under "Solving for Support or Resistance", with the major difference being that the Fan Lines produce DYNAMIC support and resistance levels (the values change for each time interval on the chart, higher for ascending lines and lower for descending lines). They also require locating patterns two ranges (top to bottom to top, or bottom to top to bottom). You simply label the extreme of range as A, B and C. For example, ranges of top to bottom and back to top would be labeled "A" for the first top, "B" for the following bottom, and "C" for the final top. The range of "B to C" is divided by the Fibonacci ratios and then lines are drawn from "A" through the divisions of the range of "B to C" out into the future. These become your support / resistance levels.
Another fascinating approach to using Fibonacci for chart analysis is to simply add the Fibonacci series numbers to any significant top or bottom to get possible future tops and bottoms.
For example, the series starting at 3 would be 3, 5, 8, 13, 21, 34, 55, etc. Add any two consecutive numbers in the series to get the next number in the series. Now locate a top or bottom on your price chart and count from there 3 bars, 5 bars, 8 bars, etc. These are time periods to watch for possible market tops and bottoms.
These are just some of the many examples and applications you can do with Fibonacci and your chart analysis. Try them yourself and I'm sure you also will be fascinated with Fibonacci!