Leonardo Pisano, was Italian mathematician born in Pisa during the middle Ages. He was renowned as one of the most talented mathematicians of his day. . The name Fibonacci itself was a nickname given to Leonardo. It was derived from his grandfather’s name and means son of Bonaccio.

While most attribute the Fibonacci Sequence to Leonardo, he was not responsible for discovering the sequence. In 1202 Leonardo published a book called, Liber Abaci. In it he derived a method for calculating the growth of the rabbit population.

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits **never die** and that the female **always** produces one new pair (one male, one female) **every month** from the second month on. The puzzle that Fibonacci posed was….

How many pairs will there be in one year?

At the end of the first month, they mate, but there is still one only 1 pair.

At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.

At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.

At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

This mathematical progression is now recognized as the Fibonacci Sequence. Starting with zero and adding one, each new number in the sequence is the sum of the previous two numbers. In our example, 0+1 = 1, 1+1=2, 1+2=3, 2+3=5, and so on.

The sequence of numbers looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, to infinity. From this sequence you can easily reason that at the end of one year there would be 233 pairs of rabbits.

This sequence has repeatedly appeared in popular culture from architecture to music to television. While the series is a powerful tool, the analysis of one number with the number up to four places to the right. The first three are shown below.

While some are not exact, if you repeat this mathematical analysis through multiple sets of data, you will see we arrive at some well known and fairly consistent ratios.

21/34 = 0.61764 ~ 0.618 | 34/21 = 1.61904 ~ 1.619 |

21/55 = 0.38181 ~ 0.382 | 55/21 = 2.61904 ~ 2.619 |

21/89 = 0.23595 ~ 0.236 | 89/21 = 4.23809 ~ 4.238 |

The dimensional properties adhering to the 1.618 ratio occur throughout nature and the ratio is most referred to as The Golden Ratio. The uncurling of a fern and the patterns found on various mollusk shells are commonly cited examples of this ratio.

This number, when added to 0.618, equals 1.

These ratios have been used for over a hundred years in the financial markets by the likes of W.D. Gann and Ralph Nelson Elliot. Up until the late 90s the tracking and use of these numbers were a manual process.

With the proliferation of real-time charting and data, software that automatically calculated and displayed these levels brought Fibonacci into the financial mainstream.

## **Fibonacci as a Technical Analysis Tool**

While there have been countless books and articles written on the use of Fibonacci in technical analysis, the basics are simple. Fibonacci Trading is an artform anyone can master with a little practice.

On the price scale, these ratios, and several others related to the Fibonacci sequence, often indicate levels at which strong resistance and support will be found. Many times, markets tend to reverse right at levels that coincide with the Fibonacci ratios. On the time scale Fibonacci ratios are one method of identifying potential market turning points. When Fibonacci levels of price and time coincide you have high probability entry points.

In the next few pages I will talk about how I use the two most common applications of Fibonacci:

- Price Retracements – A strategy for quality entry points
- Price Extensions – An approach to determining how far price will run

Then after we have covered the basics we will talk about bringing it all together and using both Fibonacci Retracements and Fibonacci Extensions a