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9

waming sign, such price action might signal that the harmonic area still is a valid trade opportunity. Sometimes, it is prudent to wait even a few price bars for a clear reversal signal.

Accepting a trade despite a waming signal can be a tricky execution. I usually will enter a trade only when a potential reversal zone is extremely harmonic. Although waiting for clear a reversal signal delays my execution, I have leamed the significance of the waming signs. Respecting these signs has prevented me from many flawed executions.

Harmonic Trading Summary

The following chapters will truly change the way you view stocks. They will clearly illustrate that these methods are reliable indicators of price frends. When a convergence of harmonic calculations exists within a specific area, the potential for a reversal is highly probable. It is essential to gauge the price action within the harmonic area to determine the validity of the reversal. Also, waming signs frequently will indicate a flawed set-up. So, it is important to wait at least one price bar, or even several, to see ifthe trade is still valid.

The harmonic techniques are most effective when you are patient. These opportunities will materialize frequently, providing ample opportunities to be consistently successful. It is important to study actual examples to achieve a greater understanding of price action. It will take some time before your "harmonic comprehension" improves. But, if you invest the time, the skill that you leam will tmly be worth the effort.



Part

Fibonacci Numbers



The Fibonacci Sequence

Fibonacci numbers are based upon the Fibonacci sequence discovered by Leonardo de Fibonacci de Pisa (b.l 170-d. 1240). Fibonacci was one of the greatest mathematicians of the Middle Ages. His most famous work, the Liber Abaci (Book of the Abacus), was one of the earliest Latin accounts of the Hindu-Arabic number system.

In this work, he presented and was mostly responsible for the use of arithmetic numbers rather than Roman numerals, which were the common means of numeric recording of that time. His book introduced the Arabic art of Algebra to the Roman civilization. Fibonacci also was renown for his study of the Great Pyramids of Egypt.

It was during this time that he developed the Fibonacci number sequence, which is historically the earliest recursive series known to date. The series was devised as the solution to a problem about rabbits. The problem is: If a newborn pair of rabbits requires one month to mature and at the end of the second month and every month thereafter reproduce itself, how many pairs will one have at the end of n months? The answer is: . This answer is based upon the equation: u+i = u+u.i.



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