Leonardo Fibonacci devised a concept now known as the Fibonacci sequence. The Italian mathematician noticed this mathematical pattern. The sequence itself begins with 1, 1, 2, 3, 5, 8, and continues.

What Fibonacci noted in his 1202 book is this pattern repeats itself in nature. Not only is each number is the sum of the previous number, but also the quotient of adjacent numbers is nearly identical all the way through the sequence! In other words, dividing a number in the sequence by the just previous number usually results in an answer of approximately 1.6!

The phenomena has been observed so often in nature that it is known alternatively as the golden mean, the golden ratio, the divine proportion, and other names.

Fibonacci sequences have long been observed in nature. Examples include sunflowers, pinecones, pineapples, petals of many flowers, broccoli, palm trees, branches and leaves on trees, the patterns of shells, the human face, the human body, even human DNA! The same sequences can be observed in the breeding of rabbits and the family tree of honeybees.

This ratio is found not only in nature, but in the works of humankind. Researchers have found Fibonacci patterns in music and other forms of art. In most cases, these patterns are not consciously placed there on purpose but “seem right” to their creators.

Mozart, for example, constructed many of his sonatas with these sequences. So far as anyone knows, he had no reason or intention of doing so “on purpose”.

Fibonacci sequences also manifest themselves in the financial markets.

From the “golden ratio”, financial experts derive “Fibonacci ratios”, most commonly, 38.2%, 50% and 61.8%. Other multiples can be computed as well. These ratios are use to create “Fibonacci fans” to plot prior and expected trend lines to make better investing decisions.

There are a total of four main methods of applying the Fibonacci sequence to the financial markets. These are retracements, arcs, fans, and time zones (or time extensions).

What justification do we have for applying the Fibonacci sequence to financial markets? The theory is that investors unconsciously gravitate to this “golden ratio”. Patterns of long straight lines in nature just don’t look right… they don’t seem “natural”. Similarly, uninterrupted upward or downward trends in financial markets don’t seem “right” and investors unknowingly seek to correct it.

While there are countless other outside influences on financial markets, ultimately it is investors that make buying and selling decisions and therefore this theory may have some merit.