FIBONACCI NUMBERS and the GOLDEN RATIO

What do the Great Pyramid, the dimensions of your credit cards, your teeth, Beethoven's 5th Symphony, moth wings, daVinci's Madonna and Child, the Panthenon, the geometrical arrangement of the solar system, and the exact way that seeds propagate on a flower (to name a few) have in common? The "Golden Section," the "Divine Proportion." Perhaps the most important single number in the universe:

.618

You could spend a lifetime exploring the interconnectedness and intricacies of the Golden Ratio, and it's easy to get off on a tangent here. The subject is fascinating. If you want to explore more about the Golden Ratio and its daily impact on our lives, try Wikipedia.

The ratio between Fibonacci Numbers, known as the "Golden Ratio," have quite a track record throughout history:

“

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler , to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

— Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number

”

How Fibonacci Numbers and the Golden Ratio Works

The Fibonacci number sequence (1,2,3,5,8,13,21,34,55,89,144,...) is constructed by adding the first two numbers to arrive at the third. The ratio of any number to the next number is 61.8 percent, which is called the "golden ratio" because of its inherent appearance throughout nature. The inverse of 61.8 percent is 38.2 percent, also used as a Fibonacci retracement number. It is the ratio of the Fibonacci sequence that is important and valuable, not the actual numbers in the sequence.

By utilizing a Fibonacci ratio of 61.8 percent or 38.2 percent to calculate three criteria; 1) the price growth in the last 26 weeks, 2) the price decline from the 26-week high, and 3) the price recovery after the decline to determine the proper price at which to sell, the backtested returns increased to an amazing 260% to 360%, depending on what period was measured!

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