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FIBONACCI NUMBERS, FIBONACCI RATIOS AND THE STOCK MARKET

What do the Great Pyramid, the shape of your credit cards, your teeth, Beethoven's 5th Symphony, moth wings, daVinci's Madonna and Child, the Pantheon, 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.

Leonardo Pisano, a 13th century mathematician, has many significant achievements but will probably always be remembered for his rabbit counting exercise which popularized the sequence of numbers known as the Fibonacci numbers. Leonardo Pisano was the son of Guglielmo Bonacci. The shortening of the Latin "filius Bonacci" (son of Bonacci) is how Leonardo Pisano came to be known as Leonardo Fibonacci, or more simply Fibonacci.

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... The next number in the sequence is the sum of the prior two. As the sequence gets larger the relationship between adjoining numbers gets closer to the Divine Proportion or Golden Ratio: 0.61803 39887... and 1.61803 39887...

Even though this sequence of numbers will forever be known as the Fibonacci Numbers, it's not the numbers themselves that are important...it's the relationship between them that matters.

You could spend a lifetime exploring the intricacies and interconnectedness of the Divine Proportion. Here's two excellent sites to get you started. Fibonacci Numbers and the Golden Section (opens in new window) and The Golden Proportion (opens in new window)

It's easy enough to go off in a tangent with this topic. For our purposes it's enough to say that we believe that the Divine Proportion is terribly important for stock market work because the human brain is hard-wired to respond to it. Identify something that exemplifies stunning beauty. Chances are that the fingerprints of the Divine Proportion are all over it. The stock market, indeed, every publicly traded liquid market, is a never ending succession of action-reaction, rally-decline. We can use the Divine Proportion to discover how those growth phases have related to each other in the past and how they may relate to each other in the future.

The three categories of ratio relationships are: Retracement, Expansion and Parallel Projection. These ratio relationships can be used to successfully forecast price and time with the right technique.

The table shows the most important Fibonacci Ratios for financial forecasting. These ratios were derived by dividing, and by squaring, and by calculating the square roots of the ratios of adjacent Fibonacci numbers and Fibonacci numbers once removed from the Divine Proportion.

 2.618 6.854 1.618 1.618 2.618 1.272 0.618 0.382 0.786 0.382 0.146 0.618
Fibonacci ratios can be a stand-alone forecasting and trading method with the addition of vigorous entry-exit techniques (opens in new window). We like to use them to help resolve the other independent price and time forecasting methods we discuss on this site.

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