The Great Depression Online

Great Depression Online Archive Issue:

Medieval Mathematics from Pisa Italy

Great Depression Online
Long Beach, CA
January 18, 2008

Inside This Issue You Will Discover…

*** Leonardo Fibonacci
*** The Fibonacci Sequence and the Golden Ratio
*** Why You Should Care
*** And More

Leonardo Fibonacci

Across the Arno River from the Leaning Tower, in Pisa, Italy, sits a modest statue.  Hardly any visitors to the Tower come across it.  And of those who do, few realize that it’s of the greatest mathematician of the medieval times.

Leonardo Fibonacci da Pisa, born in the late twelfth century, was the son of a prominent merchant and city official.  It was this unique set of circumstances that allowed Fibonacci’s unique intellect to burgeon outside of the academically stunted region that was Medieval Europe.

As a young adult, Fibonacci joined his father on many business trips around the Mediterranean

And after one trip to Egypt, he published Liber Abacci (Book of Calculation) which introduced to Europe one of the greatest mathematical discoveries of all time – the decimal system, including the placement of zero as the first digit in the number sequence.

But that’s not all…

The Fibonacci Sequence and the Golden Ratio

In Liber Abacci, Fibonacci also revealed the sequence of numbers – 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on to infinity.

Known today as the Fibonacci sequence, it follows that the sum of any two numbers in the sequence forms the next higher number in the sequence such that, 1 plus 1 equals 2, 1 plus 2 equals 3, 2 plus 3 equals 5, 3 plus 5 equals 8, and so on to infinity.

Plus the Fibonacci sequence comprises the “Golden Ratio”… 

After the first several numbers in the sequence, when you divide any Fibonacci number by the next higher number, the ratio is always approximately 0.618 to 1; and the next lower number is always approximately 1.618 to 1.

And the Golden Ratio can be used to construct the Golden Rectangle…which can be used to construct the Golden Spiral.

We know this could be getting a little tedious for some of you, but hang in there, this is going somewhere…

But first…

What’s interesting about the Golden Ratio is that it’s found throughout nature.  Pine cones, sea horses, snail shells, ocean waves, ferns, hurricane clouds, whirlpools and spiraling galaxies of outer space – all sustained by the 1.618 ratio.

The Greeks, prior to the dark ages, knew of this ratio and used it to define the proportions of the Parthenon.  Egyptian engineers even incorporated it into the Great Pyramid nearly 5,000 years ago.

Throughout the ages, the greatest intellects have honored the value of this ever-present phenomenon.

Pythagoras chose the five point star, in which every segment is in golden ratio to the next smaller segment, as the symbol of his Order.  Seventeenth century mathematician Jacob Bernoulli directed that the Golden Spiral be etched into his headstone.  Isaac Newton had the same spiral carved on the headboard of his bed.

And finally…the moment you’ve been waiting for…

Why You Should Care   

But the reason you should care about all this mathematical blather is because the Fibonacci sequence is found in markets too.  And knowledge of this fact could make you very wealthy.

We’ll confess…we’re not ones for technical analysis.  We’ve always equated it to driving while looking through the rear-view mirror.  In fact, moving averages are about all we look at…as any more staring at stock charts and we see our names being spelled in them.

Nevertheless, we like to consider different ideas.  Especially ideas that have weathered some storms over time.

You see…

In the early 1930’s, Ralph N. Elliot had some health problems and was reserved to a front porch rocking chair on Beacon Avenue, in Los Angeles.  And it was there, with all his free time, that Elliot ventured to study the price movement of the stock market.

Through this lengthy study Elliot discovered a repetitious wave phenomenon that, while esoteric, he believed was confirmed by the Fibonacci sequence.  In short, Elliot concluded that man’s collectively expressed emotions are explained by this mathematical law of nature. 

And he made a succession of market predictions that was uncannily accurate.

In the following decades, Elliot Wave Principle has carried forward an impressive track record of prescient market predictions. 

Robert R. Prechter, Jr., publisher of Elliot Wave International, is today’s foremost practitioner. 

And if you are interested in discovering for yourself the power of Elliot Waves for predicting market movements we have a free resource for you.  You can download Elliot Wave International’s Independent Investor e-Book here for free.    

We think you’ll find it exceptionally interesting…if not exceptionally profitable!


M.N. Gordon
Great Depression Online

P.S.  If you're interested in learning how to forecast the Gold and Silver Market using the Elliot Wave Principle you should check out this all inclusive and instructive book by Prechter called: How to Forecast Gold & Silver Using the Wave Principle.


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