The Fibonacci Series

The well-known "Fibonacci" series is named after Leonardo of Pisa, better known as "Fibonacci", which means "son of Bonaccio." He is thought by many to be the greatest European mathematician of the Middle Ages. The series was first mentioned in his book Liber abaci ("Book of the Abacus"), published in the year 1202. These numbers are traditionally denoted by a subscripted capital "F", as follows:

Number:F1 F2F3 F4F5 F6F7 F8F9 ...
Value:1 12 35 813 2134 ...

The series starts with F1 = 1 and F2 = 1, and each following number is obtained by adding the previous two.

For an easy-to-read review of the Fibonacci Series, see the book Mathematical Circus, by Martin Gardner, published by the Mathematical Association of America, telephone 1-800-331-1622. Gardner, who once authored the "Mathematical Recreations" column of Scientific American, notes that "The Fibonacci sequence has intrigued mathematicians for centuries, partly because it has a way of turning up in unexpected places, but mainly because the veriest amateur in number theory, with no knowledge beyond simple arithmetic, can explore the sequence and discover a seemingly endless variety of curious theorems."

There is also a journal called The Fibonacci Quarterly, published by The Fibonacci Association. The series has useful applications in computer science, and recently has been applied to stock market analysis. In fact, most search engine hits on the word "Fibonacci" on the World Wide Web relate to the application of the series to the stock market.

Click here for links to other pages on the Fibonacci numbers.

Here's a great story from The Boston Globe "Tales from the City" column, June 28, 2009:

  Math Games
In an April game last year, scoring 0, 1, 1, and 2 runs in innings one through four, the Sox were having a good offensive start, to the crowd's delight. A season ticket holder in front of me turned and said, "Three runs in the fifth, and we'll have a Fibonacci sequence."

Joe Simeone / Brookline

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