By the numbers

Popular novel renews interest in math sequence

8:53:55 AM CDT - Thursday, February 12, 2004

By Amy Geiszler-Jones

Fibonacci numbers have been called nature's numbering system, appearing in everything from the number of petals in a flower to the pattern of a seashell to the scales of a pineapple.

But they don't just appear in nature. Some stock market traders consider them a secret to their success. Patterns based on their sequencing can be found in ancient Greek architecture. Cryptographers use them to crack codes.

This curious set of sequencing has inspired a 40-year-old quarterly journal, music, dance pieces, and now a class at WSU. 

Next month, mathematician John Hutchinson will teach a class, "Golden Fibonacci Numbers," as part of the Division of Continuing Education's noncredit offerings.

The class developed in part because of the popularity of Dan Brown's best-selling novel "The Da Vinci Code," which includes references to the Fibonacci numbers.

In the thriller, a cryptologist and a Harvard symbol expert find puzzling codes at the murder scene of the Louvre's chief curator. The strange ciphers are linked to Leonardo Da Vinci's paintings and a relic guarded by a secret religious society.

While some people were intrigued by Brown's suggestion that Jesus Christ had married Mary Magdalene, Hutchinson and other "Da Vinci Code" readers like Charlotte Howard, director of WSU's continuing education division, found references to the Fibonacci numbers fascinating.

When Howard discussed the book with other readers, she found they too had been interested in the number sequence developed by a medieval mathematician.

More than 800 years ago, Italian mathematician Leonardo da Pisa introduced the Latin-speaking world to the decimal numbering system and a simple series of numbers that bears his name in his book "Liber abaci" (The Book of the Abacus).

The sequence begins with 0 and 1, and the numbers after that follow a simple rule: Add the last two numbers to get the next. You end up with the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so forth.

Hutchinson has found Fibonacci numbers fascinating for years. In some of his mathematics courses, he would teach about various number sequences and theories. He's also made presentations on Fibonacci numbers to groups of teachers.

"In the process of reading 'The Da Vinci Code,' I got interested in them again from a more nonmathematical perspective," says Hutchinson, who is also an associate vice president for academic affairs and research.

Some Fibonacci enthusiasts insist that the sequence is intentional, but Hutchinson doesn't believe that's always the case.

"I think (the numbers) are descriptive, rather than prescriptive," he says.

When a vine grows around a post and its leaves follow a Fibonacci pattern, "it's not because it knows anything about Fibonacci, but because this maximizes the amount of sunlight the lower leaves get," he explains.

In music, some composers may intentionally use the Fibonacci numbers, while others adhere to other rules.
Composer Walter Mays, the WSU Board of Trustees Distinguished Professor, says there's a lot of calculation involved in composing music, but he's a bit wary of those who find Fibonacci numbers in every composition.

"I often think Fibonacci is in the eye of the beholder," Mays says. For example, some have thought the Hungarian composer Bartok, who was a perpetual calculator, definitely adhered to the Fibonacci sequence. But now as his composition notes are coming to light, "nowhere does he make a Fibonacci calculation," Mays says.

Fibonacci numbers have provided lots of fodder for researchers. The Fibonacci Association, formed in 1963, started its quarterly journal in 1964.

"That's one of the remarkable things about Fibonacci numbers," says Hutchinson. "Every three months an issue comes out with five to 10 articles on new discoveries about Fibonacci numbers."

During the "Golden Fibonacci Numbers" class, Hutchinson will talk more about where Fibonacci numbers are found and how they are useful. The class will meet 7-9 p.m. Wednesdays, March 3 and 10, at the Eugene M. Hughes Metropolitan Complex. The fee is $49.

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