By Scott Bureau
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ….
This seemingly random sequence of numbers can be found in the spirals of a pinecone and the paintings of Leonardo DaVinci. It’s even found in brick patterns at RIT.
Known as the Fibonacci sequence, each number is created by adding the previous two together. Appearing in everything from sunflowers to computer algorithms, this elegant string of numbers and its mathematical properties have inspired human culture and fascinated mathematicians for nearly 1,000 years.
In July, more than 40 Fibonacci experts and enthusiasts, from all branches of mathematics and science, came together at RIT to discuss—and celebrate—the power of these special number sequences. The 16th International Conference on Fibonacci Numbers and their Applications was held at RIT for the second time; RIT hosted the conference back in 1998.
“It is a week full of beautiful mathematics,” said Peter Anderson, a professor emeritus of computer science and organizer of the conference. “Some people come to share how they are using these sequences in their research, while others just love the story behind the numbers.”
The Fibonacci sequence was named after—but probably not invented by—the 13th century Italian mathematician Leonardo of Pisa, more commonly known as Fibonacci. At the time, Europe was using many different systems for measurement and handling money. Fibonacci’s book, Liber Abaci (Book of Calculation), is credited with helping to spread the Arabic numeral system throughout Europe.
The book also posed a problem involving a growing population of rabbits that continued to breed, but never died. The solution was a sequence of numbers later known as Fibonacci numbers.
“This problem is very much about growth, because you need to learn from what you’ve done before you get the next piece of information,” said Anderson. “We use Fibonacci numbers and their exponential growth properties in many of our first-year computer science courses to illustrate important concepts such as recursion and iteration.”
Intimately related to the Fibonacci sequence is the golden ratio, approximately 1.618, which is commonly represented by the Greek letter φ. If you take two successive numbers in the Fibonacci sequence, their ratio will be very close to 1.618.
This ratio can be used to create the Golden Rectangle and Golden Spiral, shapes used by many artists and architects because they are considered aesthetically pleasing. They are also seen in nature in the arrangement of leaves and flower petals on plants, the proportions of the human face and the shapes of spiral galaxies and hurricanes.
At RIT, several faculty members have applied the numbers in their fields.
Anne C. Coon, a professor emerita of English, and Marcia Birken, a professor emerita of mathematics, have explored the connections between mathematics and literature, showing how the number of syllables in consecutive lines of certain poems will create a Fibonacci sequence. Al Biles, a professor in RIT’s School of Interactive Games and Media, used the Fibonacci sequence as an algorithm to compose music using a software program.
“I see the Fibonacci numbers as the entertainers of the number world,” said Arthur Benjamin, a professor of mathematics at Harvey Mudd College who attended the conference to talk about combining Fibonacci numbers with the numbers of Pascal’s triangle. “They organize themselves into so many beautiful, mind-blowing patterns that frequently show up in mathematics, science and nature.”
The next time you walk between Clark Gymnasium and the Campus Center at RIT, take a look at what’s beneath your feet. Chances are your eyes may settle on a familiar numerical pattern arranged among the light and dark brick tiles of the Quarter Mile.