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Undercolor/840101/Off Color Whos Fibonacci

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UnderColor, Volume 1, Number 1, December 10, 1984

  • Title: Off Color Whos Fibonacci
  • Author: Mark Haverstock
  • Synopsis: A light-hearted look at numbers
  • Page Scans: Link

Article

Author's Note: The following information is based on true fact, believe it or not. (Anyone know a false fact?)

Leonardo Fibonacci was an Italian mathematician who was a leading influence in mathematics during the Middle Ages. Scholars and generally polite people refer to him as Leonardo of Pisa. His neighbors in Pisa, however, called him Bigollone or "the Blockhead." His family name was of no help, either. His father's name, Bonaaccio, meant "Simpleton." Hence, Fibonacci was "Son of Simpleton."

He spent his formative years in the North African city of Bujaia, where his father was stationed as a customs official. Inquisitive young Leonardo was educated by the Muslims

there, who taught him the Arabic numeral system. He quickly realized that working with this system was far simpler than the Roman numeral system in use in Europe; any half-intelligent school child knows that 1984 is easier to deal with than MCMLXXXIV!

After returning to Pisa as a young scholar, he spent several

years contemplating this discovery. Leonardo was often seen

wandering in a fog. When inspiration hit, he would grab a

piece of chalk and absentmindedly scribble numbers on a

nearby wall. At the age of 27, he published an historic

manuscript, Liber Abaci, which introduced Arabic numerals

to the European continent. This in itself was a major accomplishment, but one section of the book contained a

theoretical problem that proved to be most interesting of all.

The solution resulted in the discovery of the Fibonacci series.

The problem goes something like this: suppose someone

placed a pair of rabbits in an enclosed area. lf these rabbits

were allowed to breed, how many pairs of rabbits would be

born over the course of one year? Fibonacci figured that every month a pair of rabbits would be born, and that rabbits begin to bear young two months after their own birth. After this hare-raising experience, it was assumed that the original rabbits and their offspring would total 233 pairs. Fibonacci listed

the number of pairs at the end of each month: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. When analyzing this group of numbers, he found that each number as the sum of the two preceding numbers. These numbers—1, 2, 3, 5, 8, 13 . . . — became known as the Fibonacci series. This series theoretically goes on forever, although you might end up with some thoroughly exhausted bunnies after awhile. By the way, there is no historical evidence that Fibonacci actually tried this experiment.

The series itself appears to be composed of seemingly random numbers, right? Well, any self respecting Fibonacci scholar would tell you that each number has a special relationship to the numbers surrounding it. lf you divide a number in the Fibonacci series by the next highest number, you will discover that the quotient is always about .6, or more precisely, 0.618034. This precise number works when the Fibonacci numbers are large enough to be precise (after about the 14th in the sequence). This number, 0.618034, is referred to as the Golden Mean. The ratio .618034 to one is the mathematical basis for eye-pleasing shapes in art, spiral galaxies, the curvature of a snail shell, and the shape of playing cards. Add T to this the occurrence of Fibonacci numbers in botany and music, and you come up with some interesting patterns.

Plant life provides many examples of Fibonacci numbers. The number of pine needles that grow in a cluster on most species of pine trees tend to be 2, 3, or 5. Counting the number of petals on a daisy will most likely yield a Fibonacci number. Phyllotaxis, the arrangement of leaves on a stem, provide further evidence that these numbers are more than mere coin-

cidence. The number of leaves and turns on a stem are almost always Fibonacci numbers.

Musicians are aware that an octave is composed of eight notes. On a keyboard instrument, this is represented by eight white keys and five black keys for flats and sharps, for a total of 13.

Being the skeptic I am, I decided to check some of the number relationships. The pineapple's scaly outer skin is supposed to be made up of three distinct groups of logarithmic spirals; five go sharply in one direction, 13 in another, and finally eight in the third spiral. A trip to the local Valu-King proved this to be true. After checking about three pineapples in the produce department, I looked up and found myself staring at a plump Italian lady with an impatient expression on her face. I could have sworn she mumbled "Bigollone" as she snatched a pineapple and left.

Fort Worth, take note. The ratio of the Color Computer 2's length to width dimensions is .7106896, substantially closer to the Golden Mean than the first Color Computer, at .93220. The esthetically ideal Color Computer would have cabinet dimensions of 10 1/4 x 16 5/8.

Bibliography for further reading:

Hoffer, William, "A Magic Ratio Recurs Throughout Nature," Smithsonian, December, 1975, pp. 110-124.

Hoggatt, Verner E., Fibonacci and Lucas Numbers, Boston: Houghton Mifflin Co., 1969.

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