Leonardo Fibonacci
By Crystal Gaudio

Leonardo Fibonacci was a twelfth century mathematician born near the year 1180 into the privileged class of Pisa. His father Bonacci was a Pisan business and government official. Because of his elevated status, Fibonacci attended public school and studied the "seven liberal arts": grammar (Latin), rhetoric, logic, geometry, astronomy, music and arithmetic. During Fibonacci's life, Pisa participated in the Commercial Revolution of the twelfth and thirteenth centuries, out of a Roman port that continued operation through the Dark Ages. Pisa was a site of extensive commercial activity requiring calculation on an abacus and recording with Roman numerals.

After his formal public education, Fibonacci followed his father to North Africa, Bugia to continue his business education. There he discovered the long established HinduArabic numerals similar to what we use today. The numerals consisted of symbols 1-9 and the extraordinary concept of zero. Fibonacci was responsible for introducing the HinduArabic numerals to Western Europe in his publication Liber abaci (Book of the Abacus). Fibonacci was also responsible for introducing the Arab method of balancing income and expenditure in the double-entry system of bookkeeping. Another section of Liber abaci calculated the progeny of a single pair of rabbits. Through systematic calculations involving logic and consistency, the "Fibonacci Sequence" was created. In subsequent months, the number of paired rabbits would theoretically continue as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...or un+1 = un + un-1 (uO = O, u1 = 1.)

The "Fibonacci Sequence" has been calculated to express the golden ratio, Phi f 1.61803398874 by dividing each number by the previous number. As the ratios continue, the result comes closer and closer to the golden ratio first used by the ancient Greeks in various architectual and artistic designs. It is said that the golden ratio or golden mean embodies aesthetic perfection.

Bibliography

1. The Day the Universe Changed. James Burke; © 1985 by London Writers Ltd.
2. The Divine Proportion. H.E. Huntley; © 1970 by Dover Publications
3. Leonard of Pisa and the New Mathematics of the Middle Ages. Gies, Joseph and Gies, Frances; © 1969 by Thomas Y. Crowell Company New York.