Decimal System

During the late twelfth and early thirteenth century, at the height of the so-called first Renaissance, there lived an Italian merchant-traveler-mathematician by the name of Leonardo Fibonacci, born in Pisa in 1175. He received his advanced education among the Muslims in Barbary, North Africa. He learned the Arabic (or decimal) system of numbering, as well as algebra. On his return to Italy he published his famous book of the Abacus, which stressed the advantages of the Arabic system of numeration over the Roman and brought about the triumph of the Hindu-Arabic system in Christian Europe. Fibonacci (Or Leonardo of Pisa, as he is often referred to) proposed a series of numbers that bear a close resemblance to the rule of the Golden Section. It is also called the Fibonacci Series, the Fibonacci Sequence, and the Summation Series. Starting with the number one, each unit is formed by adding together the two preceding numbers: l, l, 2, 3, 5, 8, 13, 21, 34, 55, and so on. The higher the series goes , the more closely it resembles the Golden Section ratio. It gives us the nearest whole number approximation to mean and extreme ratios. The simple and familiar ratios (straight integers) such as l:1, 1:2, 2:3, 3:4 are relatively static, inert, dividual. The Fibonacci ratios, by comparison, are ^dynamic and individual. They suggest a kind of sprung energy; and no doubt this is why they crop up in the study of plant and animal growth.

Fibonacci's gleanings caused great excitement at the time they were made known, but there was a lapse of some 200 years before they would strike a vital response in artists who were also mathematicians. During the first quarter of the fifteenth century, Brunelleschi (1377-1446), the scholar and architect, his protégé, the painter Masaccio (1401-1428), and a it later, those artists-mathematicians of rare spirit, Uccello (12397-1475) and Piero della Francesca (c. 1415-1492), evolved an art infused with a geometry of proportion, elegance, and space. Part and parcel of this was the new discipline of linear perspective. We may assume that their predecessors, the architects of the great Medieval cathedrals, applied more than a rule-of-thumb geometry in their marvelous, soaring structures; but the precise nature of their methods has been more difficult to pinpoint.

During the 1490s, shortly after the completion of The Last Supper, Leonardo da Vinci met Luca Pacioli, a Minorite friar and mathematician, follower of Piero della Francesca in matters pertaining to linear perspective and of Fibonacci in matters pertaining to mathematics. The two men became close friends and collaborators. Leonardo worked with Pacioli on his book Divina Proportione. This book, published in 1503 and illustrated by Leonardo, contained many of the theories about the Golden Section, or the Divine Proportion, as Pacioli chose to call it, reasoning that, if God saw fit to use this ratio in the creation of natural forms and of man, His noblest handiwork, it must indeed by divine!

This book seemed to bring into focus elements of the humanistic movement: the scientific study of perspective and the play of light and shadow (chiaroscuro: Italian Chiaro = bright + oscuro = dark) and the study of anatomy and geometrical proportion, all of which had been emerging steadily during the preceding century and had been forecast in the art of Giotto (c. 1267-1337). It was certainly to influence the character of European art for many generations.

[Harlan, Calvin. Vision & Invention, An Introduction to Art Fundamentals. Englewood Cliffs, NJ: Prentice-Hall, 1986.]

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1 Decimal adj [F décimal, fr. ML decimalis of a tithe, fr. L decima tithe -more at Dime] [1608]: numbered or proceeding by tens: a: based on the number 10; esp: expressed in or utilizing a decimal system esp. with a decimal point b: subdivided into 10th or 100th units [__ coinage]

2 Decimal n[1651]: any real number expressed in base 10; esp: Decimal Fraction

Decimal fraction n[1660]: a fraction [as .25 = 25/100 or .025 + 25/1000] or mixed number [as 3.025 + 3 25/1000] in which the denominator is a power of 10 usu. expressed by use of the decimal point