The Man of Numbers: Fibonacci's Arithmetic Revolution
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Leonardo of Pisa-better known today as Fibonacci-was the first Westerner to recognize the power of the Hindu-Arabic number system (featuring the numerals 0 through 9), which offered a much simpler method of calculation than the finger reckoning and cumbersome Roman numerals used at the time. His book Liberabbaci (The book of Calculation) remade the West as the dominant force in science, technology, and large-scale international commerce. Leonardo of Pisa is best known today for discovering the Fibonacci sequence of numbers appearing in biological structures throughout nature, but despite the ubiquity of his discoveries, he has largely slipped from the pages of history. Keith Devlin re-creates the life and enduring legacy of this brilliant yet overlooked mathematician.
Contents Cover Title Page Chapter 0. Your Days Are Numbered Chapter 1. A Bridge of Numbers Chapter 2. A Child of Pisa Chapter 3. A Mathematical Journey Chapter 4. Sources Chapter 5. Liber abbaci Chapter 6. Fame Chapter 7. The Fibonacci Aftermath Chapter 8. Whose Revolution? Chapter 9. Fibonacci’s Legacy—in Stone, Parchment, and Rabbits Acknowledgments Notes Footnotes Bibliography A Note on the Author By the Same Author Imprint
by scratching a wax tablet with a bone stylus, using the smooth side of the stylus as an eraser, both to correct errors and to clean the surface for further use. Almost certainly, Leonardo would have found computation using Roman numerals tedious. Arithmetic, particularly multiplication by repeated addition, was more speedily done with a counting board (abacus). After Leonardo had finished his preliminary instruction, his further education in mathematical matters would likely have been in a
cloisters and into the commercial world. Professional copy companies appeared, usually on the edges of the new universities—an early forerunner of today’s commercial photocopy shops. Some of them grew quite large; one early fifteenth-century copy shop in Florence employed forty-five lay copyists. Hand copying produced some attractive-looking manuscripts. With considerable time to devote to the task, the scribes, who in Leonardo’s day worked mainly for spiritual reward, developed elaborate
sixteenth century, shifting from handwritten to printed books as the primary means of publication changed from manuscript to printing.”12 In a similar vein, Kurt Vogel, in a highly regarded, authoritative article on Leonardo observed: In surveying Leonardo’s activity, one sees him decisively take the role of a pioneer in the revival of mathematics in the Christian West. Like no one before him he gave fresh consideration to the ancient knowledge and independently furthered it. In arithmetic he
through—the symbols that represent them.3 Our sense of numbers depends on the symbols, and we cannot divorce the symbols from the numbers they represent. Another remarkable thing about our number system is that using just the ten symbols (or digits) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, we can represent any of the infinitely many positive whole numbers. That efficiency is achieved by making use of the position each digit occupies. The rightmost digit in any number expression represents itself. The next