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Topic: Liber Abaci

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	The 800th birthday of the book that brought numbers to the west
		Liber abaci, the book that gave numbers to the western world, is exactly 800 years old this year.
		Liber quadratorum ("The book of squares"), published in 1225, is a book on advanced algebra and number theory, and is Fibonacci's most mathematically impressive work, revealing his substantial mathematical abilities.
		The title Liber abaci is sometimes mistranslated as "book of the abacus", but it is more accurately rendered as "book of calculation", since, not only did it say nothing about using an abacus, it described methods that eliminated the need for such a device.
	www.maa.org /devlin/devlin_10_02.html (2831 words)

	Leonardo of Pisa - LoveToKnow 1911 (Site not responding. Last check: 2007-09-21)
		In 1202 he was again in Italy and published his great work, Liber abaci, which probably procured him access to the learned and refined court of the emperor Frederick II.
		In his Practica geometriae plain traces of the use of the Roman agrimensores are met with; in his Liber abaci old Egyptian problems reveal their origin by the reappearance of the very numbers in which the problem is given, though one cannot guess through what channel they came to Leonardo's knowledge.
		The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days.
	www.1911encyclopedia.org /Leonardo_of_Pisa (996 words)

	Liber Abaci
		Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.
		In this work, Fibonacci introduced to Europe the ten numerals (0, and 1 to 9) and the place-value system he had learned while travelling with Arabs in North Africa.
		Liber Abaci was not the first Western book to describe Indian-Arabic numerals, but by addressing tradesmen rather than academics it was the book that convinced the public of the superiority of the new system.
	www.ebroadcast.com.au /lookup/encyclopedia/li/Liber_Abaci.html (203 words)

	Fibonacci biography
		Liber abaci, published in 1202 after Fibonacci's return to Italy, was dedicated to Scotus.
		Liber quadratorum, written in 1225, is Fibonacci's most impressive piece of work, although not the work for which he is most famous.
		Direct influence was exerted only by those portions of the "Liber abaci" and of the "Practica" that served to introduce Indian-Arabic numerals and methods and contributed to the mastering of the problems of daily life.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Fibonacci.html (2058 words)

	Leonardo Pisano Fibonacci Biography \| World of Mathematics
		The Holy Roman Emperor Frederick II had read and was impressed with Liber Abaci, and in 1225 he traveled to Pisa to conduct a mathematical tournament as a test of Fibonacci's skills.
		Liber quadratorum contained a collection of theorems about indeterminate analysis, specifically relating to second degree equations, and its introduction included a description of the second-degree contest problem.
		Fibonacci revised Liber abaci in 1228, and it is this text that eventually became most widely distributed in Europe.
	www.bookrags.com /biography/leonardo-pisano-fibonacci-wom (1289 words)

	Fibonacci's Liber Abaci (Book of Calculation)
		Most English-language references to the book call it Liber Abaci, but since both that spelling and Liber Abbaci are used in the book, either is probably acceptable.
		To these are still added the 144 pairs that are born in the last month; there will be 377 pairs, and this many pairs are produced from the abovewritten pair in the mentioned place at the end of the one year.
		Liber Abaci is full of word problems like this, going from simple arithmetic through fractions, then on to commercial calculations, unit conversions, square roots, cube roots, binomials, root finding, and Euclidean geometry.
	www.math.utah.edu /~beebe/software/java/fibonacci/liber-abaci.html (1103 words)

	Essay Depot - Liber Abaci
		Liber quadratorum was published in 1225("Book of SquareNumbers") was dedicated to the Holy Roman emperor, Frederick II.This book was devoted entirely to Diophantine equations of thesecond degree (i.e., containing squares).
		Although the Liber abaci was moreinfluential and broader in scope, the Liber quadratorum aloneranks its author as the major contributor to number theorybetween Diophantus and Pierre de Fermat, the 17th-century Frenchmathematician.
		His name is known to modern mathematiciansmainly because of the Fibonacci Sequence dervived from a problemin the Liber abaci: A certain man puts a pair of rabbits in a place surrounded on all sides by a wall.
	www.essaydepot.com /essayme/165 (905 words)

	liber abaci -- liber abaci (Site not responding. Last check: 2007-09-21)
		In Liber Abaci he described the nine Indian symbols together with the sign 0 for Europeans in around 1200 but it was not widely used for a long time after that.
		Liber Abaci [Categories: 13th century books] Liber Abaci (1202) is an historic book on arithmetic by (Click link for more info and facts about Leonardo of Pisa) Leonardo of Pisa, known later by his...
		Liber Abaci Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci.
	www.abacusac.com /liberabaci (4052 words)

	Amazon.ca: Fibonacci's Liber Abaci: Leonardo Pisano's Book of Calculation: Books: Laurence Sigler (Site not responding. Last check: 2007-09-21)
		First published in 1202, Fibonacci's Liber abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.
		Though it is known as an introduction to the Hindu number system and the algorithms of arithmetic that children now learn in grade school, "Liber abaci" is much more: an encyclopaedia of thirteenth-century mathematics, both theoretical and practical.
		As the first translation into a modern language of the "Liber abaci", this book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.
	www.amazon.ca /Fibonaccis-Liber-Abaci-Translation-Calculation/dp/0387407375 (429 words)

	No Title
		Fibonacci Liber abaci (Book of the Abacus), published in 1202 after his return to Italy, is based on bits of arithmetic and algebra that Fibonacci had accumulated during his travels.
		Liber abaci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe.
		A problem in Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence for which Fibonacci is best remembered today.
	www.math.tamu.edu /~don.allen/history/mideval/mideval.html (1701 words)

	Leonardo Fibonacci Numbers, Sequence, Golden Ratio
		Direct influence was exerted only by those portions of the Liber abaci and of the Practica that served to introduce Hindu-Arabic numerals and methods and contributed to the mastering of the problems of daily life.
		Fibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci and later named the Fibonacci numbers in his honour.
		The rabbit breeding problem that caused Fibonacci to write about the sequence in Liber abaci may be unrealistic but the Fibonacci numbers really do appear in nature.
	www.leonardo-fibonacci-numbers.com (1256 words)

	Liber Abaci - Wikipedia, the free encyclopedia
		In this work, Fibonacci introduced to Europe Hindu-Arabic numerals, also known as the decimal system, which he had learned by studying with Arabs while living in North Africa with his father, Guilielmo, who wished for him to become a merchant.
		Liber Abaci was not the first Western book to describe Hindu-Arabic numerals, but by addressing tradesmen rather than academics, it was the book that convinced the public of the superiority of the new system.
		This page was last modified 23:22, 8 September 2006.
	en.wikipedia.org /wiki/Liber_Abaci (251 words)

	Leonardo Fibonacci
		Some years afterwards (perhaps in 1228) Leonardo dedicated to the well-known astrologer Michael Scott the second edition of his Liber abaci, which was printed with Leonardo's other works by Prince Bald Boncompagni (Rome, 1857-62, 2 vols.).
		The other works consist of the Practica geometriae and some most striking papers of the greatest scientific importance, amongst which the Liber quadratorum may be specially mentioned.
		The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of later days.
	www.nndb.com /people/922/000095637 (864 words)

	matematicos
		Liber abaci, publicado en el 1202 después de retornar a Italia, esta basado en trozos de aritmética y álgebra que Fibonacci había acumulado durante sus viajes.
		Un problema en Liber abaci permite la introducción de los números de Fibonacci y la serie de Fibonacci por las cuales Fibonacci es recordado hoy en día.
		También en Liber quadratorum del año 1225 aproximó las raíces cúbicas obteniendo una respuesta que en la notación decimal es correcta en 9 dígitos.
	www.mat.usach.cl /histmat/html/fibo.html (233 words)

	Find liber abaci here (Site not responding. Last check: 2007-09-21)
		The 800th birthday of the book that brought numbers to the west Liber abaci, the book that gave numbers to the western world, is exactly 800 years old this year.
		First published in 1202, Fibonacci's "Liber abaci" was one of the most important books on mathematics in the Middle Ages,...
		Il suo Liber abaci introdusse il sistema decimale Hindu-Arabico e l'uso dei numeri arabi in Europa.
	www.futureseducation.com /futures-market52/liber-abaci.html (506 words)

	Algorythmythica: In Plato's Cave - Fibonacci in Plato's Cave
		Arabic, Persian, and Hindu achievements in algebra were funneled to Europe, especially to Italy in the 13th and 14th centuries.
		An important link in this process was Liber Abaci (Book of the Abacus) of 1202 by the Italian mathematician and merchant Fibonacci.
		He was influenced by Al-Khowarizimi, who used the Arabic term al jabar--consolidation--and hence Fibonacci’s "algebra." In his groundbreaking paper Fibonacci elucidated a problem of rabbit breeding, and what came to be known as Fibonacci numbers.
	algorythmythica.com /act2_1.html (153 words)

	Abacus in various number systems
		Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth.
		Yet the written notations did not have a symbol for zero until it was borrowed by Arabs from Hindus and eventually introduced into Europe in 1202 by Leonardo Fibonacci of Piza in his Liber Abaci (The Book of Abacus).
		According to D. Knuth, counting with abaci was so convenient and easy that, at the time when only few knew how to write, it might have seemed preposterous to scribble some symbols on expensive papyrus when an excellent calculating device was readily available.
	www.cut-the-knot.org /blue/Abacus.shtml (599 words)

	La serie di Fibonacci
		Dei suoi libri sono rimaste alcune copie di Liber abaci (1202), Practica geometriae (1220), Flos (1225), e Liber quadratorum, altri testi invece sono andati persi.
		Liber Abaci (1202) è considerato tutt'ora il miglio libro di aritmetica, fu il mezzo principale di dimostrazione e introdusse gli enormi vantaggi del sistema di numerazione Indo-Arabo sul sistema romano.
		La sua algebra appare oggi di tipo curiosamente verbale, in quanto la soluzione è illustrata con parole anzichè raggiunta coi consueti passi con cui si risolvono le equazioni.
	digilander.libero.it /roberto20129/matematica/fibonacci.html (4800 words)

	Leonardo Pisano Fibonacci
		The science in those times obviously was not "in a center of society attention".
		In these conditions appearance of the mathematical book "Liber abaci" ("the book about an abacus"), written in 1202 by the Italian mathematician Leonardo Pisano (by the nickname of Fibonacci) was the relevant event in the "scientific life of society".
		The book "Liber abaci" is the most known of them.
	www.goldenmuseum.com /0401fibonacci_engl.html (1212 words)

	fibonacci (Site not responding. Last check: 2007-09-21)
		ome other ideas included in Liber abaci are methods for all calculations with whole numbers and fractions, extraction of square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions and calculation of compound interest.
		he third section of Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence.
		The sequence is where each number is the sum of the two numbers before it.
	www.saintjoe.edu /~kmh4088/fibonacci.html (272 words)

	Fibonacci, Leonardo da Pisa (ca. 1170-ca. 1240) -- from Eric Weisstein's World of Scientific Biography
		Fibonacci exposed the new alternate computing method--based on written algorithms rather than on counting objects--in his Liber Abaci, first issued in 1202.
		Fibonacci distinguished himself in the mathematical competitions proposed at the court of Emperor Frederick II of Hohenstaufen, King of the Two Sicilies, who had his royal seat in Palermo.
		His striking ability in solving algebraic equations of higher degree clearly emerges from his works entitled Liber Quadratorum and Flos, both of which appeared in 1225.
	scienceworld.wolfram.com /biography/Fibonacci.html (385 words)

	Fibonacci series (Site not responding. Last check: 2007-09-21)
		Liber Abaci was published in 1202, and was based on the arithmetic and algebra that Fibonacci had accumulated during his travels.
		The book, which went on to be widely copied and imitated, introduced to Europe the Hindu-Arabic place-valued decimal system, the use of Arabic numerals, and simultaneous linear equations.
		Many of the problems that Fibonacci considers in Liber Abaci were similar to those appearing in Arab sources.
	www.thescreamonline.com /links/fibonacci.html (314 words)

	Leonardo Fibonacci
		While he was there, he was able to learn both the mathematics of the scholars and the calculating schemes in popular use, at the time.
		A problem in the third section of Liber abaci led to the introduction of the Fibonacci numbers :
		Direct influence was exerted only by those portions of the Liber abaci and of the Practica that served to introduce Hindu-Arabic numerals and methods and contributed to the mastering of the problems of daily life.
	milan.milanovic.org /math/english/leonardo/leonardo.html (804 words)

	The life and numbers of Fibonacci
		In 1200 he returned to Pisa and used the knowledge he had gained on his travels to write Liber abaci in which he introduced the Latin-speaking world to the decimal number system.
		Fibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci and later named the Fibonacci numbers in his honour.
		The rabbit breeding problem that caused Fibonacci to write about the sequence in Liber abaci may be unrealistic but the Fibonacci numbers really do appear in nature.
	plus.maths.org /issue3/fibonacci (941 words)

	The Universe of Discourse : Mixed fractions in Liber Abaci (Site not responding. Last check: 2007-09-21)
		The Universe of Discourse : Mixed fractions in Liber Abaci
		Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation
		Soldiers are so called after the solidi with which they were paid.
	www.plover.com /blog/math/liber-abaci-fractions.html (832 words)

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