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Topic: Leonardo Fibonacci

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	Leonardo Fibonacci
		Leonardo's works are mainly developments of the results obtained by his predecessors; the influences of Greek, Arabian, and Indian mathematicians may be clearly discerned in his methods.
		Leonardo's method, therefore, when the difference was a fixed condition of the problem, was necessarily very different from the Arabian, and, in all probability, was his own discovery.
		Fibonacci's series is a sequence of numbers such that any term is the sum of the two preceding terms: 1, 1, 2, 3, 5, 8, 13, 21, etc. The series is intimately connected to the so-called golden ratio (phi, or 0.61803...), and finds much presence in natural phenomena, trigonometry, art and architecture.
	www.nndb.com /people/922/000095637 (864 words)

	Leonardo Pisano Fibonacci (Site not responding. Last check: 2007-10-19)
		Fibonacci was a contemporary of Jordanus but he was a far more sophisticated mathematician and his achievements were clearly recognised, although it was the practical applications rather than the abstract theorems that made him famous to his contemporaries.
		Fibonacci proves that the root of the equation is neither an integer nor a fraction, nor the square root of a fraction.
		Fibonacci was also the teacher of the "Cossists", who took their name from the word causa which was first used in the West by Fibonacci in place of res or radix.
	erntheburn.tripod.com /fibbonaccisequence/history (2009 words)

	Leonardo Fibonacci
		Fibonacci lived in the days before printing, so his books were hand written and the only way to have a copy of one of his books was to have another hand-written copy made.
		Fibonacci's influence was more limited than one might have hoped and apart from his role in spreading the use of the Hindu-Arabic numerals and his rabbit problem, Fibonacci's contribution to mathematics has been largely overlooked.
		Fibonacci was also the teacher of the "Cossists", who took their name from the word 'causa' which was first used in the West by Fibonacci in place of 'res' or 'radix'.
	milan.milanovic.org /math/english/leonardo/leonardo.html (804 words)

	Leonardo of Pisa - Wikipedia, the free encyclopedia
		Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci).
		Perceiving that arithmetic with Arabic numerals (see that article) is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200.
		Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science.
	en.wikipedia.org /wiki/Leonardo_of_Pisa (384 words)

	MSN Encarta - Fibonacci
		Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and who made contributions to the mathematical fields of algebra and number theory.
		Fibonacci was born in Pisa, Italy, a commercial city, where he learned the basics of business calculation.
		Fibonacci used this experience to improve on the commercial computing techniques he knew and to extend the work of classical mathematical writers, such as the Greek mathematicians Diophantus and Euclid.
	encarta.msn.com /encnet/refpages/RefArticle.aspx?refid=761579463 (277 words)

	Fibonacci
		Leonardo Pisano Fibonacci was born in 1170 in Pisa [1, p.
		Fibonacci was also known by the nickname "Bigollo", which may be taken to mean loafer, and may have expressed the general lack of interest in the purely theoretical mathematics Fibonacci showed interest in.
		Fibonacci ended his travels in approximately 1200 and settled down in Pisa, where for the next twenty five years he composed a number of texts in which he did important work in number theory and the solution of algebraic equations among other important things.
	www.math.rutgers.edu /courses/436/436-s99/Papers1999/oneill.html (2163 words)

	Fibonacci numbers
		Fibonacci numbers are ratios, which are mathematical in nature derived from the Fibonacci sequence, which was developed by Leonardo Fibonacci.
		Fibonacci retracements are commonly drawn from the beginning of Wave 1 to the top of Wave 3 to find a target to the Wave 4 retracehment.
		Fibonacci numbers are the numbers in the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,.
	www.stockstoshop.com /fibonaccinumbers.htm (459 words)

	Leonardo Fibonacci (Site not responding. Last check: 2007-10-19)
		Leonardo Pisano Fibonacci was born in 1170 in Pisa, Itlay.
		Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21...
		Fibonacci became the greatest mathmetician of the Middle Ages.
	www.northstar.k12.ak.us /schools/ryn/connections/1000-1200/LF.html (223 words)

	Leonardo Fibonacci: A Who2 Profile
		Leonardo Fibonacci introduced to Europe and popularized the Hindu-Arabic number system (also called the decimal system).
		Fibonacci was also known as Leonardo of Pisa.
		He is also known for the Fibonacci Series, a numerical series found frequently in the natural world.
	www.who2.com /leonardofibonacci.html (149 words)

	Mathematics & Music (Site not responding. Last check: 2007-10-19)
		Leonardo Fibonacci originally from Pisa, Italy developed a mathematic theory in 1202 that constructs a series of numbers.
		While Fibonacci's geometry is visually pleasing in and of itself, his peculiar sequence of numbers is represented in literally thousands of pieces of art by way of formal design.
		Although the Fibonacci series may be represented abstractly in a piece of music by such things as instrumentation or harmonic texture, it is perhaps easiest to identify this sequence of numbers according to the linear timeline of a piece of music.
	www.davesabine.com /music/mathematics.asp?action=fibonacci (985 words)

	fUSION Anomaly. Fibonacci
		The Fibonacci SEQUENCE 0, 1, 1, 2, 3, 5, 8, 13, 21, , in which each term is the sum of the two preceding terms, occurs in higher mathematics in various connections.
		In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence.
		Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and contributed to algebra and number theory.
	www.fusionanomaly.net /fibonacci.html (757 words)

	[No title]
		Fibonacci or Leonard of Pisa, played an important role in reviving ancient mathematics and made significant contributions of his own.
		Leonardo Pisano is better known by his nickname Fibonacci.
		Fibonacci was born in Italy but was educated in North Africa where his father held a diplomatic post.
	www.italian-american.com /fibonacc.htm (235 words)

	FIBONACCI
		Fibonacci was probably the greatest genius of number theory during the 2000 years between Diophantus and Fermat.
		Fibonacci, also known as Leonardo of Pisa, was born in Pisa, home of the famous leaning tower (inclined at an angle of 16.5 degrees to the vertical).
		Fibonacci is thought to be a contraction of Filiorm Bonacci ("of the family of Bonacci") or Filius Bonacci ("son of Bonacci").
	faculty.evansville.edu /ck6/bstud/fibo.html (4484 words)

	BBC - Radio 4 - 5 Numbers - The Golden Ratio
		Leonardo Fibonacci was an Italian mathematician with a penchant for decimalization and rabbits!
		The Fibonacci sequence is generated by adding the previous two numbers in the list together to form the next and so on and so on...
		Fibonacci used his sequence of numbers to investigate the population growth of his favourite furry lop-eared friend, the rabbit.
	www.bbc.co.uk /radio4/science/5numbers3.shtml (457 words)

	Leonardo Pisano (Fibonacci)
		Liber abbaci was based on the arithmetic and algebra that Fibonacci had accumulated during his travels.
		Fibonacci first notes that square numbers can be constructed as sums of odd numbers, essentially describing an inductive construction using the formula n
		Fibonacci proved that a congruum must be divisible by 24 and he also showed that for x, c such that x
	www.stetson.edu /~efriedma/periodictable/html/F.html (765 words)

	Fibonacci (Site not responding. Last check: 2007-10-19)
		Fibonacci treats numbers such as sqrt(10) in the fourth section, both with rational approximations and with geometric constructions.
		R Franci and L Toti Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus 72 (1-3) (1985), 17-82.
		P Freguglia, The determination of ¹ in Fibonacci's 'Practica geometriae' in a fifteenth-century manuscript (Italian), in Contributions to the history of mathematics (Modena, 1992), 75-84.
	alas.matf.bg.ac.yu /~mm97106/math/fibo/standrew.htm (2306 words)

	Biography Fibonacci Leonardo
		Leonardo Fibonacci (PORTRAIT - 42K) was born in Pisa, Italy around 1170, the son of...
		Fibonacci, Leonardo of Pisa, Leonardo Pisano, lived in Pisa around 1200 and gave his name to the Fibonacci numbers.
		Leonardo Pisano Fibonacci Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy) Leonardo Pisano is better known by his nickname Fibonacci.
	www.spreadtrade2win.com /2/biography-fibonacci-leonardo.html (574 words)

	The life and numbers of Fibonacci
		Fibonacci, or more correctly Leonardo da Pisa, was born in Pisa in 1175AD.
		The Fibonacci numbers are studied as part of number theory and have applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science.
		This article was based on material written by Dr R. Knott, a lecturer in the Department of Computing Studies at the University of Surrey and additional material by Dr D. Quinney, a lecturer in the Department of Mathematics, University of Keele.
	pass.maths.org.uk /issue3/fibonacci (937 words)

	Who was Fibonacci?
		Fibonacci is a shortening of the Latin "filius Bonacci", used in the title of his book Libar Abaci (of which mmore later), which means "the son of Bonaccio".
		Fibonacci himself wrote both "Bonacci" and "Bonaccii" as well as "Bonacij"; the uncertainty in the spelling is partly to be ascribed to this mixture of spoken Italian and written Latin, common at that time.
		Fibonacci says his book Liber Abaci (the first edition was dated 1202) that he had studied the "nine Indian figures" and their arithmetic as used in various countries around the Mediterranean and wrote about them to make their use more commonly understood in his native Italy.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibBio.html (3315 words)

	Biography of Leonardo Fibonacci
		Since Fibonacci was the son of a merchant, he was able go travel freely all over the Byzantine Empire.
		The Fibonacci Society was founded in 1962, and a journal, The Fibonacci Quarterly, first appeared in 1963, and was dedicated to unraveling its secrets.
		This project was prepared and presented by students Jeremy Priest and Jonathan Wagner in 1998.
	www.andrews.edu /~calkins/math/biograph/199899/biofibo.htm (584 words)

	Leonardo of Pisa -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		Perceiving that arithmetic with (One of the symbols 1,2,3,4,5,6,7,8,9,0) Arabic numerals is simpler and more efficient than with (A symbol in the old Roman notation; I,V,X,L,C,D,M represent 1,5,10,50,100,500,1000 respectively in Arabic notation) Roman numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200.
		In 1202, at age 27, he published what he had learned in (additional info and facts about Liber Abaci) Liber Abaci, or Book of Calculation.
		Leonardo became a guest of the Emperor (The Holy Roman Emperor who led the Sixth Crusade and crowned himself king of Jerusalem (1194-1250)) Frederick II, who enjoyed mathematics and science.
	www.absoluteastronomy.com /encyclopedia/l/le/leonardo_of_pisa.htm (359 words)

	Leonardo Fibonacci
		Leonardo's father (Guglielmo Bonaccio) was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France.
		Since Fibonacci in Latin is "filius Bonacci" and means "the son of Bonacci", two early writers on Fibonacci (Boncompagni and Milanesi) regard Bonacci as the family name so that Fib-Bonacci is like the English names of Robin-son or John-son.
		The system that Fibonacci introduced into Europe came from India and Arabia and used the Arabic symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 with, most importantly, a symbol for zero 0.
	web.ukonline.co.uk /mathematiciansinhistory/Fibonacci.htm (937 words)

	Fibonacci, Fibonacci Numbers, Fibonacci Sequence
		Fibonacci enunciated a sequence of numbers, the Fibonacci Numbers, based on a simple arithmetic relationship..
		In the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8,...), each number is the sum of the two previous numbers (ie: 2+3=5, 3+5=8,...
		The Fibonacci Spiral is inherent in the Fibonacci numbers and the Golden Ratio.
	mathematicianspictures.com /FIBONACCI/Fibonacci.htm (350 words)

	Fibonacci Numbers, the Golden section and the Golden String
		Fibonacci and the original problem about rabbits where the series first appears, the family trees of cows and bees, the golden ratio and the Fibonacci series, the Fibonacci Spiral and sea shell shapes, branching plants, flower petal and seeds, leaves and petal arrangements, on pineapples and in apples, pine cones and leaf arrangements.
		Here is a brief biography of Fibonacci and his historical achievements in mathematics, and how he helped Europe replace the Roman numeral system with the "algorithms" that we use today.
		These General Fibonacci series are called the G series but the Fibonacci series and Phi again play a prominent role in their mathematical properties.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fib.html (1948 words)

	Leonardo Pisano -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-19)
		English Leonardo of Pisa, original name Leonardo Fibonacci medieval Italian mathematician who wrote Liber abaci (1202; “Book of the Abacus”), the first European work on Indian and Arabian mathematics.
		These numbers were first noted by the medieval Italian mathematician Leonardo Pisano (“Fibonacci”) in his Liber abaci (1202; “Book of the Abacus”), which also popularized Hindu-Arabic numerals and the decimal number system in...
		Ranging from a summary of the historical setting of the Italian Renaissance to comparisons of drawings from Leonardo's notebooks and modern-day inventions, the treatment is broad yet sufficiently detailed and informative.
	www.britannica.com /eb/article-9047817 (639 words)

	Forex Fibonacci Book. Series of Free Forex ebooks
		Leonardo Fibonacci is a famous Italian mathematician, founder of a simple series of numbers that refer to ratios valid for natural proportions of things on the planet.
		A few examples of Fibonacci numbers are pine cones, sunflowers, pineapples, palm trees, spider webs, snail shells, DNA molecules and millions of other things in the universe.
		Fibonacci retracement and extension levels carry important information for experienced as well as novice Forex traders as they help to identify entry and exit points during the trade.
	www.fibonaccibook.com (323 words)

	The life and numbers of Fibonacci
		Fibonacci, or more correctly Leonardo da Pisa, was born in Pisa in 1175AD.
		The Fibonacci numbers are studied as part of number theory and have applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science.
		This article was based on material written by Dr R. Knott, a lecturer in the Department of Computing Studies at the University of Surrey and additional material by Dr D. Quinney, a lecturer in the Department of Mathematics, University of Keele.
	plus.maths.org /issue3/fibonacci (933 words)

	Fibonacci Series
		Leonardo Fibonacci discovered the series which converges on phi
		In the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi.
		Starting with 0 and 1, each new number in the series is simply the sum of the two before it.
	goldennumber.net /fibonser.htm (216 words)

	Leonardo Fibonacci Biography / Biography of Leonardo Fibonacci Main Biography
		Leonardo Fibonacci was born in Pisa and was brought up in Bougie, Algeria, where his father was a warehouse official.
		Fibonacci traveled extensively for business and pleasure throughout Europe and in Egypt, Syria, and Greece.
		In the Liber abaci (1202; revised version 1228), a thorough treatise on algebraic methods and problems, Fibonacci strongly advocates the use of the new Indian numerals, that is, the nine numerals, plus the zephirum, or symbol for zero.
	www.bookrags.com /biography-leonardo-fibonacci (231 words)

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