Fibonacci 17949 225933531 2008-07-16T02:20:26Z ClueBot 4928500 Reverting possible vandalism by [[Special:Contributions/219.88.101.39|219.88.101.39]] to version by 90.191.146.112. False positive? [[User:ClueBot/FalsePositives|Report it]]. Thanks, [[User:ClueBot]]. (441164) (Bot) {{two other uses||the number sequence|Fibonacci number|the Prison Break character|Otto Fibonacci}} {{Infobox Scientist |box_width = 300px |name = Leonardo of Pisa (Fibonacci) |image = Fibonacci2.jpg |image_width = 150px |caption = Leonardo of Pisa, "Fibonacci" |birth_date = c. [[1170]] |birth_place = [[Pisa]], [[Italy]] |death_date = c. [[1250]] |death_place = [[Pisa]], [[Italy]] |residence = {{flag|Italy}} |citizenship = |nationality = {{flag|Italy|name=Italian}} |ethnicity = |fields = [[Mathematician]] |workplaces = |alma_mater = |doctoral_advisor = |academic_advisors = |doctoral_students = |notable_students = |known_for = [[Fibonacci number]]</br>[[Fibonacci prime]]</br>[[Brahmagupta-Fibonacci identity]]</br>[[Fibonacci polynomials]]</br>[[Fibonacci pseudoprime]]</br>[[Fibonacci word]]</br> [[Reciprocal Fibonacci constant]]</br>[[Fibonacci family]]</br>Introduction of [[Hindu-Arabic numeral system|digital notation]] to Europe</br>[[Pisano period]]</br>[[Practical number]] |author_abbrev_bot = |author_abbrev_zoo = |influences = |influenced = |awards = |religion = [[Catholic]] |signature = <!--(filename only)--> |footnotes = }} '''Leonardo of Pisa''' (c. [[1170]] – c. [[1250]]), also known as '''Leonardo Pisano''', '''Leonardo Bonacci''', '''Leonardo Fibonacci''', or, most commonly, simply '''Fibonacci''', was an [[Italy|Italian]] [[mathematician]], considered by some "the most talented mathematician of the [[Middle Ages]]".<ref>[[Howard Eves]]. ''An Introduction to the History of Mathematics''. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.</ref> Fibonacci is best known to the modern world for:<ref>[http://www.britannica.com/eb/article-4153/Leonardo-Pisano Leonardo Pisano - page 3: "Contributions to number theory"]. [[Encyclopædia Britannica]] Online, 2006. Accessed 18 September 2006.</ref> * The spreading of the [[Arabic numeral system]] in [[Europe]], primarily through the publication in the early 13th century of his ''Book of Calculation'', the ''[[Liber Abaci]]''. * A modern number [[sequence]] named after him known as the [[Fibonacci number]]s, which he did not discover but used as an example in the ''Liber Abaci''.<ref>Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". ''Math''. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]</ref> ==Biography== Leonardo was born in [[Pisa, Italy]]. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was [[posthumous name|posthumously]] given the nickname Fibonacci (derived from ''filius Bonacci'', meaning son of Bonaccio).<ref>See the [[incipit]] of the ''Liber Abaci'': "Incipit liber Abaci Compositus a leonardo '''filio Bonacij''' Pisano" (copied from the [[Wikisource:La:Liber abbaci - Prologus|"Prologus" of the ''Liber Ab(b)aci'' at Latin Wikisource]] - emphasis added), in English: "Here starts the book of Calculation Written by leonardo son of Bonaccio, from Pisa"</ref> Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in [[Bugia]], a port east of Algiers in the [[Almohad]] dynasty's sultanate in [[North Africa]] (now [[Bejaia]], [[Algeria]]). As a young boy, Leonardo traveled there to help him. This is where he learned about the [[Arabic numeral system]]. [[Image:Leonardo da Pisa.jpg|thumb|right|180px|Statue of Fibonacci. Camposanto, Pisa.]] Recognizing that arithmetic with [[Hindu numerals]] 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. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in ''[[Liber Abaci]]'' (''Book of Abacus'' or ''Book of Calculation''), and thereby introduced Hindu-Arabic numerals to Europe. Leonardo became an amicable guest of the Emperor [[Frederick II, Holy Roman Emperor|Frederick II]], who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, referred to as Leonardo Bigollo,<ref>See the incipit of ''[[Flos]]'': "Incipit flos Leonardi '''bigolli''' pisani..." (quoted in the [[MS Word]] document [http://www.g4g4.com/MyCD5/SOURCES/SOURCE1.DOC ''Sources in Recreational Mathematics: An Annotated Bibliography''] by David Singmaster, 18 March 2004 - emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."<br>The basic meanings of "bigollo" appear to be "good-for-nothing" and "traveller" (so it could be translated by "vagrant", "vagabond" or "tramp"). A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of [http://faculty.evansville.edu/ck6/bstud/fibo.html "Eight hundred years young"]), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.</ref> by granting him a salary. In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the [[Camposanto Monumentale|Camposanto]], historical cemetery on the [[Piazza dei Miracoli]].<ref>[http://www.epsilones.com/documentos/d-fibonacci.html#fibonacci-ingles Fibonacci's Statue in Pisa]</ref> ==''Liber Abaci''== {{main|Liber Abaci}} In the ''[[Liber Abaci]]'' (1202), Fibonacci introduces the so-called ''modus Indorum'' (method of the Indians), today known as Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and [[place value]]. The book showed the practical importance of the new [[numeral system]], using [[lattice multiplication]] and [[Egyptian fractions]], by applying it to commercial [[bookkeeping]], conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought. Nevertheless, the use of decimal numerals did not become widespread until much later.{{Fact|date=December 2007}} ''Liber Abaci'' also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as [[Fibonacci number]]s. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci's ''Liber Abaci'' that introduced it to the West. ==Fibonacci sequence== [[Image:Fibonacci.JPG|thumb|right|180px|Chimney of Turku Energia, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian artist Mario Merz for an environmental art project (1994)]] {{main|Fibonacci number}} In the Fibonacci sequence of numbers, each number after the first two is the sum of the previous two numbers. Thus the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc. The higher up in the sequence, the closer two consecutive numbers of the sequence divided by each other will approach the [[golden ratio]] (approximately 1&nbsp;:&nbsp;1.618 or 0.618&nbsp;:&nbsp;1). ==In popular culture== * Fibonacci's name was adopted by a [[Los Angeles]]-based [[art rock]] group, [[The Fibonaccis]], that recorded from 1982-1987. * Fibonacci and the [[Fibonacci number]]s are mentioned as a code to unlock a vessel in [[Dan Brown]]'s best selling novel, ''[[The DaVinci Code]]'', and its [[The Da Vinci Code (film)|movie adaptation]]. * A youthful Fibonacci is one of the main characters in the novel [[Crusade in Jeans]] (1973). He was left out of the 2006 [[Crusade in Jeans (film)|movie version]], however. ==Books written by Fibonacci== * ''[[Liber Abaci]]'' (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002) * ''[[Practica Geometriae]]'' (1220), a compendium on [[geometry]] and [[trigonometry]]. * ''[[Flos]]'' (1225), solutions to problems posed by Johannes of [[Palermo]] * ''Liber quadratorum'', ("''[[The Book of Squares]]''") on [[Diophantine equation]]s, devoted to Emperor [[Frederick II, Holy Roman Emperor|Frederick II]]. See in particular [[Fibonacci's identity]]. * ''Di minor guisa'' (on commercial arithmetic; lost) * ''Commentary on Book X of [[Euclid]]'s Elements'' (lost) ==References== <!--<nowiki> See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref> and </ref> tags, and the template below </nowiki>--> {{reflist}} == Bibliography == * Goetzmann, William N. and Rouwenhorst, K.Geert, ''The Origins of Value: The Financial Innovations That Created Modern Capital Markets'' (2005, Oxford University Press Inc, USA), ISBN 0195175719. * Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99-104. * A. F. Horadam, "Eight hundred years young," ''The Australian Mathematics Teacher'' 31 (1975) 123-134. ==See also== * [[Brahmagupta-Fibonacci identity]] * [[Fibonacci heap]] * [[Pisano period]] * [[Lagged Fibonacci generator]] * [[Fibonacci coding]] * [[Fibonacci prime]] * [[Reciprocal Fibonacci constant]] * [[Fibonacci search technique]] * [[Fibonacci family]] * [[Golden ratio]] * [[Retracement]] * [[Lucas number]] * [[Negafibonacci]] * [[Elliott wave principle]] * [[Acharya Hemachandra]] * [[Zeckendorf's theorem]] * [[Viswanath's constant]] * [[Casey Mongoven]] * [[Hylomorphism (computer science)]] * [[Verner Emil Hoggatt, Jr.]] * [[Practical number]] * [[Virahanka]] * [[Carmichael's theorem]] * [[Primefree sequence]] * [[Engel expansion]] * [[Egyptian fraction]] * [[NegaFibonacci coding]] ==External links== *www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html * Goetzmann, William N., ''Fibonacci and the Financial Revolution'' (October 23, 2003),[[Yale School of Management]] International Center for Finance Working Paper No. 03-28 [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=461740] * Charles Burnett, [http://www.muslimheritage.com/topics/default.cfm?ArticleID=472 Leonard of Pisa (Fibonacci) and Arabic Arithmetic] - the Medieval background to Fibonacci's work *[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=630&bodyId=1002 Fibonacci] at [http://mathdl.maa.org/convergence/1/ Convergence] * wallstreetcosmos.com, ''[http://www.wallstreetcosmos.com/elliot.html Fibonacci numbers and stock market analysis]'', (2008). * [http://www-history.mcs.st-and.ac.uk/~john/ O'Connor, John J] and [http://www-history.mcs.st-and.ac.uk/~edmund/ Robertson, Edmund F]. [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html "Leonardo Pisano Fibonacci &ndash; 1170 - 1250"] in [http://turnbull.mcs.st-and.ac.uk/~history/ ''The MacTutor History of Mathematics archive'']. [[University of St Andrews]] website, Scotland, 1998. *[http://liberabaci.blogspot.com/ Liber Abaci and its Egyptian fraction methods] <!-- Metadata: see [[Wikipedia:Persondata]] --> {{Persondata |NAME= Leonardo of Pisa |ALTERNATIVE NAMES=Fibonacci;Pisano, Leonardo; Bonacci, Leonardo; Fibonacci, Leonardo |SHORT DESCRIPTION= |DATE OF BIRTH= c. [[1170]] |PLACE OF BIRTH= [[Pisa]], [[Italy]] |DATE OF DEATH= c. 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