Fibonacci
Fibonacci (/ˌfɪbəˈnɑːtʃi/,^{[3]} also US: /ˌfiːb/,^{[4]}^{[5]} Italian: [fiboˈnattʃi]; c. 1170 – c. 1240–50),^{[6]} also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ("Leonardo the Traveller from Pisa"),^{[7]} was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".^{[8]}
Fibonacci  

Statue of Fibonacci (1863) by Giovanni Paganucci in the Camposanto di Pisa^{[a]}  
Born  c. 1170 Pisa,^{[2]} Republic of Pisa 
Died  c. 1250 (aged 79–80) Pisa, Republic of Pisa 
Other names  Leonardo Fibonacci, Leonardo Bonacci, Leonardo Pisano 
Occupation  Mathematician 
Known for 

Parent(s)  Guglielmo "Bonacci" (father) 
The name he is commonly called, Fibonacci, was made up in 1838 by the FrancoItalian historian Guillaume Libri^{[9]}^{[10]} and is short for filius Bonacci ("son of Bonacci").^{[11]}^{[b]} However, even earlier in 1506 a notary of the Roman Empire Perizolo mentions Leonardo as "Lionardo Fibonacci".^{[12]}
Fibonacci popularized the Hindu–Arabic numeral system in the Western World primarily through his composition in 1202 of Liber Abaci (Book of Calculation).^{[13]}^{[14]} He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci.^{[15]}
HistoryEdit
Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official.^{[7]} Guglielmo directed a trading post in Bugia, Algeria.^{[16]} Fibonacci travelled with him as a young boy, and it was in Bugia that he learned about the Hindu–Arabic numeral system.^{[17]}^{[6]}
Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic.^{[18]} He soon realised the many advantages of the HinduArabic system, which, unlike the Roman numerals used at the time, allowed easy calculation using a placevalue system. In 1202, he completed the Liber Abaci (Book of Abacus or The Book of Calculation),^{[19]} which popularized Hindu–Arabic numerals in Europe.^{[6]}
Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo)^{[20]} by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens:^{[21]}
«Considerantes nostre civitatis et civium honorem atque profectum, qui eis, tam per doctrinam quam per sedula obsequia discreti et sapientis viri magistri Leonardi Bigolli, in abbacandis estimationibus et rationibus civitatis eiusque officialium et aliis quoties expedit, conferuntur; ut eidem Leonardo, merito dilectionis et gratie, atque scientie sue prerogativa, in recompensationem laboris sui quem substinet in audiendis et consolidandis estimationibus et rationibus supradictis, a Comuni et camerariis publicis, de Comuni et pro Comuni, mercede sive salario suo, annis singulis, libre xx denariorum et amisceria consueta dari debeant (ipseque pisano Comuni et eius officialibus in abbacatione de cetero more solito serviat), presenti constitutione firmamus».^{[22]}
The date of Fibonacci's death is not known, but it has been estimated to be between 1240^{[23]} and 1250,^{[24]} most likely in Pisa.
Liber AbaciEdit
In the Liber Abaci (1202), Fibonacci introduced the socalled modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system.^{[25]}^{[26]} The book advocated numeration with the digits 0–9 and place value. The book showed the practical use and value of the new HinduArabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, moneychanging, and other applications. The book was wellreceived throughout educated Europe and had a profound impact on European thought. No copies of the 1202 edition are known to exist.^{[27]}
The 1228 edition, first section introduces the HinduArabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into HinduArabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with a HinduArabic numeral system was an advance in making business calculations easier and faster, which assisted the growth of banking and accounting in Europe.^{[28]}^{[29]}
The second section explains the uses of HinduArabic numerals in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses irrational numbers and prime numbers.^{[27]}^{[28]}^{[29]}
Fibonacci sequenceEdit
Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century.^{[30]}^{[31]}^{[32]}^{[33]}
In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" included today and began the sequence with 1, 1, 2, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.^{[34]}^{[35]} Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.
LegacyEdit
In the 19th century, a statue of Fibonacci was constructed and raised in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.^{[1]}^{[36]}
There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.
WorksEdit
 Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, 2002)^{[25]}
 Practica Geometriae (1220), a compendium of techniques in surveying, the measurement and partition of areas and volumes, and other topics in practical geometry (English translation by Barnabas Hughes, Springer, 2008).
 Flos (1225), solutions to problems posed by Johannes of Palermo
 Liber quadratorum ("The Book of Squares") on Diophantine equations, dedicated to Emperor Frederick II. See in particular congruum and the Brahmagupta–Fibonacci identity.
 Di minor guisa (on commercial arithmetic; lost)
 Commentary on Book X of Euclid's Elements (lost)
See alsoEdit
NotesEdit
ReferencesEdit
 ^ ^{a} ^{b} "Fibonacci's Statue in Pisa". Epsilones.com. Retrieved 20100802.
 ^ Smith, David Eugene; Karpinski, Louis Charles (1911), The Hindu–Arabic Numerals, Boston and London: Ginn and Company, p. 128.
 ^ "Fibonacci, Leonardo". Lexico UK Dictionary. Oxford University Press. Retrieved 23 June 2019.
 ^ "Fibonacci series" and "Fibonacci sequence". Collins English Dictionary. HarperCollins. Retrieved 23 June 2019.
 ^ "Fibonacci number". MerriamWebster Dictionary. Retrieved 23 June 2019.
 ^ ^{a} ^{b} ^{c} MacTutor, R. "Leonardo Pisano Fibonacci". wwwhistory.mcs.stand.ac.uk. Retrieved 20181222.
 ^ ^{a} ^{b} ^{c} Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (First trade paperback ed.). New York City: Broadway Books. pp. 92–93. ISBN 0767908163.
 ^ Eves, Howard. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0030295580 (6th ed.), p. 261.
 ^ Devlin, Keith (2017). Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World. Princeton University Press. p. 24.
 ^ Colin Pask (7 July 2015). Great Calculations: A Surprising Look Behind 50 Scientific Inquiries. Prometheus Books. p. 35. ISBN 9781633880290.
 ^ Keith Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution,A&C Black, 2012 p. 13.
 ^ Drozdyuk, Andriy; Drozdyuk, Denys. (2010). Fibonacci, his numbers and his rabbits. Toronto: Choven Pub. p. 18. ISBN 9780986630019. OCLC 813281753.CS1 maint: multiple names: authors list (link)
 ^ "Fibonacci Numbers". www.halexandria.org.
 ^ Leonardo Pisano: "Contributions to number theory". Encyclopædia Britannica Online, 2006. p. 3. Retrieved 18 September 2006.
 ^ Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan, 20(1):28–30, 1986. ISSN 00476269]
 ^ G. Germano, New editorial perspectives in Fibonacci's Liber abaci, «Reti medievali rivista» 14, 2, pp. 157–173.
 ^ Thomas F. Glick; Steven Livesey; Faith Wallis (2014). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 172. ISBN 9781135459321.
 ^ In the Prologus of the Liber abaci he said: Ubi ex mirabili magisterio in arte per novem figuras Indorum introductus, scientia artis in tantum mihi pre ceteris placuit et intellexi ad illam, quod quicquid studebatur ex ea apud Egyptum, Syriam, Greciam, Siciliam et Provinciam cum suis variis modis, ad que loca negotiationis causa postea peragravi, per multum studium et disputationis didici conflictum, «Having been introduced there to this art with an amazing method of teaching by means of the nine figures of the Indians, I loved the knowledge of such an art to such an extent above all other arts and so much did I devote myself to it with my intellect, that I learned with very earnest application and through the technique of contradiction anything to be studied concerning it and its various methods used in Egypt, in Syria, in Greece, in Sicily, and in Provence, places I have later visited for the purpose of commerce» (translated by G. Germano, New editorial perspectives in Fibonacci's Liber abaci, «Reti medievali rivista» 14, 2, pp. 157–173.
 ^ The English edition of the Liber abaci was published by L.E. Sigler, Leonardo Pisano’s book of calculation, New York, SpringerVerlag, 2003
 ^ See the incipit of Flos: "Incipit flos Leonardi bigolli pisani..." (quoted in the MS Word document 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..."
The basic meanings of "bigollo" appear to be "bilingual" or "traveller". A. F. Horadam contends a connotation of "bigollo" is "absentminded" (see first footnote of "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.  ^ Keith Devlin (7 November 2002). "A man to count on". The Guardian. Retrieved 7 June 2016.
 ^ F. Bonaini, Memoria unica sincrona di Leonardo Fibonacci, novamente scoperta, «Giornale storico degli archivi toscani» 1, 4, 1857, pp. 239–246.
 ^ Koshy, Thomas (2011), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, p. 3, ISBN 9781118031315.
 ^ Tanton, James Stuart (2005), Encyclopédia of Mathematics, Infobase Publishing, p. 192, ISBN 9780816051243.
 ^ ^{a} ^{b} Sigler, Laurence E. (trans.) (2002), Fibonacci's Liber Abaci, SpringerVerlag, ISBN 0387954198
 ^ Grimm 1973
 ^ ^{a} ^{b} Gordon, John Steele. "The Man Behind Modern Math". Retrieved 20150828.
 ^ ^{a} ^{b} "Fibonacci: The Man Behind The Math". NPR.org. Retrieved 20150829.
 ^ ^{a} ^{b} Devlin, Keith. "The Man of Numbers: Fibonacci's Arithmetic Revolution [Excerpt]". Retrieved 20150829.
 ^ Singh, Pamanand (1985). "The socalled fibonacci numbers in ancient and medieval India". Historia Mathematica. 12 (3): 229–244. doi:10.1016/03150860(85)900217.
 ^ Goonatilake, Susantha (1998). Toward a Global Science. Indiana University Press. p. 126. ISBN 9780253333889.
Virahanka Fibonacci.
 ^ Knuth, Donald (2006). The Art of Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4. AddisonWesley. p. 50. ISBN 9780321335708.
 ^ Hall, Rachel W. Math for poets and drummers Archived 20120212 at the Wayback Machine. Math Horizons 15 (2008) 10–11.
 ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci Numbers)". The OnLine Encyclopedia of Integer Sequences. OEIS Foundation.
 ^ Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857). Scritti: Il Liber Abbaci. Tip. delle Scienze Fisiche e Matematiche. p. 231 – via Google Books.
 ^ Devlin, Keith (2010). "The Man of Numbers: In Search of Leonardo Fibonacci" (PDF). Mathematical Association of America. pp. 21–28.
Further readingEdit
 Devlin, Keith (2012). The Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Books. ISBN 9780802779083.
 Goetzmann, William N. and Rouwenhorst, K.Geert (2005). The Origins of Value: The Financial Innovations That Created Modern Capital Markets. Oxford University Press Inc, US, ISBN 0195175719.
 Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03–28
 Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104.
 Horadam, A. F. "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123–134.
 Gavin, J., Schärlig, A., extracts of Liber Abaci online and analyzed on BibNum [click 'à télécharger' for English analysis]
External linksEdit
Wikisource has the text of the 1911 Encyclopædia Britannica article Leonardo of Pisa. 
 "Fibonacci, Leonardo, or Leonardo of Pisa." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. (April 20, 2015). [1]
 Fibonacci at Convergence
 O'Connor, John J.; Robertson, Edmund F., "Leonardo Pisano Fibonacci", MacTutor History of Mathematics archive, University of St Andrews.
 Fibonacci (2 vol., 1857 & 1862) Il liber abbaci and Practica Geometriae – digital facsimile from the Linda Hall Library
 Fibonacci, Liber abbaci Bibliotheca Augustana