1424:«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». F. Bonaini,
439:
55:
1311:
he said: "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
551:
In the
Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next
1312:
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,
511:, and methods to convert numbers to it. The second section explains uses in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses
488:, converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. Replacing Roman numerals, its
418:
honored
Fibonacci (referred to as Leonardo Bigollo) 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.
1384:), 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.
538:
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
1973:
379:
coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which, unlike the
2213:
1149:
507:
The original 1202 manuscript is not known to exist. In a 1228 copy of the manuscript, the first section introduces the numeral system and compares it with others, such as
454:
showing (in box on right) the
Fibonacci sequence with the position in the sequence labeled with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals
1373:
The basic meanings of "bigollo" appear to be "bilingual" or "traveller". A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of
548:
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.
1560:
2001:
2178:
1952:
790:
177:
1792:
1734:
943:
368:, in modern-day Algeria. Fibonacci travelled with him as a young boy, and it was in Bugia (Algeria) where he was educated that he learned about the
1627:
920:
2208:
2102:
1990:
1595:
172:
1403:
2173:
1728:
1698:
1277:
1135:
1080:
318:
1003:
2128:
2123:
2118:
700:
576:
327:('son of Bonacci'). However, even earlier, in 1506, a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci".
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451:
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889:
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1035:
862:
1968:"Fibonacci, Leonardo, or Leonardo of Pisa." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. (April 20, 2015).
2188:
664:
407:
1371:
by David
Singmaster, 18 March 2004 – emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."
1125:
473:
369:
331:
156:
1377:
1320:
1249:
489:
868:
364:
Fibonacci was born around 1170 to
Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in
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1552:
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1209:
934:
584:
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2017:
1921:
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496:
for calculations, was an advance in making business calculations easier and faster, which assisted the growth of
786:
1995:
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In the 19th century, a statue of
Fibonacci was set in Pisa. Today it is located in the western gallery of the
2040:
900:
1718:
929:
565:
2168:
2020:
1623:
917:
1585:
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1720:
The Art of
Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4
1395:
686:
660:
2139:
2079:
1985:
1981:
1932:
1590:
656:
569:
481:
1053:
Finding
Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World
2097:
2033:
2012:
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999:
512:
384:
60:
1690:
1230:
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414:, posed several questions based on Arab mathematical works for Fibonacci to solve. In 1240, the
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484:. The book showed the practical use and value of this by applying the numerals to commercial
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35:
1969:
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299:
133:
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1901:
The Origins of Value: The Financial Innovations That Created Modern Capital Markets
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553:
365:
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844:
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485:
445:
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390:
337:
307:
148:
1928:
1221:
Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers".
54:
17:
1066:
501:
1755:
1145:
615:(1202), a book on calculations (English translation by Laurence Sigler, 2002)
622:
1170:
1586:"The Man of Numbers: Fibonacci's Arithmetic Revolution [Excerpt]"
668:
638:
410:, who enjoyed mathematics and science. A member of Frederick II's court,
296:
162:
1362:
850:
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
579:
because of a connection to the Fibonacci numbers. Examples include the
497:
1547:
1545:
894:
763:
is "good-natured", so the full name means "son from a good-natured ".
634:
493:
1072:
Great Calculations: A Surprising Look Behind 50 Scientific Inquiries
1916:
1428:, «Giornale storico degli archivi toscani» 1, 4, 1857, pp. 239–246.
556:
as the limit of the ratio of consecutive numbers in this sequence.
306:, considered to be "the most talented Western mathematician of the
591:. Beyond mathematics, namesakes of Fibonacci include the asteroid
469:
437:
422:
Fibonacci is thought to have died between 1240 and 1250, in Pisa.
334:
in the Western world primarily through his composition in 1202 of
1426:
Memoria unica sincrona di Leonardo Fibonacci, novamente scoperta
630:
477:
79:
2029:
1807:
Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857).
1650:"The so-called fibonacci numbers in ancient and medieval India"
1368:
Sources in Recreational Mathematics: An Annotated Bibliography
261:
229:
226:
2025:
1520:, translated by Sigler, Laurence E., Springer-Verlag, 2002,
1786:
1269:
Medieval Science, Technology, and Medicine: An Encyclopedia
232:
217:
647:(1225), solutions to problems posed by Johannes of Palermo
1813:. Tip. delle Scienze Fisiche e Matematiche. p. 231.
641:(English translation by Barnabas Hughes, Springer, 2008).
211:
1924:
International Center for Finance Working Paper No. 03–28
552:
place, the value 377. Fibonacci did not speak about the
59:
Statue of Fibonacci (1863) by Giovanni Paganucci in the
1899:
Goetzmann, William N. and Rouwenhorst, K.Geert (2005).
1266:
Thomas F. Glick; Steven Livesey; Faith Wallis (2014).
1112:
The Man of Numbers: Fibonacci's Arithmetic Revolution,
811:
Smith, David Eugene; Karpinski, Louis Charles (1911),
403:), which popularized Hindu–Arabic numerals in Europe.
317:, was made up in 1838 by the Franco-Italian historian
1881:
The Man of Numbers: Fibonacci's Arithmetic Revolution
1838:"The Man of Numbers: In Search of Leonardo Fibonacci"
1314:
New editorial perspectives in Fibonacci's Liber abaci
1243:
New editorial perspectives in Fibonacci's Liber abaci
258:
255:
223:
208:
205:
817:, Boston and London: Ginn and Company, p. 128,
264:
214:
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2090:
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383:used at the time, allowed easy calculation using a
220:
186:
139:
129:
109:
90:
67:
45:
1878:
1682:
1935:, Vol. 11, No. 1, February 1973, pp. 99–104.
1199:Leonardo Pisano: "Contributions to number theory"
853:(First trade paperback ed.). New York City:
346:) and also introduced Europe to the sequence of
1787:"Sequence A000045 (Fibonacci Numbers)"
1212:Online, 2006. p. 3. Retrieved 18 September 2006.
1579:
1577:
2041:
1512:
1510:
1441:Fibonacci and Lucas Numbers with Applications
1028:An Introduction to the History of Mathematics
8:
1938:Horadam, A. F. "Eight hundred years young,"
1946:
729:Fibonacci's actual appearance is not known.
608:
543:
533:
464:(1202), Fibonacci introduced the so-called
459:
443:
388:
351:
335:
322:
146:
2048:
2034:
2026:
1124:Drozdyuk, Andriy; Drozdyuk, Denys (2010).
53:
42:
2214:Court of Frederick II, Holy Roman Emperor
1793:On-Line Encyclopedia of Integer Sequences
1665:
1055:. Princeton University Press. p. 24.
781:
779:
2103:Greedy algorithm for Egyptian fractions
1991:MacTutor History of Mathematics Archive
993:
991:
989:
839:
837:
835:
775:
722:
1917:Fibonacci and the Financial Revolution
1614:
1612:
1406:from the original on 17 September 2016
1127:Fibonacci, his numbers and his rabbits
621:(1220), a compendium of techniques in
34:. For the Prison Break character, see
1945:Gavin, J., Schärlig, A., extracts of
1903:. Oxford University Press Inc., US,
1342:Leonardo Pisano's book of calculation
750:('Leonardo the Traveller from Pisa').
276:
7:
2129:Generalizations of Fibonacci numbers
2124:List of things named after Fibonacci
2119:Fibonacci numbers in popular culture
2002:Fibonacci (2 vol., 1857 & 1862)
1929:The Autobiography of Leonardo Pisano
1689:. Indiana University Press. p.
1553:"Fibonacci: The Man Behind The Math"
1482:, Infobase Publishing, p. 192,
1444:, John Wiley & Sons, p. 3,
701:Fibonacci numbers in popular culture
27:Italian mathematician (c. 1170–1245)
2179:13th-century Italian mathematicians
1846:Mathematical Association of America
1130:. Toronto: Choven Pub. p. 18.
1940:The Australian Mathematics Teacher
1817:from the original on 13 March 2023
1316:, «Reti medievali rivista» 14, 2,
1245:, «Reti medievali rivista» 14, 2,
1089:from the original on 13 March 2023
25:
1344:, New York, Springer-Verlag, 2003
946:from the original on 12 June 2012
350:, which he used as an example in
1394:Keith Devlin (7 November 2002).
1225:. Ed. Siwan, 20(1):28–30, 1986.
1075:. Prometheus Books. p. 35.
1002:. www-history.mcs.st-and.ac.uk.
681:(on commercial arithmetic; lost)
637:, and other topics in practical
313:The name he is commonly called,
251:
201:
1856:from the original on 2015-09-07
1737:from the original on 2023-03-13
1630:from the original on 2015-08-23
1598:from the original on 2014-06-18
1563:from the original on 2011-07-16
1496:from the original on 2023-03-13
1458:from the original on 2023-03-13
1286:from the original on 2023-03-13
1181:from the original on 2019-10-13
1152:from the original on 2020-02-17
1006:from the original on 2019-10-28
871:from the original on 2023-03-13
821:from the original on 2023-03-13
793:from the original on 2014-02-22
490:ancient Egyptian multiplication
452:Biblioteca Nazionale di Firenze
375:Fibonacci travelled around the
2209:Italian expatriates in Algeria
1723:. Addison-Wesley. p. 50.
1681:Goonatilake, Susantha (1998).
1340:was published by L.E. Sigler,
971:Merriam-Webster.com Dictionary
673:Brahmagupta–Fibonacci identity
581:Brahmagupta–Fibonacci identity
577:concepts named after Fibonacci
476:, with ten digits including a
1:
2174:13th-century writers in Latin
2011:– digital facsimile from the
1476:Tanton, James Stuart (2005),
568:, historical cemetery on the
289:
282:
94:
71:
30:For the number sequence, see
1667:10.1016/0315-0860(85)90021-7
1624:"The Man Behind Modern Math"
787:"Fibonacci's Statue in Pisa"
575:There are many mathematical
387:. In 1202, he completed the
190:Guglielmo "Bonacci" (father)
1986:"Leonardo Pisano Fibonacci"
1756:Math for poets and drummers
1479:Encyclopédia of Mathematics
1375:"Eight hundred years young"
1336:The English edition of the
1000:"Leonardo Pisano Fibonacci"
474:Hindu–Arabic numeral system
370:Hindu–Arabic numeral system
157:Hindu–Arabic numeral system
2230:
1783:Sloane, N. J. A.
1361:pisani..." (quoted in the
1272:. Routledge. p. 172.
1114:A&C Black, 2012 p. 13.
935:Collins English Dictionary
585:Fibonacci search technique
526:
431:
332:Indo–Arabic numeral system
330:Fibonacci popularized the
173:Fibonacci–Sylvester method
29:
2134:The Fibonacci Association
1922:Yale School of Management
1825:– via Google Books.
1357:: "Incipit flos Leonardi
814:The Hindu–Arabic Numerals
406:Fibonacci was a guest of
52:
1996:University of St Andrews
1810:Scritti: Il Liber Abbaci
1648:Singh, Pamanand (1985).
685:Commentary on Book X of
2189:Italian Roman Catholics
2018:Fibonacci, Liber abbaci
1951:online and analyzed on
1914:Goetzmann, William N.,
1685:Toward a Global Science
1518:Fibonacci's Liber Abaci
1210:Encyclopædia Britannica
901:Oxford University Press
748:Leonardo Bigollo Pisano
542:. Although Fibonacci's
401:The Book of Calculation
1947:
1877:Devlin, Keith (2012).
1836:Devlin, Keith (2010).
1717:Knuth, Donald (2006).
1438:Koshy, Thomas (2011),
609:
595:and the art rock band
544:
534:
472:), today known as the
460:
455:
444:
442:A page of Fibonacci's
389:
352:
336:
323:
147:
104:Pisa, Republic of Pisa
2021:Bibliotheca Augustana
1030:. Brooks Cole, 1990:
897:UK English Dictionary
890:"Fibonacci, Leonardo"
661:Diophantine equations
492:method, and using an
441:
278:[fiboˈnattʃi]
1982:Robertson, Edmund F.
1920:(October 23, 2003),
1705:Virahanka Fibonacci.
1654:Historia Mathematica
930:"Fibonacci sequence"
667:. See in particular
665:Emperor Frederick II
408:Emperor Frederick II
2140:Fibonacci Quarterly
2080:The Book of Squares
2008:Practica Geometriae
1980:O'Connor, John J.;
1933:Fibonacci Quarterly
1620:Gordon, John Steele
1591:Scientific American
1396:"A man to count on"
1353:See the incipit of
1175:www.halexandria.org
1171:"Fibonacci Numbers"
657:The Book of Squares
619:Practica Geometriae
570:Piazza dei Miracoli
482:positional notation
344:Book of Calculation
2204:Medieval geometers
2098:Fibonacci sequence
2013:Linda Hall Library
1942:31 (1975) 123–134.
1849:. pp. 21–28.
1796:. OEIS Foundation.
1761:2012-02-12 at the
1380:2008-12-19 at the
1323:2021-07-09 at the
1252:2021-07-09 at the
1204:2008-06-17 at the
1038:(6th ed.), p. 261.
966:"Fibonacci number"
923:2019-06-23 at the
918:"Fibonacci series"
857:. pp. 92–93.
523:Fibonacci sequence
513:irrational numbers
456:
385:place-value system
116:Leonardo Fibonacci
61:Camposanto di Pisa
2184:Fibonacci numbers
2151:
2150:
1958:
1730:978-0-321-33570-8
1700:978-0-253-33388-9
1279:978-1-135-45932-1
1137:978-0-9866300-1-9
1082:978-1-63388-029-0
974:. Merriam-Webster
789:. Epsilones.com.
759:The etymology of
687:Euclid's Elements
652:Liber quadratorum
629:and partition of
540:Fibonacci numbers
348:Fibonacci numbers
321:and is short for
243:
194:
193:
168:Fibonacci numbers
155:Popularizing the
101:(aged 79–80)
16:(Redirected from
2221:
2199:People from Pisa
2194:Number theorists
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2036:
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1998:
1957:
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1896:
1885:. Walker Books.
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903:. Archived from
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744:Leonardo of Pisa
740:Leonardo Bonacci
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706:Republic of Pisa
614:
547:
537:
529:Fibonacci number
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416:Republic of Pisa
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304:Republic of Pisa
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178:Fibonacci method
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119:Leonardo Bonacci
110:Other names
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84:Republic of Pisa
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57:
43:
32:Fibonacci number
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1979:
1965:
1927:Grimm, R. E., "
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1871:Further reading
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1584:Devlin, Keith.
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1069:(7 July 2015).
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711:Adelard of Bath
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663:, dedicated to
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468:(method of the
436:
430:
412:John of Palermo
362:
319:Guillaume Libri
292:
285:
273:
254:
245:
244:
204:
200:
182:
125:
122:Leonardo Pisano
105:
102:
98:
86:
77:
74:
63:
48:
39:
28:
23:
22:
18:Leonard of Pisa
15:
12:
11:
5:
2227:
2225:
2217:
2216:
2211:
2206:
2201:
2196:
2191:
2186:
2181:
2176:
2171:
2166:
2156:
2155:
2149:
2148:
2146:
2145:
2144:
2143:
2131:
2126:
2121:
2115:
2113:
2109:
2108:
2106:
2105:
2100:
2094:
2092:
2088:
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2085:
2084:
2076:
2067:
2065:
2061:
2060:
2055:
2053:
2052:
2045:
2038:
2030:
2024:
2023:
2015:
2004:Il liber abaci
1999:
1977:
1976:at Convergence
1971:
1964:
1963:External links
1961:
1960:
1959:
1943:
1936:
1925:
1912:
1897:
1892:978-0802779083
1891:
1872:
1869:
1867:
1866:
1828:
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1774:
1747:
1729:
1709:
1699:
1673:
1660:(3): 229–244.
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1608:
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1100:
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1016:
985:
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910:
907:on 2021-05-12.
881:
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772:
769:
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731:
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720:
718:
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713:
708:
703:
696:
693:
692:
691:
682:
679:Di minor guisa
676:
648:
642:
616:
604:
601:
597:The Fibonaccis
593:6765 Fibonacci
561:
558:
527:Main article:
524:
521:
509:Roman numerals
432:Main article:
429:
424:
397:Book of Abacus
381:Roman numerals
366:Bugia (Béjaïa)
361:
358:
324:filius Bonacci
293: 1240–50
192:
191:
188:
184:
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181:
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143:
141:
140:Known for
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36:Otto Fibonacci
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2226:
2215:
2212:
2210:
2207:
2205:
2202:
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2069:
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2066:
2062:
2058:
2051:
2046:
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2039:
2037:
2032:
2031:
2028:
2022:
2019:
2016:
2014:
2010:
2009:
2005:
2000:
1997:
1993:
1992:
1987:
1983:
1978:
1975:
1972:
1970:
1967:
1966:
1962:
1956:
1955:
1949:
1944:
1941:
1937:
1934:
1930:
1926:
1923:
1919:
1918:
1913:
1910:
1909:0-19-517571-9
1906:
1902:
1898:
1894:
1888:
1883:
1882:
1875:
1874:
1870:
1852:
1848:
1847:
1839:
1832:
1829:
1816:
1812:
1811:
1803:
1800:
1795:
1794:
1788:
1784:
1778:
1775:
1772:(2008) 10–11.
1771:
1768:
1767:Math Horizons
1764:
1760:
1757:
1751:
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1736:
1732:
1726:
1722:
1721:
1713:
1710:
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1702:
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1692:
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1677:
1674:
1668:
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1659:
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1379:
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1370:
1369:
1364:
1360:
1356:
1350:
1347:
1343:
1339:
1333:
1330:
1326:
1322:
1319:
1315:
1310:
1306:
1300:
1297:
1285:
1281:
1275:
1271:
1270:
1262:
1259:
1255:
1251:
1248:
1244:
1238:
1235:
1232:
1228:
1224:
1218:
1215:
1211:
1207:
1203:
1200:
1195:
1192:
1180:
1176:
1172:
1166:
1163:
1151:
1147:
1143:
1139:
1133:
1129:
1128:
1120:
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1109:
1104:
1101:
1088:
1084:
1078:
1074:
1073:
1068:
1062:
1059:
1054:
1050:
1049:Devlin, Keith
1044:
1041:
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1036:0-03-029558-0
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1001:
998:MacTutor, R.
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992:
990:
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940:HarperCollins
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906:
902:
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891:
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882:
870:
866:
864:0-7679-0816-3
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852:
851:
846:
840:
838:
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832:
820:
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804:
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709:
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680:
677:
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670:
666:
662:
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653:
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632:
628:
624:
620:
617:
613:
612:
607:
606:
602:
600:
598:
594:
590:
589:Pisano period
586:
582:
578:
573:
571:
567:
559:
557:
555:
549:
546:
541:
536:
530:
522:
520:
518:
517:prime numbers
514:
510:
505:
503:
499:
495:
491:
487:
483:
479:
475:
471:
467:
466:modus Indorum
462:
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447:
440:
435:
428:
425:
423:
420:
417:
413:
409:
404:
402:
398:
393:
392:
386:
382:
378:
377:Mediterranean
373:
371:
367:
359:
357:
354:
349:
345:
340:
339:
333:
328:
325:
320:
316:
311:
309:
305:
301:
300:mathematician
298:
279:
269:
248:
237:
198:
189:
185:
179:
176:
174:
171:
169:
166:
164:
161:
158:
154:
151:
150:
145:
144:
142:
138:
135:
134:Mathematician
132:
128:
121:
118:
115:
114:
112:
108:
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89:
85:
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70:
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62:
56:
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33:
19:
2169:1170s births
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2078:
2070:
2056:
2007:
2003:
1989:
1953:
1939:
1915:
1900:
1880:
1858:. Retrieved
1844:
1831:
1819:. Retrieved
1809:
1802:
1790:
1777:
1769:
1766:
1750:
1739:. Retrieved
1719:
1712:
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1684:
1676:
1657:
1653:
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1632:. Retrieved
1600:. Retrieved
1589:
1565:. Retrieved
1556:
1535:
1517:
1498:, retrieved
1478:
1471:
1460:, retrieved
1440:
1433:
1425:
1420:
1408:. Retrieved
1400:The Guardian
1399:
1389:
1367:
1358:
1354:
1349:
1341:
1338:Liber abacci
1337:
1332:
1313:
1309:Liber abacci
1308:
1304:
1299:
1288:. Retrieved
1268:
1261:
1242:
1241:G. Germano,
1237:
1222:
1217:
1194:
1183:. Retrieved
1174:
1165:
1154:. Retrieved
1126:
1119:
1111:
1108:Keith Devlin
1103:
1091:. Retrieved
1071:
1061:
1052:
1043:
1027:
1024:Eves, Howard
1019:
1008:. Retrieved
976:. Retrieved
969:
960:
948:. Retrieved
933:
913:
905:the original
893:
884:
873:. Retrieved
849:
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823:, retrieved
813:
806:
795:. Retrieved
760:
755:
747:
743:
739:
734:
725:
684:
678:
650:
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563:
554:golden ratio
550:
532:
506:
465:
457:
426:
421:
405:
400:
396:
374:
363:
343:
329:
314:
312:
196:
195:
99:(1250-00-00)
40:
2164:1250 deaths
2072:Liber Abaci
1948:Liber Abaci
1821:20 December
1318:pp. 157–173
1247:pp. 157–173
627:measurement
611:Liber Abaci
545:Liber Abaci
535:Liber Abaci
504:in Europe.
486:bookkeeping
461:Liber Abaci
446:Liber Abaci
434:Liber Abaci
427:Liber Abaci
391:Liber Abaci
353:Liber Abaci
338:Liber Abaci
308:Middle Ages
286: 1170
149:Liber Abaci
75: 1170
2158:Categories
1860:2018-12-21
1741:2020-11-11
1634:2015-08-28
1602:2015-08-29
1567:2015-08-29
1539:Grimm 1973
1500:2015-12-12
1462:2015-12-12
1290:2018-12-07
1185:2015-04-29
1156:2020-01-26
1093:19 January
1067:Colin Pask
1010:2018-12-22
875:2018-12-19
825:2016-03-02
797:2010-08-02
771:References
587:, and the
566:Camposanto
502:accounting
130:Occupation
2057:Fibonacci
1974:Fibonacci
1365:document
1231:0047-6269
1146:813281753
847:(2003) .
623:surveying
450:from the
360:Biography
315:Fibonacci
302:from the
295:) was an
197:Fibonacci
159:in Europe
47:Fibonacci
2091:Theories
1851:Archived
1815:Archived
1759:Archived
1735:Archived
1628:Archived
1596:Archived
1561:Archived
1494:archived
1456:archived
1404:Archived
1378:Archived
1321:Archived
1305:Prologus
1284:Archived
1250:Archived
1202:Archived
1179:Archived
1150:Archived
1087:Archived
1051:(2017).
1004:Archived
944:Archived
921:Archived
869:Archived
819:archived
791:Archived
695:See also
671:and the
669:congruum
639:geometry
274:Italian:
163:Congruum
2112:Related
1785:(ed.).
1557:NPR.org
1363:MS Word
1359:bigolli
1307:of the
1303:In the
978:23 June
950:23 June
761:Bonacci
635:volumes
498:banking
470:Indians
458:In the
297:Italian
2083:(1225)
2075:(1202)
1954:BibNum
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717:Notes
631:areas
603:Works
2006:and
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1887:ISBN
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1791:The
1725:ISBN
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1484:ISBN
1446:ISBN
1412:2016
1355:Flos
1274:ISBN
1227:ISSN
1223:Math
1142:OCLC
1132:ISBN
1095:2020
1077:ISBN
1032:ISBN
980:2019
952:2019
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