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==Fibonacci-sekvenco==
{{Ĉefartikolo|Fibonaĉi-nombro}}
''Liber Abaci'' posedmetis, andkaj solvedsolvis, aproblemon problempri involvingla thekresko growthde ofpopulacio ade population of rabbits[[kuniklo]]j basedbazita onsur idealizedidealaj assumptionssupozoj. TheLa solutionsolvo, generationgeneracio bypost generationgeneracio, wasestis asekvenco sequencede ofnombroj numbersposte laterkonataj known askiel [[ Fibonacci numberFibonaĉi-nombro]] sj. AlthoughKvankam la verko de Fibonacci 's nome ''Liber Abaci'' containsenhavas thela earliestplej knownfrua descriptionkonata ofpriskribo thede sequencela outsidesekvenco ofekster IndiaHindio, thela sekvenco sequenceestis hadjam beenuzataj notedde byhindiaj Indianmatematikistoj mathematicianstiom asfrue earlykiom asĉirkaŭ thela sixth6a centuryjarcento.<ref>{{cite journal|first=Pamanand|last=Singh|title=The so-called fibonacci numbers in ancient and medieval India|journal=Historia Mathematica|volume=12|year=1985|pages=229–244|doi=10.1016/0315-0860(85)90021-7}}</ref><ref>{{cite book |title = Toward a Global Science | first = Susantha | last = Goonatilake |publisher = Indiana University Press |year = 1998 |page = 126 |isbn = 978-0-253-33388-9 |url = https://books.google.com/?id=SI5ip95BbgEC&pg=PA126&dq=Virahanka+Fibonacci }}</ref><ref>{{cite book |title = The Art of Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4 |first=Donald |last = Knuth |publisher=Addison-Wesley |year=2006 |isbn=978-0-321-33570-8 | page=50 |url=https://books.google.com/?id=56LNfE2QGtYC&pg=PA50&dq=rhythms}}</ref><ref>Hall, Rachel W. [http://www.sju.edu/~rhall/mathforpoets.pdf Math for poets and drummers]. ''Math Horizons'' '''15''' (2008) 10–11.</ref> ▼{{redaktata}}
▲''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 number]]s. Although Fibonacci's ''Liber Abaci'' contains the earliest known description of the sequence outside of India, the sequence had been noted by Indian mathematicians as early as the sixth century.<ref>{{cite journal|first=Pamanand|last=Singh|title=The so-called fibonacci numbers in ancient and medieval India|journal=Historia Mathematica|volume=12|year=1985|pages=229–244|doi=10.1016/0315-0860(85)90021-7}}</ref><ref>{{cite book |title = Toward a Global Science | first = Susantha | last = Goonatilake |publisher = Indiana University Press |year = 1998 |page = 126 |isbn = 978-0-253-33388-9 |url = https://books.google.com/?id=SI5ip95BbgEC&pg=PA126&dq=Virahanka+Fibonacci }}</ref><ref>{{cite book |title = The Art of Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4 |first=Donald |last = Knuth |publisher=Addison-Wesley |year=2006 |isbn=978-0-321-33570-8 | page=50 |url=https://books.google.com/?id=56LNfE2QGtYC&pg=PA50&dq=rhythms}}</ref><ref>Hall, Rachel W. [http://www.sju.edu/~rhall/mathforpoets.pdf Math for poets and drummers]. ''Math Horizons'' '''15''' (2008) 10–11.</ref>
InEn thela Fibonacci sequencesekvenco ofde numbersnombroj, eachĉiu numbernombro isestas thela sumsumo ofde thela previousantaŭaj twodu numbersnombroj. Fibonacci begankomencis thela sequencesekvencon notne withper 0, 1, 1, 2, askiel modernfaras mathematiciansmodernaj domatematikistoj butsed withper 1, 1, 2, etcktp. Li Heportis carriedla thekalkuladon calculationĝis upla to13an the thirteenth placelokon (fourteenth14an en inla modernmoderna countingkalkulado), thattio isestas 233, thoughkvankam anotheralia manuscriptmanuskripto carriesplialtigas itĝin toĝis thela nextvenonta placeloko: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.<ref>[http://oeis.org/A000045 Fibonacci Numbers] from [http://oeis.org/ The On-Line Encyclopedia of Integer Sequences].</ref><ref>[https://books.google.com/books?id=gvRFAAAAcAAJ&printsec=frontcover&dq=liber+abbaci&hl=en&sa=X&ei=MrGzUfC8LYS-0AG2pYCwDg&ved=0CDAQ6AEwAA#v=snippet&q=3%205%208%2013%2021%2034&f=false ''Il Liber Abbaci'', eldono de 1857 edition, p. 231. Onlinerete atĉe]</ref> Fibonacci didne notparolis speakpri about thela [[goldenora ratioproporcio]] askiel thelimo limitde ofla theproporcio ratiode ofsinsekvaj consecutivenombroj numbers inen thistiu sequencesekvenco.
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La '''fibonaĉiFibonaĉi-nombroj''', tiel nomataj pro la itala [[matematikisto]] [[Fibonacci]], konsistigas [[progresio]]n kies [[termo]]j difinitas per:
:<math>F(n + 2) = F(n) + F(n + 1)</math>,
kaj la ekkondiĉoj:
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