Editing Fibonacci (section)

==Fibonacci sequence==
{{Main|Fibonacci number}}
{{Lang|la|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 {{Lang|la|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.<ref>{{cite journal|first=Pamanand|last=Singh|title=The so-called fibonacci numbers in ancient and medieval India|journal=Historia Mathematica|volume=12|issue=3|year=1985|pages=229–244|doi=10.1016/0315-0860(85)90021-7|doi-access=free}}</ref><ref>{{cite book |title = Toward a Global Science | first = Susantha | last = Goonatilake |publisher = Indiana University Press |year = 1998 |page = [https://archive.org/details/towardglobalscie0000goon/page/126 126] |isbn = 978-0-253-33388-9 |url = https://archive.org/details/towardglobalscie0000goon |url-access = registration |quote = 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/books?id=56LNfE2QGtYC&q=rhythms&pg=PA50 |access-date=2020-11-11 |archive-date=2023-03-13 |archive-url=https://web.archive.org/web/20230313121953/https://books.google.com/books?id=56LNfE2QGtYC&q=rhythms&pg=PA50 |url-status=live }}</ref><ref>Hall, Rachel W. [http://www.sju.edu/~rhall/mathforpoets.pdf Math for poets and drummers] {{Webarchive|url=https://web.archive.org/web/20120212145748/http://www.sju.edu/~rhall/mathforpoets.pdf |date=2012-02-12 }}. ''Math Horizons'' '''15''' (2008) 10–11.</ref>

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 place, the value 377.<ref>{{Cite OEIS|1=A000045|2=Fibonacci Numbers}}</ref><ref>{{cite book |url=https://books.google.com/books?id=gvRFAAAAcAAJ&pg=PA231 |title=Scritti: Il Liber Abbaci |first1=Leonardus |last1=Pisanus |first2=Baldassarre |last2=Boncompagni |date=1 January 1857 |page=231 |publisher=Tip. delle Scienze Fisiche e Matematiche |via=Google Books |access-date=20 December 2018 |archive-date=13 March 2023 |archive-url=https://web.archive.org/web/20230313121953/https://books.google.com/books?id=gvRFAAAAcAAJ&pg=PA231 |url-status=live }}</ref> Fibonacci did not speak about the [[golden ratio]] as the limit of the ratio of consecutive numbers in this sequence.