Editing Arithmetic progression (section)

== History ==
According to an anecdote of uncertain reliability,<ref name="hayesreckoning">{{cite journal |author=Hayes |first=Brian |date=2006 |title=Gauss's Day of Reckoning |url=https://www.americanscientist.org/article/gausss-day-of-reckoning |url-status=live |journal=[[American Scientist]] |volume=94 |issue=3 |page=200 |doi=10.1511/2006.59.200 |archive-url=https://web.archive.org/web/20120112140951/http://www.americanscientist.org/issues/id.3483,y.0,no.,content.true,page.1,css.print/issue.aspx |archive-date=12 January 2012 |access-date=16 October 2020}}</ref> in primary school [[Carl Friedrich Gauss]] reinvented the formula <math>\tfrac{n(n+1)}{2}</math> for summing the integers from 1 through <math>n</math>, for the case <math>n=100</math>, by grouping the numbers from both ends of the sequence into pairs summing to 101 and multiplying by the number of pairs. Regardless of the truth of this story, Gauss was not the first to discover this formula. Similar rules were known in antiquity to [[Archimedes]], [[Hypsicles]] and [[Diophantus]];<ref>{{cite book |author=Tropfke, Johannes |url=https://books.google.com/books?id=9dJ_F4lCXTQC |title=Analysis, analytische Geometrie |publisher=Walter de Gruyter |year=1924 |isbn=978-3-11-108062-8 |pages=3–15 |url-access=limited}}</ref> in China to [[Zhang Qiujian]]; in India to [[Aryabhata]], [[Brahmagupta]] and [[Bhaskara II]];<ref>{{cite book |author=Tropfke, Johannes |url=https://books.google.com/books?id=7UW0DwAAQBAJ |title=Arithmetik und Algebra |publisher=Walter de Gruyter |year=1979 |isbn=978-3-11-004893-3 |pages=344–354 |url-access=limited}}</ref> and in medieval Europe to [[Alcuin]],<ref name="a">[https://www.jstor.org/stable/3620384 Problems to Sharpen the Young], John Hadley and David Singmaster, ''The Mathematical Gazette'', '''76''', #475 (March 1992), pp. 102–126.</ref> [[Dicuil]],<ref>Ross, H.E. & Knott, B.I. (2019) Dicuil (9th century) on triangular and square numbers, ''British Journal for the History of Mathematics'', 34:2, 79-94, https://doi.org/10.1080/26375451.2019.1598687</ref> [[Fibonacci]],<ref>
{{cite book |author=Sigler, Laurence E. (trans.) |url=https://archive.org/details/fibonaccislibera00sigl |title=Fibonacci's Liber Abaci |publisher=Springer-Verlag |year=2002 |isbn=0-387-95419-8 |pages=[https://archive.org/details/fibonaccislibera00sigl/page/n260 259]–260 |url-access=limited}}</ref> [[Sacrobosco]],<ref>
{{cite book |author=Katz, Victor J. (edit.) |url=https://books.google.com/books?id=39waDQAAQBAJ |title=Sourcebook in the Mathematics of Medieval Europe and North Africa |publisher=Princeton University Press |year=2016 |isbn=9780691156859 |pages=91,257 |url-access=limited}}</ref> and anonymous commentators of [[Talmud]] known as [[Tosafot|Tosafists]].<ref>Stern, M. (1990). 74.23 A Mediaeval Derivation of the Sum of an Arithmetic Progression. The Mathematical Gazette, 74(468), 157-159. doi:10.2307/3619368</ref> Some find it likely that its origin goes back to the [[Pythagoreans]] in the 5th century BC.<ref>Høyrup, J. The "Unknown Heritage": trace of a forgotten locus of mathematical sophistication. Arch. Hist. Exact Sci. 62, 613–654 (2008). https://doi.org/10.1007/s00407-008-0025-y</ref>