Editing Farey sequence (section)

==History==
:''The history of 'Farey series' is very curious'' — Hardy & Wright (1979)<ref>{{cite book |author1-link=G. H. Hardy |author1=Hardy, G.H. |author2-link=E. M. Wright |author2=Wright, E.M. |year=1979 |title=An Introduction to the Theory of Numbers |edition=Fifth |publisher=Oxford University Press |isbn=0-19-853171-0 |at=[https://archive.org/details/introductiontoth00hard/page/ Chapter&nbsp;III] |url=https://archive.org/details/introductiontoth00hard/page/ }}</ref>

:''... once again the man whose name was given to a mathematical relation was not the original discoverer so far as the records go.'' — Beiler (1964)<ref name=Beiler>{{cite book |author=Beiler, Albert H. |year=1964 |title=Recreations in the Theory of Numbers |edition=Second |publisher=Dover |isbn=0-486-21096-0 |at=Chapter&nbsp;XVI}} Cited in {{cite web |url=http://www.cut-the-knot.org/blue/FareyHistory.shtml |title=Farey Series, A Story |publisher=[[Cut-the-Knot]]}}</ref>

Farey sequences are named after the [[United Kingdom|British]] [[geologist]] [[John Farey, Sr.]], whose letter about these sequences was published in the ''[[Philosophical Magazine]]'' in 1816.<ref>{{citation | url=https://archive.org/details/s2id13416200/page/384/mode/2up | author=[[John Farey Sr.]] | title=On a curious property of vulgar fractions | journal=Philosophical Magazine | volume=47 | year=1816 | pages=385–386}}</ref> Farey conjectured, without offering proof, that each new term in a Farey sequence expansion is the [[mediant (mathematics)|mediant]] of its neighbours. Farey's letter was read by [[Cauchy]], who provided a proof in his ''Exercices de mathématique'', and attributed this result to Farey. In fact, another mathematician, [[Charles Haros]], had published similar results in 1802 which were not known either to Farey or to Cauchy.<ref name=Beiler/> Thus it was a historical accident that linked Farey's name with these sequences. This is an example of [[Stigler's law of eponymy]].