Talk:Farey sequence

message: The mediant link currently leads to a musical term.
Charles Matthews 11:58, 23 Feb 2004 (UTC)
replies: text: Fixed. Dominus 14:21, 8 Feb 2005 (UTC)
thread_title: Mediants

message: there is an interesting equivalent formulation of the Riemann hypothesis using Farey sequences which is mentioned in that article. Perhaps a cross-reference could be added here? Via strass 20:35, 8 August 2006 (UTC)
replies: text: Sounds good to me; want to take a stab at it?  --Piet Delport 20:22, 10 August 2006 (UTC)
thread_title:  link to the Riemann hypothesis 

message: Maybe I'm missing something, but the section on Farey neighbors seems pretty foolish to me. Consider that in F1, the two terms present are neighbors. In F2, the first and third are neighbors of the 2nd term. Continue on, and by extension ALL simplified fraction are 'Farey neighbors,' regardless of what they are. What's the significance of that?  —Preceding unsigned comment added by 24.208.253.57 (talk) 01:59, 23 April 2009 (UTC)
replies: text: I think you have misunderstood the definition of Farey neighbours. Two fractions can only be Farey neighbours if they appear next to each other in some generation of the Farey sequence. 1/3 and 2/3 are not Farey neighbours because 1/2 will always be between them. 1/3 and 3/7 are not Farey neighbours because 2/5 is always between them. On the other hand, 1/3 and 2/7 are Farey neighbours because the first time that 2/7 apperas, in F7, it is right next to 1/3. Gandalf61 (talk) 10:59, 23 April 2009 (UTC)
thread_title:  Neighbors 

message: So since a Farey sequence is: 
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.
What is the name of the sequence where we don't care to limit the denominators to n? 
Ie. What is the name of this sequence:
:F1 = {0⁄1, 1⁄1}
:F2 = {0⁄1, 1⁄2, 1⁄1}
:F3 = {0⁄1, 1⁄3, 1⁄2, 2⁄3, 1⁄1}
:F4 = {0⁄1, 1⁄4, 1⁄3, 2⁄5, 1⁄2, 3⁄5, 2⁄3, 3⁄4, 1⁄1}
:F5 = {0⁄1, 1⁄5, 1⁄4, 2⁄7, 1⁄3, 3⁄8, 2⁄5, 3⁄7, 1⁄2, 4⁄7, 3⁄5, 5⁄8, 2⁄3, 5⁄7, 3⁄4, 4⁄5, 1⁄1}  
Caimbul (talk) 20:12, 7 December 2009 (UTC)
thread_title:  I'm Confused.. 

message: There is a typo in the middle of the explanation which precedes the Python code: The right-hand side of the equation following "In other words" is missing a floor operation around the outside.  I assume this could be added by imitating the coding of the next two equations, but if there is a way to do it which leaves the equation in the flowing text, that might be superior.  In any case, I'll have to leave the changes to a more accomplished editor than I..
Micro-Parallel (talk) 17:01, 5 June 2011 (UTC)
thread_title:  Next Term 

message: Could somebody add code for generating Farey sequnces in other programming languages – say, C++? BCG999 (talk) 15:51, 14 January 2013 (UTC)
thread_title:  Suggestion for Programmatic Representation 

message: It's "a historical accident" that they're called "Farey". Which makes me wonder, is there a section in half the pages on things named after Newton (for example), explaining it was merely "a historical accident" that they're named after him, as the Indians who discovered them centuries earlier were not known in the west? Something curious here.  — Preceding unsigned comment added by 110.20.158.134 (talk) 09:10, 14 December 2015 (UTC)
replies: text: Wikipedia:Wikipedia is a work in progress. Hyacinth (talk) 13:18, 18 May 2017 (UTC)
thread_title:  Historical accidents 

message: mediant of a/b and c/d is (a+c)/(b+d)
so sequence starts:
0/1 1/1
0/1 1/2 1/1
0/1 1/3 1/2 2/3 1/1
0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1
Darcourse (talk) 06:17, 16 February 2018 (UTC)
thread_title:  constructing FS from mediants? 

message: One can read near the end of the article:
rationals can often take advantage of the Farey series
but near the begining, one can read that the word "sequence" should be use in this context. Could some one clarify whether this is consistent?  — Preceding unsigned comment added by 2001:6B0:E:2B18:0:0:0:80 (talk) 06:52, 1 January 2021 (UTC)
thread_title:  series vs. sequence 

message: In https://en.wikipedia.org/w/index.php?title=Farey_sequence&type=revision&diff=1105657955&oldid=1104796601 I moved the Austin2008 article information into its own subsection.  In its original location it broke the flow of the section.  The quality of the discussion there doesn't live up to the original article, either, which made matters worse.  — Preceding unsigned comment added by 98.225.50.10 (talk) 05:40, 21 August 2022 (UTC)
thread_title:  "Equivalent area" details 

message: The initial terms of the Farey sequence with denominators up to 25 are as follows: 0/1, 1/25, 1/24, 1/23, 1/22, 1/21, 1/20, 1/19, 1/18, 1/17, 1/16, 1/15, 1/14, 1/13, 2/25, ...
The diagram agrees with the sequence until the term 1/14, then indicates the next fraction has denominator 25, which is not the case. There could be other mistakes, but I did not check the rest. I do not have the ability to fix this diagram, sorry, because the most reasonable option would be generating it using some code. — Preceding unsigned comment added by 63.216.63.70 (talk • contribs) 22:27, 8 May 2023 (UTC)
thread_title:  Error in the F_25 picture? 

message: :
That word by is a recent change from than, and I disapprove. Greater by 1 than what?  Than the term that otherwise preceded the final 1, but that is not mentioned in the context.  That the new final term exceeds 1 is also true. —Tamfang (talk) 05:00, 10 September 2023 (UTC)
thread_title:  greater than/by 1 

message: I feel that |F| for the length of F is unhappy; at least a word of explanation seems in order. 151.29.137.229 (talk) 23:52, 24 September 2023 (UTC)
thread_title:  unhappy symbol