Talk:Farey sequence
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The mediant link currently leads to a musical term.
Charles Matthews 11:58, 23 Feb 2004 (UTC)
- Fixed. Dominus 14:21, 8 Feb 2005 (UTC)
Now added the mathematical sense. Please check it for correctness. -- Anon.
MEDIANTS:
Currently, the article reads that for the first p/q that is between a/b and c/d, p/q = (a+b)/(c+d). This is not true. The letters are somewhat confused. In actuality, the mediant p/q = (a+c)/(b+d). That is, the sum of the numerators over the sum of the denominators. This also makes it clearer why p/q will first appear in row b+d.
Ex.:
F(0) = 0/1 1/1 F(1) = 0/1 (0+1)/(1+1) = 1/2 1/1 F(2) = 0/1 1/3 1/2 2/3 1/1 etc.
The mediant method is the quickest way to construct the Farey sequence.
-- Barry Revzin --
[edit] link to the Riemann hypothesis
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)
- Sounds good to me; want to take a stab at it? --Piet Delport 20:22, 10 August 2006 (UTC)
[edit] Applications
Could anybody please add a section on the real-life applications of the Farey Sequence (e.g. the Fibonacci Sequence article with a section on the sequence's appearances in music, art, and nature). A section of this sort would be greatly appreciated.
