# Talk:Continued fraction

WikiProject Mathematics (Rated C-class, High-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 C Class
 High Importance
Field:  Analysis

## Merge discussion

The article Convergent (continued fraction) does not discuss anything that would not be better discussed in context here. I propose merging it into this article. RockMagnetist (talk) 17:48, 14 January 2013 (UTC)

As a separate article it does not have any merit, since convergents are discussed here in all details. Also, I doubt that the dab page Convergent is a good solution, but still unsure whether it should be redirected to Limit (mathematics) #Convergence and fixed point. Incnis Mrsi (talk) 18:34, 14 January 2013 (UTC)
I also agree Joseph2302 (talk) 01:03, 24 January 2015 (UTC)
Well it looks already kind-of merged. Except that both articles are almost unwieldy in length, so some kind of multiple-article structuring is needed. There's a vast amount of material on continued fractions that neither of these articles touch on. e.g. bounds on the rate of convergence, the topology of Baire space, the relation of Pellian equations and characters and Gauss height of finite fields stuff, which is equivalent to the Riemann hypothesis ... none of this stuff is mentioned here. Not sure how this article got a B-class rating without even mentioning such critical info. 67.198.37.16 (talk) 19:28, 19 September 2015 (UTC)

## Contradicts itself in "Continued fraction expansions of pi"

It says: The third convergent of π is [...] 355/113. Then later on it says "The third convergent, therefore, is 333/106." I think the first statement should say "The fourth convergent ..." Olliehaffenden (talk) 10:49, 17 July 2014 (UTC)

Yes, you are right. 355/113 is the fourth convergent, not the third. I have changed the text in the article. Gandalf61 (talk) 14:51, 17 July 2014 (UTC)

## Not a B-class article

There's a vast amount of material on continued fractions that this article does not even begin to touch on. e.g. bounds on the rate of convergence, the topology of Baire space, the relation of Pellian equations and characters and Gauss height of finite fields and classification os solution of the Pellian eqns, which is equivalent to the Riemann hypothesis ... and even more basic things, like the Stern-Brocot tree is the continued-fraction homeomorphism to Baire space... none of this stuff is mentioned here. Not sure how this article got a B-class rating without even mentioning such broad swaths of info.67.198.37.16 (talk) 19:34, 19 September 2015 (UTC)

The French and particularly the German versions of this article seem to be considerably more comprehensive. 67.198.37.16 (talk) 19:43, 19 September 2015 (UTC)
Also missing are simpler results: e.g. that the expansions of square-roots of integers contain repeated blocks of palindromes(!). There are also general identities (given e.g. in the wolfram website) that show that continued fractions can be reversed backwards-forwards. 84.15.191.139 (talk) 22:33, 15 November 2015 (UTC)

## Pell's equation statement

the section on Pell's equation states: Continued fractions play an essential role in the solution of Pell's equation. For example, for positive integers p and q, and non-square n, it is true that p2nq2 = ±1 if and only if p/q is a convergent of n.

But if I try this with convergents from Wolfram Alpha with Convergents[sqrt(119),8] I get {10, 11, 109/10, 120/11, 2509/230, 2629/241, 26170/2399, 28799/2640} and not all convergents satisfy Pell's equation as stated with if and only if above

## Convergent definition

I changed the name of the section "Infinite continued fractions" to "Infinite continued fractions and convergents" and changed the type of "convergent" from italics to bold in the text. "Convergent" is defined here, and used in many places later in the article, so it should be bold and its definition should appear in the table of contents.—Anita5192 (talk) 17:31, 17 January 2017 (UTC)

I also inserted two citations for the definition.—Anita5192 (talk) 17:33, 17 January 2017 (UTC)