Talk:Periodic continued fraction

Expanding this article

Today I wrote an initial version of this article. I intend to expand it along the following lines.

• Add a section about reduced quadratic surds.
• Add a section about the fact that the repeating block in the regular continued fraction expansion of every reduced quadratic surd contains a palindromic string.
• Add a section about bounds on the partial quotients in a periodic continued fraction.
• Add a section about the length of the repeating block.
• Add an example illustrating the construction of the regular continued fraction expansion of one or two particular quadratic irrational numbers.

If anyone else is interested in this stuff, I welcome your collaboration. DavidCBryant 19:30, 24 April 2007 (UTC)

I'd appreciate it if you wouldn't qualify me as "you tagger(s)". :-) I'm interested in CFs and happy to see good content on them. I still think that periodic continued fraction and quadratic surds should be merged because they are closely related, as seen in your list above. I also think the article as it stands needs to be slimmed down a bit; since this is Wikipedia, and we have Wikilinks, we don't need to repeat the full definition of a continued fraction, of a quadratic surd, etc. --Macrakis 13:14, 26 April 2007 (UTC)

I'm sorry if I ruffled your feathers, Macrakis. It's just that it's kind of upsetting, to me, to have people slapping templates on articles that are clearly still under construction. I've even been hit by a "PROD" tag within three minutes after I started to write a new article! That was no fun.

Anyway, if you can see a good way to tighten this up, please go for it. I aim to write for the reader with little mathematical sophistication, so I probably do get more long-winded than I ought to be.

I'd like to put some of the more clearly algebraic features of quadratic irrational numbers in the other article … things like the fact that the integral domain formed by adjoining the (irrational) square root of a positive integer to the integers is not a unique factorization domain. I'd kind of like to tie that in with the story about Kummer's failed attempt to prove Fermat's last theorem, but I need to rustle up a couple of good references first, to refresh my memory.

I don't have a real strong opinion about merging this into quadratic irrational one way or the other. I was just planning to work on both articles, and since I've been reading Rockett and Szüsz recently, this one was easier to write. Oh -- I did notice one other thing. "Periodic continued fraction" has been on the list of missing math articles for a long time.

Have a great day! ;^> DavidCBryant 16:31, 26 April 2007 (UTC)

verification tag

Someone put a "verification required" tag on the sqrt(2). In fact it follows from the section on quadratic irrationals, but I thought I'd make the expression explicit at the same time. Simplifix (talk) 20:05, 17 February 2008 (UTC)

Relation to quadratic irrationals

One reads: a perfect square, and Q divides the quantity P² − D

There is a need to clarify the need for Q to divide the quantity P²−D and to use examples such as (3+√2)/2. — Preceding unsigned comment added by 2001:6B0:E:4040:0:0:0:114 (talk) 21:09, 11 June 2014 (UTC)

Problem with use of phrase "regular continued fraction"

The very first reference to the phrase regular continued fraction appears in the beginning of the section Purely periodic and periodic fractions as follows:

"Since all the partial numerators in a regular continued fraction . . .".

But it makes no sense to tell this to the reader when the phrase "regular continued fraction" has not been previously defined in this article nor does the article contain any clear link to its definition.Daqu (talk) 10:38, 16 June 2014 (UTC)