Talk:Khinchin's constant

Untitled

it has not been proven for any specific real number.

That surely ought to be rephrased, or else I could specify a number by a continued fraction, which worked. Charles Matthews 14:05, 19 Mar 2005 (UTC)

I see the problem; but I don't think this is the solution: the present text leaves open the possibility that there is a number which

is of some interest in any other context,
has a known continued fraction and
does satisfy Khinchin's condition. Septentrionalis PMAnderson 13:26, 6 August 2007 (UTC)[reply]

Algorithm

Why does it take Mathematica 5 so damn long to calculate the constant to 10000 decimal place, while it can calculate it to 2000 places in 0. seconds

Khinchin's constant is very expensive to calculate even for just a few thousand digits. It seems that Mathematica has the 5000 first digits or so pre-computed. Fredrik Johansson 11:03, 19 November 2006 (UTC)[reply]

Euler-Mascheroni constant

How is that rational numbers do not posses this property, yet the Euler-Mascheroni constant does? 121.216.136.243 (talk) 19:57, 16 May 2008 (UTC)[reply]

Nevermind, I think the wording threw me off. Maybe the second sentence of that paragraph should come first? 121.216.136.243 (talk) 20:00, 16 May 2008 (UTC)[reply]

New Relevant Result?

I just learned (from [1]) that there has been a recent advance on this problem, but I have not accessed the paper (and might not be best placed to evaluate it in any case).

Title: A Khinchin Sequence Author(s): Thomas Wieting Journal: Proc. Amer. Math. Soc. 136 (2008), 815-824. —Preceding unsigned comment added by Josephorourke (talk • contribs) 19:18, 31 December 2009 (UTC)[reply]

Irrational / Transcendental ?

Is it known if Khinchin's constant is transcendental, or at least irrational? 71.225.89.166 (talk) 08:26, 21 January 2012 (UTC)[reply]

Neither is known. VladimirReshetnikov (talk) 20:00, 21 January 2012 (UTC)[reply]

Since it's not known to be transcendental, how can we be sure that no solutions of quadratic equations with rational coefficients have Khinchin's property (as claimed in the article)? The geometric mean of their coefficients always converges to an n-th root of an integer m, and for any given integers n>0 and m, one can construct a quadratic irrational whose coefficients mean converges to the n-th root of m. --Roentgenium111 (talk) 11:32, 15 July 2014 (UTC)[reply]

I agree with Roentgenium111, and I have removed the claim on general quadratic algebraic numbers. /195.249.119.154 (talk) 13:41, 1 August 2014 (UTC)[reply]

External links modified

Hello fellow Wikipedians,

I have just modified one external link on Khinchin's constant. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

Added archive https://web.archive.org/web/20081101100001/http://mpmath.googlecode.com/svn/data/khinchin.txt to http://mpmath.googlecode.com/svn/data/khinchin.txt

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 21:24, 9 December 2017 (UTC)[reply]