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I want to know the period of digit 5 in the number 2546789378 both in Indian number system as well as in International Number System. — Preceding unsigned comment added by 59.93.221.129 (talk) 16:41, 11 June 2008 (UTC)[reply]

Are all periods necessarily definable numbers? Tkuvho (talk) 18:58, 29 July 2010 (UTC)[reply]

Yes. It's even written in the article.—Emil J. 10:54, 4 August 2010 (UTC)[reply]

Never mind, I didn't notice it was you who put it there. But anyway it's true (and it's much easier to see directly than via computability of the numbers).—Emil J. 10:59, 4 August 2010 (UTC)[reply]

You mean, it is definable because it is defined by an integral? What argument did you have in mind? Tkuvho (talk) 12:01, 4 August 2010 (UTC)[reply]

Because it is defined by an integral, and because the integrated function is itself definable, which in turn follows from definability of every rational.—Emil J. 12:15, 4 August 2010 (UTC)[reply]

Why wouldn't that prove computability, as well? Tkuvho (talk) 12:19, 4 August 2010 (UTC)[reply]

Proving that volume of a given semialgebraic set (which is what the definition of a period actually calls for, it's not really an integral) can be approximated to an arbitrary given accuracy by an algorithm is nontrivial, or at least quite tedious. The obvious algorithm is to count the lattice points in the set, but then you have to prove (computable) estimates on how fine a lattice suffices to get the answer with the wanted accuracy.—Emil J. 13:53, 4 August 2010 (UTC)[reply]

Let it be provided prove, why π should be included here or not included. If you can not do it with π, please do it with some other number, and ask someone who know about π to come here and give more information in the article about π. I feel emotionally that π shouldn't be here, but it is included in the article. Thank you for your cooperation. — Preceding unsigned comment added by 46.10.229.1 (talk) 11:34, 16 September 2014 (UTC)[reply]

I'm not quite sure what you're asking. π is a period because it is the area of the unit circle. The best place for more information on periods is Kontsevich and Zagier's original paper. Ozob (talk) 14:07, 16 September 2014 (UTC)[reply]

Belkale, Prakash; Brosnan, Patrick (2003) claim the Euler-Mascheroni constant is already an exponential period. (see section Generalizations) MuCepheiBetelgeuse (talk) 11:26, 11 August 2024 (UTC)[reply]