Talk:List of formulae involving π

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Articles for deletion This article was nominated for deletion on 25 January 2007. The result of the discussion was Keep.

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[edit] Article created

I have created the article. Regarding the name: Wiktionary says "formulae in scientific use, formulas in informal use." - but if anyone objects (or to any other aspect of the name), we can move. In any case, we can place here all the forumlae that are interesting, but not important enough to be included in Pi. I've placed a few formulae for starters. Of course, comments and expansions are welcome. -- Meni Rosenfeld (talk) 09:24, 7 April 2006 (UTC)

[edit] Article name

Apart from the burning question whether it should be "formulas", "formulae", or "formulæ", involving "Pi" or "π", isn't the notion of "involving" somewhat broad? What about sin n π = 0 and arctan 1 = π/4? Does that belong here or not?

Yes, I also think that the title of the page is too broad and the word 'involving' should be removed from the title to be replaced by some more appropriate word. Deepak.sachan 22:44, 8 April 2006 (UTC)
I'm open to suggestions. -- Meni Rosenfeld (talk) 06:10, 9 April 2006 (UTC)

With very few exceptions, the formulas listed could be used to define pi. Should we make that the distinguishing feature? If not, is there any discerning criterion as to what can go here? (Remember: Wikipedia is NOT a collection of indiscriminate information). LambiamTalk 14:15, 8 April 2006 (UTC)

I guess every formula involving pi can be be used to define it, with sufficient conditions. For example, for sin π = 0 you can define: π is the smallest positive number such that sin x = 0. So I don't know how much can be worked out from such a criterion. The criterion should probably be how interesting and elegant the formula is, while trying to avoid too many formulae around the same theme. So it's okay to write π/4 = arctan 1 and give a series expansion, but we wouldn't write it as the arctan of every possible number. Although we probably would include several efficient Machin-like formulae. -- Meni Rosenfeld (talk) 17:35, 8 April 2006 (UTC)

[edit] New approximation

Is the new formula by Fredrik really notable? It is basically just a discretization of \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}. -- Meni Rosenfeld (talk) 12:55, 4 May 2006 (UTC)

It's not mine; it's the Borweins'. Regardless of whether it is trivial (I think not), the fact that such approximations can be constructed at all is certainly noteworthy. Fredrik Johansson 13:57, 4 May 2006 (UTC)

I don't see why; It's just a brute force calculation of the integral, and an impractical one as well. If one is serious about calculating Pi by evaluating the integral, he is much more likely to use Gaussian quadrature or the like. I have a mind to remove the formula, unless you strongly object. -- Meni Rosenfeld (talk) 14:20, 4 May 2006 (UTC)

That's a bit like omitting 355/133 because it's just a truncated continued fraction, or for that matter, log(6403203+744)/1631/2 because it's easily extracted from the series expansion of the j-function. It may be obvious to you, but that's because you already know the math behind it. Most readers won't. It'd be more helpful to amend the section with an explanation. Fredrik Johansson 14:39, 4 May 2006 (UTC)

Can't say that I agree, but I understand - so I'll leave it there. If the idea of removing it surfaces again, though, I will support the removal. -- Meni Rosenfeld (talk) 15:36, 4 May 2006 (UTC)

[edit] Name

Would the page titles Formulae involving π or Formulae using π be more appropriate for this article? Deathbob 07:28, 15 January 2007 (UTC)

I think not. The prefix "list of..." is common for pages which are, in fact, lists. -- Meni Rosenfeld (talk) 17:54, 15 January 2007 (UTC)

[edit] a suggestion

after reading the afd discussion, i was thinking it'd be good to have a prose description at the top of the article of what types of formulas are in the article. that is, explain that only certain formulas of historical significance or intellectual significance appear here. (or whatever criteria editors want to set.)

links to related articles are nice, too, and many of the formulas already have them. on a quick glance, i noticed the borwein formula for hexadecimal digits of pi doesn't have a link. hasn't some mad pi fanatic already created a wiki article on that?  ;)

cheers, Lunch 17:45, 25 January 2007 (UTC)

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