Talk:List of formulae involving π

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)

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). Lambiam^Talk 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)

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)/163^1/2 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)

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)

a suggestion

after reading the AFD discussion (Wikipedia:Articles_for_deletion/List_of_formulae_involving_π), 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)

It probably should have been deleted. There's still nothing important here. (But don't waste time discussing it.) -A876 (talk) 22:05, 14 May 2014 (UTC)

sin(1/5555)

Does anyone have a source for the sin(1/5555) limit? 70.116.1.27 (talk) 07:01, 2 December 2010 (UTC)

I don't have a source, but it follows from the following:

${\frac {1}{180}}={\frac {5}{900}}=0.0055555\cdots$

$\Rightarrow \lim _{x\rightarrow \infty }\sin \left({\frac {1}{x}}^{o}\right)={\frac {\pi }{180x}}=(0.005555\cdots ){\frac {\pi }{x}}$ Gandalf61 (talk) 13:46, 2 December 2010 (UTC)

Explanation of move from "π" to "pi"

It is unconventional to use a math symbol in a title even when that symbol is universally understood. It's Three Blind Mice, not "3 Blind Mice", a Dirac delta function, not a δ function, and so forth. In this case, "pi" is a far more common usage than "π". On Google books, the formula pi -wikipedia gets vastly more hits than formula π -wikipedia. CNN uses "pi", the BBC uses "pi", and the New York Times uses "pi". The entry in Britannica is entitled "pi," as is the entry in Merriam-Webster. Math journals can go either way. Check here and here for journal articles with "pi" in their titles. Kauffner (talk) 04:10, 19 April 2011 (UTC)

It was NOT moved (apparently not officially proposed). It remains at "List of formulae involving π". -A876 (talk) 22:05, 14 May 2014 (UTC)

Move discussion in progress

There is a move discussion in progress on Talk:Liu Hui's pi algorithm which affects this page. Please participate on that page and not in this talk page section. Thank you. —RM bot 07:16, 27 April 2011 (UTC)

It was moved to "Liu Hui's π algorithm". It remains there. -A876 (talk) 22:05, 14 May 2014 (UTC)

Move discussion in progress

There is a move discussion in progress on Talk:Pi which affects this page. Please participate on that page and not in this talk page section. Thank you. —RM bot 13:15, 2 June 2011 (UTC)

It was NOT moved. It remains at "Pi". -A876 (talk) 22:05, 14 May 2014 (UTC)

Is there a source for this?

Under Other infinite series and with $\zeta (2n)$, is there a source for this equation? What does the $B_{2n}$ mean? John W. Nicholson (talk) 02:29, 22 September 2013 (UTC)

Why am I disgruntled?

Instead of removing my editions again and again, I would have expected constructive messages like: "You have to explain the interest, importance and novelty of that formulas", "Add references of papers, books, etc, by other authors concerning those formulas", "please move the content to the page "Approximations of Pi" because..., etc.

My guess of why you have not done it (after reading that the whole page was nominated for deletion on 25 January 2007), is that you had confused me with a previous contributor.

How can I change my username?

As it is not possible to cancel an account, at least remove the history corresponding to me.

Jguillera (talk) 12:07, 7 July 2017 (UTC)