Wikipedia:Articles for deletion/List of formulae involving π

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Keep – Pea ceNT 07:15, 30 January 2007 (UTC)[reply]

List of formulae involving π[edit]

Wikipedia is not an indiscriminate collection of information. This list is completely indiscriminate. There's no significance to this collection of equations. Yes, they all contain pi. So what? There are literally millions of equations that contain pi. There is no reason for including any of these equations, or excluding countless other equations, other than individual whimsy. Should we have List of formulae involving cosine or List of forumlae involving division, as well? Delete as indiscriminate information. eaolson 05:10, 25 January 2007 (UTC)[reply]
Keep: yes, there are literally millions of formula involving pi, but this page only lists historically notable or mathematically significant ones. This list is thus not indiscriminate. I would not place

\cos \left({\frac {9583\pi }{4}}\right)={\frac {1}{\sqrt {2}}}

on it, and I would delete it from the article if I found it. Gracenotes ^T § 05:38, 25 January 2007 (UTC)[reply]

Comment. What's "mathmatically significant" about:

12\sum _{k=0}^{\infty }{\frac {(-1)^{k}(6k)!(13591409+545140134k)}{(3k)!(k!)^{3}640320^{3k+3/2}}}={\frac {1}{\pi }}

eaolson 05:44, 25 January 2007 (UTC)[reply]

History of numerical approximations of π#Other classical formulae Gracenotes ^T § 05:51, 25 January 2007 (UTC)[reply]

OK, point taken. But still, without a coherent reason for this article, it's all just pi-related trivia. eaolson 06:28, 25 January 2007 (UTC)[reply]

Since when is "a coherent reason" a requirement? Sorry to be a bit confrontational, but many of the arguments on this (and on the physics formulae afd above) can be resolved by a simple move, or even a sentence in the intro. In this case, the article could be moved to "List of formulas used to calculate pi," or the intro could be adjusted to make it more clear what the criteria for inclusion were. I definitely understand the impulse to delete, but I think it's very important to keep Wikipedia indexed. --N Shar 06:34, 25 January 2007 (UTC)[reply]

Notice the connection between this formula and the Heegner numbers. DavidCBryant 19:03, 25 January 2007 (UTC)[reply]

Aw damnit - but WP:ILIKEIT. But, no, seriously, it's informative, so keep. Patstuart^talk|edits 05:40, 25 January 2007 (UTC)[reply]
Strong keep per Gracenotes. I can't think of any possible use for this article, but uselessness is no reason for deletion. --N Shar 06:27, 25 January 2007 (UTC)[reply]
Strong keep, I could use this for my math assignments... --Candy-Panda 07:12, 25 January 2007 (UTC)[reply]
Strong keep The deletion arguments above could be resolved for the most part by editing. Notable, encyclopedic, and useful formulae belong in an encyclopedia. Edison 07:45, 25 January 2007 (UTC)[reply]
Split/merge most into some other page(s). Mathematical numerical methods for approximating π are one category; physics and geometry are distinct. The former is clearly important per Gracenotes and relates (and partially restates) that section of the History page. That is a focused topic with clear inclusion criteria (or at least it could be if the intro described it as such). Maybe those parts of this page and the other one should be merged together into their own Numerical methods of approximating pi page? The physics/geometry parts of the page here see, weaker keep...more indiscriminate list-like. Area/volume/surface-area of many curvy-things involve π, what are the inclusion criteria? Appearance in relations among physical constants is a controlled class of equations, but geometry and "physics equations using it" (Coulomb's law, etc) gets less discriminating. No limit on what geometric shapes or physical relationships are included here. Coulomb's law is just a special case of inverse-squares that happens to have a constant involving π...that constant would be included in the "relations among physical constants". DMacks 09:33, 25 January 2007 (UTC)[reply]
Keep. One of the more interesting things about π is that it figures in so many places, and equations which on their surface seem to have little to do with circles. This is a worthwhile supplement to the article on π itself, and could not be merged with it without detracting from the article in chief's readability. In fact, my recommendation would be to move more equations out of the article in chief to this page. - Smerdis of Tlön 14:54, 25 January 2007 (UTC)[reply]
Keep, but change the name to formulae involving π or formulas involving π or identities involving π or the like. And certainly (obviously) there are possible uses for this article; one can easily imagine (after the article is expanded far beyond its current size) a mathematician finding some odd identity here that they didn't know before and that proves useful in their research. Michael Hardy 16:57, 25 January 2007 (UTC)[reply]

Comment. That's just a call to open up Wikipedia to articles about anything. If the criteria for keeping an article is that someone, somewhere might find some tidbit of information useful, we could never delete an article at all. Like, List of books with an elephant on the cover. I don't think there are a lot of mathematicians doing pi-related research, anyway. As it stands, this article is just a bunch of mathematical pi-related trivia. eaolson 18:33, 25 January 2007 (UTC)[reply]

Weak delete, I understand that the article contains only historically significant formulas, but grouping formulas because they contain pi seems rather arbitrary. I like the idea of having lists of significant formulas, but it would be much more useful to group them by use (chemistry, classical physics, quantum physics, topology, etc.) rather than by what constants they use. mikm_t 17:08, 25 January 2007 (UTC)[reply]
Keep per many reasons above (most ILIKEIT :D). If this list was "completely indiscriminate", it would certainly include more elephants and burritos. Therefore, it is not "completely indiscriminate". --- RockMFR 17:56, 25 January 2007 (UTC)[reply]
Keep but merge content from the "Formulae" section of the main π article. There are formulae in π (and names and references for formulae) that are not in this page, and should be, and the "Formulae" section of π is rather cluttered. One of the uses I see for the article under discussion here is to offload content from π and thereby make it easier to read. But also ILIKEIT because all those formulas together in one place are pretty — they convey well a sense of wonder at the beauty of mathematics. —David Eppstein 18:31, 25 January 2007 (UTC)[reply]
Keep. Pi is arguably the most historically significant real number in all of mathematics, and almost all these formulae are of interest to students of analysis. DavidCBryant 19:03, 25 January 2007 (UTC)[reply]
Comment Nomination is a misapplication of WP:NOT#INDISCRIMINATE. That section of policy does not deal with whether or not information is "important". Rather, it specifies certain types of articles which present problems for inclusion (and thus are discriminated against for inclusion). It has nothing to do with "trivia" or "significance". If the nominator wishes to argue those points, then he should refer instead to with WP:V or Wikipedia:Notability and attempt to claim that the article is either unreferenced or not notable. Dugwiki 19:16, 25 January 2007 (UTC)[reply]
Keep: the editors can delete the unimportant formulae. Some physics formulae simply depend on how the fundamental constants are defined. So if ℏ is used instead of h, a π disappears. Stephen B Streater 20:05, 25 January 2007 (UTC)[reply]
Delete. Formulas *for* π are included in π, Computing π, and other articles. Physical formulas using π should be kept in articles about the specific branches of physics and engineering which they are used in. There are too many formulas with π to keep in one indiscriminate list. Argyriou (talk) 21:56, 25 January 2007 (UTC)[reply]

What about formulas not used for computing π and not physical formulas? For example,

\int _{-\infty }^{\infty }e^{-x^{2}/2}\,dx={\sqrt {2\pi \,}}

or

\Gamma \left({1 \over 2}\right)={\sqrt {\pi }},

or

\lim _{n\to \infty }{n!e^{n} \over n^{n+1/2}}{\sqrt {2\pi \,}}=1,

etc. Michael Hardy 23:58, 25 January 2007 (UTC)[reply]

Once again, Wikipedia is not a textbook. There are lists of integrals and other mathematical formulæ here, grouping them together just because they include π makes about as much sense as grouping all formulas which include the number 9. Argyriou (talk) 01:30, 26 January 2007 (UTC)[reply]

Keep Fg2 01:23, 26 January 2007 (UTC)[reply]
keep The problem of computing pi is so central to much of mathematics and now computer science over the centuries that this article is useful, and N, and of course V. Bu the nature of the topic, the list is not indiscriminate. DGG 01:57, 26 January 2007 (UTC)[reply]
- comment I agree that methods for computing pi is important, and an article exists on that already. I do not think that formulas should be listed together merely because they contain pi (imagine having an article on "list of formulas containing 0.5"). Whether or not a formula contains pi is trivial - it is dubious that somebody will actually need to find formulas that contain pi just because they contain pi. mikm_t 02:50, 26 January 2007 (UTC)[reply]
  - But 0.5 isn't pi. Pi is a special number, and it's absolutely facinating (to me at least) how it keeps appearing all over mathematics where you might least expect it.
Keep This list is not indiscriminate. It meets none of the deletion criteria and doesn't violate any policies, so there's no rule-based reason for deletion, and it's interesting and mathematically significant. —Mets501 (talk) 04:05, 26 January 2007 (UTC)[reply]
Keep Useful index list of significant examples, mostly linked to related articles. Not indiscriminate. Will meet WP:LISTV if the inclusion criteria are made a little tighter. Gandalf61 13:18, 26 January 2007 (UTC)[reply]

Keep. A well-chosen and well-linked list. The physics formulas are maybe a bit dubious, since the appearance of π is generally a matter of choice of units or purely mathematical, but there are only a few of those anyway.--OinkOink 20:58, 26 January 2007 (UTC)[reply]
- Comment If a whole section is dubious, how "well-chosen" is it really? Maybe needs a narrower scope? Scrapping the physics ones would us the list of numerical-approximation recipes, which is already covered elsewhere (though could be consolidated or shuffled if it deserves its own page). DMacks 21:05, 26 January 2007 (UTC)[reply]
It's a small section and not inherently invalid. In fact, it's instructive to compare formulas of electromagnetism in SI and Gaussian units, to see how eliminating π in one place makes it pop up in another, like playing whack-a-mole. It could be helped by links leading to context. For example, the connection between the Heisenberg uncertainty principle and the relevant theorem giving a similar relation between a function and its Fourier transform (thus the Heisenberg uncertainty principle follows automatically once you say that momentum is essentially the Fourier transform of position).--OinkOink 04:26, 27 January 2007 (UTC)[reply]
Strong Delete; the mathematical formulas are (all or almost all) in pi and related articles; the appearances of π in the physical formulas are all choices of unit, and side effects of the fact that the volume of 3-spheres and 4-spheres both contain π. Eaolson is right. Wikibooks may be willing to take this, but it doesn't belong here. Septentrionalis PMAnderson 23:27, 29 January 2007 (UTC)[reply]
Strong Keep Incredibly useful and encyclopedic. S h a r k f a c e 2 1 7 01:42, 30 January 2007 (UTC)[reply]

Comment. "Useful" in what way? I can understand how an article on pi, or even an article on the different ways to derive pi might be useful in understanding the constant and it's study through history. I've been trying, and I can't think of any circumstances where I'd have a use for a list of equations that included pi, just because they included pi. Unless it's doing a term paper of some sort on pi. eaolson 03:56, 30 January 2007 (UTC)[reply]

Delete. This list is the epitome of indiscriminate information per Wikipedia:Lists in Wikipedia#Set clear, neutral, and unambiguous criteria. As it is now, I can just make up A = 4 π²/G³ and it qualifies for the list, since it involves π. ~ trialsanderrors 03:38, 30 January 2007 (UTC)[reply]
- Keep for now. I added an unambiguous criterion: The list contains only formulae whose significance is established either in the article on the formula itself, or in the articles on π or Computing π. ~ trialsanderrors 04:17, 30 January 2007 (UTC)[reply]
Keep per comments above and the evident consensus. Newyorkbrad 03:51, 30 January 2007 (UTC)[reply]
- By way of addendum, since challenges have been made to a prior closing as an obvious consensus Keep, in further reviewing the article, I see useful references and links to articles about several of the formulas, a reference (more can be added), and a collection of equations that does not appear in the other pi-related articles. I also endorse the keep comments of Mets501 and DGG. Newyorkbrad 04:06, 30 January 2007 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.