Wikipedia:Articles for deletion/Proof that 22/7 exceeds 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 of the debate was Keep but suggest continued discussion for a rename/merge be furtherd in the article talk. — xaosflux  Talk  04:50, 20 March 2006 (UTC)

Proof that 22 over 7 exceeds π
Wikipedia is not the place for something that's just a proof. A proof originally written by someone else and available freely belongs in wikisource, math articles can (and probably should) contain proofs, but a proof on its own isn't an encyclopedia article, and the article isn't about the proof, it is the proof and little more. This is an old article, around since 2003 at least, and I think our standards have tightened since then in a way that it wouldn't pass muster if created today. Either merge into something, transwiki to somewhere more appropriate (though I can't think of one) or just delete. Night Gyr 09:29, 15 March 2006 (UTC)
 * Transfer to wikisource. --Hetar 09:32, 15 March 2006 (UTC)
 * Transwiki to wikibooks obviously. Alba 12:55, 15 March 2006 (UTC)
 * Merge with π. 22/7 is a very common ersatz π, so it wouldn't be out of place there. And it's not very long. David Sneek 17:09, 15 March 2006 (UTC) Keep, as per others below. David Sneek 11:16, 16 March 2006 (UTC)
 * Keep Pi is a very long article, and this is a reasonable subarticle. Septentrionalis 21:03, 15 March 2006 (UTC)
 * delete. why stop there? if we need a page to prove that 3.1429 is bigger than 3.1416 then why not Proof that four is bigger than three?  BL Lacertae -  kiss the lizard  01:08, 16 March 2006 (UTC)
 * The notability lies in the proof, not in what is being proven. After all, isn't that what the article is about, the proof? --  127 . * . * . 1  17:57, 16 March 2006 (UTC)
 * strong delete per bl -- pm_shef 01:10, 16 March 2006 (UTC)
 * weak keep – The article is well-written and gives historical background. Obiously there are many numbers exceeding π, but 22/7 is perhaps the most-common approximation of π. —BenFrantzDale 01:14, 16 March 2006 (UTC)
 * It's not just "the most common approximation"; it's an early convergent in the continued fraction expansion of &pi;. Michael Hardy 01:21, 16 March 2006 (UTC)
 * Stong Keep. It is absurd to say a proof on its own is not an encyclopedia article.  What about all of the other pages devoted mainly to mathematical proofs?  Will you nominate ALL of them for deletion?  What about  ALL OF THE ARTICLES IN list of topics related to pi??   Should the ALL get merged into pi?  That is absurd!  Wikipedia is NOT supposed to be only for beginners.  "Night Gyr", may I inquire about your experience with Wikipedia's mathematics articles?  "Kiss the Lizard" very clumsily misses the point of this article.  22/7 is of course one of the earliest convergents in the continued fraction expansion of &pi;.  By contrast, those decimal expansions are rather arbitrary.  "kiss the lizard", what is the nature and degree of your experience with Wikipedia mathematics articles? Michael Hardy 01:19, 16 March 2006 (UTC)
 * Our mathematics articles contain proofs to enlighten and back up statements, not just to be a collection of proofs. The first line of WikiProject Mathematics/Proofs is "This is an encyclopedia, not a collection of math texts."  The fact that there's a particular proof out there may be mathematically interesting, but the proof alone does not constitute an encyclopedia article.  There are other places for such raw texts, and I listed several above. Night Gyr 01:35, 16 March 2006 (UTC)
 * To enlighten is exactly what this article is obviously for! It's not merely proving a brute fact; the unusual simplicity and elegance of the integral and the startling result are enlightening and charming.  It's really hard for me to see how anyone could have thought otherwise. Michael Hardy 02:10, 16 March 2006 (UTC)
 * And now someone who voted for deletion tells me that he never heard of a mathematical equation, theorem, proof, or the like being called "elegant"! Never!  Is it too much to ask that people on Wikipedia who've hardly even heard of mathematics at all might realize that mathematicians on Wikipedia know something about the subject? Michael Hardy 02:28, 16 March 2006 (UTC)
 * Keep, I see nothing in WP:NOT that says it doesn't belong. It's not original research since it is verifiable.  It is not in the list of indiscriminate information list (nowhere close actually).  I see no policy or guideline that applies.  Policies & guidelines aside, I think it should stay.  Otherwise, there's a long list of articles to delete. Cburnett 02:09, 16 March 2006 (UTC)
 * Keep or Move/Merge into a larger article on the fraction 22/7 - the proof should probably exist in Wikipedia somewhere, but I'm not sure if it deserves its own article. --AySz88 ^ -  ^  02:20, 16 March 2006 (UTC)


 * Keep Do not merge into Pi. As a last resort, merge as AySz88 suggested into 22/7. Fg2 02:27, 16 March 2006 (UTC)
 * Keep, of course. Dysprosia 02:53, 16 March 2006 (UTC)
 * Keep, after Michael Hardy. Ryan Reich 03:11, 16 March 2006 (UTC)
 * Keep; possibly merge to 22/7, but this is an interesting, elementary and elegant result in diophantine approximation. If people don't understand why this holds more interest than a "proof that 4 exceeds 3" would, then they have failed to understand the article.  Remember there was a time when people hadn't worked out the value of pi.  Knowing that it's close to 22/7, but not exactly, might lead one to wonder whether 22/7 is an over-approximation or an under-approximation.  This proof makes it clear that 22/7 is high, so the true value of pi is somewhere below it.  Sure, we know now that pi=3.14159, approximately, but people had to work that out somehow. -GTBacchus(talk) 03:25, 16 March 2006 (UTC)
 * If that topic is the reason it's notable, why does neither article make reference to the other? Night Gyr 05:59, 16 March 2006 (UTC)
 * Good point. This article now links to Diophantine approximation, but I wouldn't say "that topic is the reason why it's notable".  It's notable because pi is one of the most important numbers in mathematics, and methods of calculating it are therefore notable.  There's not much sense linking from Diophantine approximation unless that article grows significantly and acquires a list of particluar methods of approximation, of which this is a kind of ad hoc one, as far as that goes. -GTBacchus(talk) 06:10, 16 March 2006 (UTC)


 * Keep. This article does not violate any WP:NOT criteria IMHO.  Might need a title change though and some more text to explain what is going on. --Midnighttonight 06:50, 16 March 2006 (UTC)
 * Weak keep: π is not just any number, and many of the proofs connected with it often involve interesting mathematics. I'm not sure every such proof would justify a separate article, though. In particular the fact that π > 22/7 is not as significant as the fact that π is really, really close to 22/7. Peter Grey 07:21, 16 March 2006 (UTC)
 * Keep: does not violate WP:NOT; important and interesting derivation; merits its own article. Gandalf61 10:25, 16 March 2006 (UTC)
 * Keep. Mathematical proofs can be notable and encyclopaedic. David | Talk 10:27, 16 March 2006 (UTC)
 * Keep. --Kompik 11:03, 16 March 2006 (UTC)
 * Strong Keep. --Saned 11:03, 16 March 2006 (UTC)
 * Strong keep — only, I suggest renaming it "22/7 (number)". Lambiam 13:26, 16 March 2006 (UTC)
 * Keep and add GTBacchus' relevant comments to the article.Kwagle 14:00, 16 March 2006 (UTC)
 * Keep. Agree that Pi is long, and this is a reasonable subarticle.  If an article Approximations of &pi; were to be created, it might be merged into that. &mdash; Arthur Rubin | (talk) 15:45, 16 March 2006 (UTC)
 * Keep: Not all proofs are notable but this one certainly is. --  127 . * . * . 1  15:52, 16 March 2006 (UTC)
 * Keep &mdash; an elegant proof of an elegant statement. Oleg Alexandrov (talk) 15:56, 16 March 2006 (UTC)
 * And I disagree with any renaming, this article has the right name I think. Oleg Alexandrov (talk) 15:57, 16 March 2006 (UTC)


 * Keep -- I hardly need to say it now, but I consider this to be encyclopediaic, and the fact that it was created over two years ago and nobody has had a problem with it before suggests that it is unlikely to be suitable for deletion. Our 'standards', if we have any, are things like neutrality, verifiability, accuracy and so forth, none of which are violated by this article -- Gurch 17:27, 16 March 2006 (UTC)
 * Keep. A notable proof is notable, obviously. Charles Matthews 17:41, 16 March 2006 (UTC)
 * Keep. Notable enough for me. Doesn't need renaming. Paul August &#9742; 17:57, 16 March 2006 (UTC)
 * Keep as above.--David.Mestel 18:00, 16 March 2006 (UTC)
 * Keep and add an overview of Archimedes proof. If the article were about that I don't think there would be a question of notability. Gazpacho 18:54, 16 March 2006 (UTC)
 * Keep There is no reason for deleting this article --CheSudaka 19:44, 16 March 2006 (UTC)


 * Comment In the February 2006 issue of the American Mathematical Monthly on pages 156-151 we find "A Sequence of Polynomials for Approximating Arctangent" by Herbert A. Medina. Near the end of that article is says (verbatim):
 * The results herein were stumbled upon after the author became intrigued by and curious about the fact that


 * $$\int_0^1 {x^4 (1-x)^4 \over 1+x^2}\,dx = {22 \over 7} -\pi;$$




 * This fact is just the sort of thing one would expect people to find intriguing and curiosity-provoking. That's why it's notable. Michael Hardy 17:35, 16 March 2006 (UTC)
 * Well, not necessarily. Reflect on the statement "intriguing and curiosity-provoking facts are notable" for a while, and now imagine the articles this policy could defend. It's not a pretty sight.
 * Off hand, I cannot think of any hypothetical articles that could be "intriguing and curiosity-provoking" but "not a pretty sight". By all means, tell me what you have in mind, if you can.  Perhaps I should add to "intriguing and curiosity-provoking", that this article could lead to insights that in turn lead to further discoveries.  People who see this argument often wonder if this is the first in a long sequence of integrals with a neat pattern, that correspond to the successive convergents in the continued fraction expansion of &pi;, just as this corresponds to 22/7. Michael Hardy 00:11, 17 March 2006 (UTC)
 * I don't think anyone disputes that the fact that 22/7 is really close to π should be included in Wikipedia. Whether a property of an integral cast in proof form qualifies is another matter. And whether the dozens if not hundreds of equally intriguing mathematical curios should have articles is yet another.
 * Then again, notability has never been a useful criterion on Wikipedia, and the "cui malo?" argument seems to apply aptly here. This proof is probably not any less notable than, say, any of the invalid proofs we have on record. 82.92.119.11 20:19, 16 March 2006 (UTC)


 * Comment The key problem here is that despite all the claims to elegance and such, there's no objective criteria for inclusion that we're using to justify this article. The other articles in category:proofs are either about methods used in proofs or specific proofs that are well known and specifically named.  This proof doesn't have any historical importance attached to it in the way that a proof of a major problem in math is&mdash;mathematicians have known pi<22/7 far longer than they've been doing calculus.  "indiscriminate collection of information" applies because this proof becomes the equivalent of an "interesting fact" about a person--worthy of inclusion in the article on the person, but not worth its own article.  On its own, it's unencyclopedic. Night Gyr 23:29, 16 March 2006 (UTC)
 * Then we can conceivably expand the article to include other proofs of &pi;<22/7 that may have been used in antiquity (If my memory serves me correctly, I do believe there is a geometric demonstration of that inequality). Just because the article as it stands only includes one method of proof does not mean that it can never have more than one method of proof. Dysprosia 08:30, 17 March 2006 (UTC)
 * "have known pi<22/7 far longer than" But what's important here is the method of proof, rather than just the fact being proved. Michael Hardy 01:01, 19 March 2006 (UTC)
 * Keep. I don't have any really precise criterion (please don't use "criteria" in the singular!!!) for what proofs should be allowed, but this is a really pretty proof, with a verified and interesting story behind it. I don't think I'd really like to see the door opened to textbook-style routine proofs in general; certainly techniques can be outlined, but people who want the details probably should get the textbook. But I don't see why we can't have a few articles on proofs that are interesting in themselves (as distinct from the results they prove). --Trovatore 03:45, 17 March 2006 (UTC)
 * Keep, though merging would also be OK. R.e.b. 06:09, 17 March 2006 (UTC)
 * Keep, don't merge, per Michael Hardy. linas 23:23, 17 March 2006 (UTC)
 * Strong Keep, no question about it.  --Deville (Talk) 03:34, 18 March 2006 (UTC)
 * Keep, don't merge (I agree with Michael Hardy). --Pokipsy76 14:52, 18 March 2006 (UTC)
 * Weak keep as per BenFrantzDale: "The article is well-written and gives historical background." Moreover, it is notable for being short and elementary, while still not trivial. --Aleph4 16:27, 18 March 2006 (UTC)
 * Keep, Pi is very important. This article, well, I would merge if Pi weren't so long.
 * keep, obviously William M. Connolley 22:18, 18 March 2006 (UTC)
 * keep - but I am somewhat concerned by some of the lack of WP:CIVIL in this debate. Please try to refrain from personal attacks here folks - questioning other wikipedians' knowledge is hardly helpful. Grutness...wha?  01:06, 19 March 2006 (UTC)
 * Someone accused me of questioning his knowledge of mathematics. In fact, I was seeking information about his knowledge of Wikipedia customs. Michael Hardy 01:17, 19 March 2006 (UTC)
 * keep Not a POV/OR fork of Pi, obviously notable enough, etc.  JeffBurdges 04:30, 19 March 2006 (UTC)
 * Keep. This is a fine addition to the mathematical content of Wikipedia.  I find the argument that a proof can't be an article unconvincing.  As long as it's not crap, OR, etc., I see no reason why a proof can't be an article.  I think the reason this article is not part of another is that it serves some purpose to have these standalone articles.  I can easily envision other articles about famous theorems that would require separate articles on different proofs.  I can even imagine that in the near future (a project I'm pondering), one would even need separate articles for parts of of an immense outline of a proof in addition to separate articles just for historical background (and motivation) about the theorem and proof. --C S (Talk) 23:29, 19 March 2006 (UTC)
 * Comment: Just to correct an inaccuracy above, I'm not at all convinced one can flatly state that this result was around before calculus. Archimedes and his peers certainly knew versions of at least the integral calculus and some geometric versions of special cases of the fundamental theorem.   --C S (Talk) 23:29, 19 March 2006 (UTC)
 * Indeed, see how Archimedes used infinitesimals. But I wouldn't be surprised if this was known before Archimedes. Michael Hardy 00:07, 20 March 2006 (UTC)


 * 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.