Wikipedia:Articles for deletion/Hadley's theorem


 * 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   delete. Ron Ritzman (talk) 23:19, 26 September 2010 (UTC)

Hadley's theorem

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Delete. Lack of significant coverage in reliable sources that are independent of the subject. Article provides no references; removed PROD; and indicates that the subject may be original research. After removing the PROD, author stated, "Theorem not previously noted, most likely because it is far from obvious. Theorem is surprisingly nice, and reminiscent of Pythagoras. The 'simple' proof uses a little-known theorem from Euclid." The request for feedback stated, "A hitherto unrecorded mathematical theorem after Pythagoras is presented." Recommendation to delete based on original research and lack of notability. Cindamuse (talk) 14:28, 19 September 2010 (UTC)
 * Delete 'pleasing' though it may be, the only thing I'm seeing on Google is a youtube video. At best, this is original research, at worst it's pitiful youtube spam. Andrew Lenahan -  St ar bli nd  16:11, 19 September 2010 (UTC)
 * Andrew, since you write as you do, I must surmise that you don't actually know who Norman Wildberger is. Let us note that the research involved is not his, and he's a competent professional who reviewed it. Michael Hardy (talk) 22:43, 20 September 2010 (UTC)


 * Delete per WP:OR and WP:MADEUP. If it's a real theorem, it is not for sure known by this name, judging from looking in sources. -- Cycl o pia talk  20:31, 19 September 2010 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.  -- • Gene93k (talk) 23:02, 19 September 2010 (UTC)
 * Delete as per nomination. A google turns up lots of references to the Youtube video and little else, so no reliable sources. The 'proof' itself indicates it's not original, based on an older one by some illegible name, so seems unlikely to be named after its transcriber.-- JohnBlackburne wordsdeeds 00:49, 20 September 2010 (UTC)
 * Retain Any Wikipedian mathematicians here? Michael Hardy, who kindly fixed my original crumby rendition of this page, certainly is one. The theorem is proven correct, it's interesting, and it has a prior literature reference in the form of Professor Norman Wildberger's treatment of it in the video modestly pointed to by the "External Link". Prof Wildberger is a well respected authority in the field. I believe the name attributed to the original proof is "McCloskey" [clarification: if the article survives this process there exists an earlier, geometrical, proof by Frank Hadley himself c.1980 which is noteworthy in itself, for the article, I think Extcetc (talk) 06:07, 20 September 2010 (UTC)] but the prover doesn't necessarily get his name attached to a theorem, more often it would be named for the theorem's propounder. In this case that would be Frank Hadley (whom I am not).Extcetc (talk) 03:01, 20 September 2010 (UTC)
 * comment Don't wait, add the earlier geometric proof now, or at least add the reference so others can look at it now and maybe add it later. A Youtube video is not usually enough for notability on its own, so in this case having another more traditional source could make all the difference to whether notability is established.-- JohnBlackburne wordsdeeds 07:18, 20 September 2010 (UTC)
 * comment Thanks for this suggestion (sorry I've only just noticed it). Shall do, but a proof by the theorem's author probably doesn't help much with the test for "notability" Extcetc (talk) 02:22, 21 September 2010 (UTC)


 * Comment Perhaps Wikipedia's conventions call for refereed publication, but calling this "made up" is silly. Michael Hardy (talk) 03:39, 20 September 2010 (UTC)
 * That the theorem is correct or interesting is practically irrelevant. A single Youtube video is not a reliable source to establish notability. Are there academic papers on the theorem? These would help a lot. -- Cycl o pia talk  03:41, 20 September 2010 (UTC)
 * comment Thanks Cyclopia, none of which I'm aware Extcetc (talk) 02:30, 21 September 2010 (UTC)
 * That's sad. Is there any chance that there is a merge target for the article, under some other article on Euclidean geometry? -- Cycl o pia talk  02:40, 21 September 2010 (UTC)
 * I considered the suitability of the article as an addition to an existing page but found none. Then, I'm not an authority on the subject (Norman Wildberger is). Extcetc (talk) 03:35, 21 September 2010 (UTC)


 * Delete. There is apparently no published proof, so there are no grounds for calling it a "theorem", nor is there any evidence of notability. -- Radagast 3 (talk) 07:25, 20 September 2010 (UTC)
 * Is that what you take to be the definition of a theorem? A proposition whose proof has been published?  If we adhere to a standard of forbidding Wikipedia articles on results not published in refereed journals, that in no way means that a theorem is not a theorem until its proof is published.  I've never heard of that definition before. Michael Hardy (talk) 19:55, 20 September 2010 (UTC)
 * A theorem has to have a valid proof, but under WP:OR and WP:V, we can't claim that a valid proof exists until we have a peer-reviewed published source. -- Radagast 3 (talk) 20:26, 20 September 2010 (UTC)


 * DELETE: pure YouTube BS with no backing from non-trivial reliable sources. Protector of Wiki (talk) 16:03, 20 September 2010 (UTC)
 * Could we have some sobriety here? The comment above is pure Wikipedia BS.  Saying it hasn't been published in a refereed source is one thing; calling it BS is another.  Wildberger is an eccentric with some axes to grind, but also a competent mathematician.  There's no reason to accuse him of "BS". Michael Hardy (talk) 19:57, 20 September 2010 (UTC)
 * Michael Hardy and Extcetc need to STOP BABBLING about the merits of the author and the validity of the theorem. This page WILL be deleted if you do not provide non-trivial reliable sources that mention this theorem. The YouTube video DOES NOT CUT IT. Protector of Wiki (talk) 00:12, 21 September 2010 (UTC)
 * I never said anything about the merits of the author. I know nothing about the author. Michael Hardy (talk) 12:56, 22 September 2010 (UTC)
 * comment Note that there are accepted Wikipedia standards of civility in discourse. Also note that Frank Hadley and Norman Wildberger are separate individuals Extcetc (talk) 02:22, 21 September 2010 (UTC)


 * Comment I've checked. By a plodding pedestrian method---reducing it to the law of cosines and taking into account the constraints on the angles.  It is indeed a theorem.  Hadley's proof is probably far more elegant than that. Michael Hardy (talk) 21:07, 20 September 2010 (UTC)
 * But your checking, valid though I'm sure it is, constitutes WP:OR, and doesn't substitute for a published source. -- Radagast 3 (talk) 08:19, 21 September 2010 (UTC)


 * Comment Further to Michael's comment (thanks Michael!) I'd add that any competent mathematician shown it will accept Hadley's offered proof of the theorem as valid, and/or be able to prove it him/herself from scratch. So it is a "theorem". Wildberger's peer-reviewed publication record makes him an authority by Wikipedia standards as I read them Extcetc (talk) 21:40, 20 September 2010 (UTC)
 * Both statements are nice but, I suspect, not entirely relevant to the issue. Are there publications mentioning the theorem and its proof? -- Cycl o pia talk  22:20, 20 September 2010 (UTC)
 * The question is now whether to regard the youtube video as a publication mentioning the theorem and it's proof. No one doubts that Norman Wildberger, whose youtube channel it is, is a competent professional who has doubtless refereed various publications, and the research involved is not his, but someone else's. Michael Hardy (talk) 22:41, 20 September 2010 (UTC)
 * It's not peer-reviewed, it fairly obviously doesn't satisfy WP:RS. -- Radagast 3 (talk) 08:19, 21 September 2010 (UTC)
 * Peer-review is a gold standard, not a minimum standard. It seems clear that it doesn't obviously fail WP:RS. Wildberger is an authority more than capable of passing the peer-review standard himself, and he has reviewed it. But is there a good reason people wish to hold this particular article on an uncontentious subject to the gold standard of peer-review? Extcetc (talk) 08:42, 21 September 2010 (UTC)
 * Verifiability is a core principle of Wikipedia, not a "gold standard." And YouTube and other video-sharing sites are not reliable sources. Also, notability determines whether a topic merits its own article... if no reliable third-party sources can be found on a topic, then it should not have a separate article. -- Radagast 3 (talk) 10:52, 21 September 2010 (UTC)
 * That's silly. The question is not whether youtube is a reliable source; obviously it's not.  The question is whether peer-review by Wildberger satisfies Wikipedia's need for peer-review. Michael Hardy (talk) 16:45, 21 September 2010 (UTC)
 * Where Wildberger is the editor of a journal, then yes; where Wildberger is the author of a YouTube video, then no. -- Radagast 3 (talk) 09:18, 22 September 2010 (UTC)
 * But it's still silly to speak of whether youtube is a reliable source. If you get a letter or a phone call from Norman Wildberger and are wondering about it's reliability, would you say that the postal service or the phone company are not reliable sources, and base your decision on that? Michael Hardy (talk) 19:26, 22 September 2010 (UTC)
 * The policy on reliable sources is here. It describes two main classes of reliable sources: published academic works from vetted sources and reports published by mainstream news organisations. Neither applies here. Immediately after it classes self-published content as "largely not acceptable", and these YouTube videos are self published.-- JohnBlackburne wordsdeeds 20:09, 22 September 2010 (UTC)
 * Hardy, it is not silly: it is all what it counts. We are not debating the theorem correctness but the notability of the topic. Now, I am quite a strong inclusionist, so you're talking with someone who has a lenient approach on notability; yet for sure if there's something should not be on WP, this is things that a guy happens to put on Youtube, and it not discussed anywhere else. It is irrelevant if the guy is a Nobel prize or my grandma. It is also irrelevant if it's a groundbreaking mathematical theorem or a lolcat farting. All what it matters is that we're talking of something that hasn't been published directly in academic papers, nor indirectly discussed by secondary sources. It falls under WP:MADEUP: If you have invented something novel in school, your garage, or the pub, but it has not yet become well known to the rest of the world, please do not write about it in Wikipedia.. That's the case. This theorem and its proof are still not published by anything reliable. So, we can't take it as a subject for a standalone article. -- Cycl o pia talk  23:26, 24 September 2010 (UTC)


 * COMMENT: That a primary source the subject created himself is being waved as establishing notability demonstrates that these people clearly do not COMPREHEND the policies that ALL commoners (and even mods in rare cases) abide by. Protector of Wiki (talk) 00:12, 21 September 2010 (UTC)
 * comment Note as above that Norman Wildberger is not Frank Hadley Extcetc (talk) 02:22, 21 September 2010 (UTC)
 * True, but neither Norman Wildberger nor Frank Hadley seem to have a peer-reviewed publication of the theorem. -- Radagast 3 (talk) 08:22, 21 September 2010 (UTC)


 * Delete as much as I hate removing some of the too-few science articles, the notability here is not established in the article. Nergaal (talk) 14:46, 21 September 2010 (UTC)
 * Comment Away from the issues being debated acrimoniously above, would some mathematicians clarify a point for me? If this is an obtuse angled triangle, how does it have a hypotenuse? I was under the impression that "A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle." Peridon (talk) 16:58, 21 September 2010 (UTC)
 * You are right, a hypotenuse is normally the longest side of a right or right angled triangle, and the usage here is incorrect. I had not noticed that when reading it but the way the proof is presented, as a barely readable scan, means it would require an unreasonable amount of work to judge its correctness, so I did not try.-- JohnBlackburne wordsdeeds 17:16, 21 September 2010 (UTC)
 * It seems the word "hypotenuse" was used just to emphasize the analogy between this and the Pythagorean theorem. But of course it's not correct. Michael Hardy (talk) 20:07, 21 September 2010 (UTC)
 * Peridon, it was allusion to the Pythagorean theorem which this theorem resembles that motivated me to use the word. The etymology of "hypotenuse" would support this usage at a short stretch but I'm not aware of any precedent for it. It was brief and allusive, sorry; I just liked it. Extcetc (talk) 22:15, 21 September 2010 (UTC)


 * COMMENT: It really doesn't matter how competent Hadley is or how valid the theorem is. As long as the proponents of retention cannot provide non-trivial reliable sources to verify the information, this article is headed down the deletion path. They have yet to provide sources, save for an unreliable YouTube video. Protector of Wiki (talk) 20:44, 21 September 2010 (UTC)
 * How exactly did you conclude the video is unreliable? I find someone above saying youtube is not reliable.  But it's the reliability of the person who put the material on youtube that is the relevant question.  Obviously youtube itself is not reliable in this matter. Michael Hardy (talk) 22:04, 21 September 2010 (UTC)
 * Comment Protector: Hadley's competence is irrelevant to the article and the discussion (Wildberger's is not). A mathematical theorem either exists or it doesn't. Extcetc (talk) 22:15, 21 September 2010 (UTC)
 * You basically reiterated my words. I said that it "really doesn't matter". Protector of Wiki (talk) 07:34, 22 September 2010 (UTC)


 * Delete: This is basically exercise in geometry and while the proof given is unusual, it's straightforward to find a proof based on the law of sines and the law of cosines. There is no historical interest and the theorem has no applications. It might be fun so assign it as an extra credit problem in a geometry class but there's no encyclopedic value here. This is in addition to the fact that it doesn't meet notability criteria.--RDBury (talk) 05:25, 22 September 2010 (UTC)
 * Comment. I am also uncertain of the copyright status of the images in the article. They are scans of hand-written notes by Hadley, and are presumably not public domain. -- Radagast 3 (talk) 09:09, 22 September 2010 (UTC)
 * Delete. I could find no third-party published sources for "Hadley's theorem" or "Hadley triangle" on either Google books or Google scholar.  Notability obviously demands something more than a Youtube video, whoever it might belong to.  I suppose it is possible that this result might be called something else more commonly in the literature, but better sources need to be presented.   Sławomir Biały  (talk) 12:45, 22 September 2010 (UTC)
 * Delete - The proof, regardless of its correctness or elegance, has no coverage in reliable sources. -- Whpq (talk) 17:55, 23 September 2010 (UTC)
 * Comment I did find a "Hadley's theorem" with a small t, but it was a reference to something quite other, to do with "Reciprocity, World Prices, and Welfare" (whatever the heck that is...). I do like the theorem in question, partly because it would seem to be virtually useless, and partly because I can understand it..... Peridon (talk) 20:33, 24 September 2010 (UTC)
 * Comment Ah Peridon you write like a pure mathematician :) I think the theorem is notable (in the normal sense) in that I know of no others that deal with thirds of angles; for its elegance; and for its resemblance to the Pythagorean (yet need only for Euclid to prove it) Extcetc (talk) 00:49, 25 September 2010 (UTC)
 * Redirect after incorporating this as an example in some other geometry article. Perhaps Pythagorean theorem, or maybe some trigonometry article (there are lots of those).  Maybe rational trigonometry. Michael Hardy (talk) 02:44, 25 September 2010 (UTC)
 * Comment A geometer has just reminded me of Morley's_trisector_theorem dealing with trisection and triangles. Perhaps Trisection itself? Extcetc (talk) 08:37, 25 September 2010 (UTC)
 * How would you incorporate this theorem as "an example in some other geometry article" when no reliable sources verify its existence? Protector of Wiki (talk) 19:21, 25 September 2010 (UTC)


 * comment it has nothing to do with trisection. From "C [is] $2/3$ the complement of A" I get $3/2$C + A = 90° or B = $A/2$ + 90°. No way I can see to derive one-third a given angle from this. It's easy to show that the general solution of trisecting an angle is algebraically a cubic, so the algebra is also too trivial.-- JohnBlackburne wordsdeeds 08:57, 25 September 2010 (UTC)
 * Comment See the proof, wherein an angle (your 3/2C) of the construction is trisected. But no this theorem itself is not about trisection, which is why I put it up on its own. On the other hand it may have originally appeared in the course of somebody's exploration of angle trisection (see the construction in the proof). Do you have a suggestion to add to Michael's? How do you like Hadley's original proof, by the way? Extcetc (talk) 10:09, 25 September 2010 (UTC)
 * that's not how trisection works: the general idea is take an angle and trisect it, not start with a triangle with two angles related by a factor $2/3$. On your questions the 1980 proof is no more legible than the first, and as it still has no reliable sources my recommendation is still delete.-- JohnBlackburne wordsdeeds 10:23, 25 September 2010 (UTC)
 * The theorem is not about trisection and you would rather delete it than find somewhere, as Michael suggests, to add it? - your position seems clear, thanks. Extcetc (talk) 11:29, 25 September 2010 (UTC)
 * As in the case of Morley's theorem, nothing in this implies that every angle can be trisected; rather, it deals with those angles that can be trisected. Michael Hardy (talk) 18:03, 25 September 2010 (UTC)
 * PLEASE DO NOT DIVERGE FROM THE TOPIC AT HAND. We are discussing the article and whether it merits inclusion, not the validity of the theorem. Protector of Wiki (talk) 19:29, 25 September 2010 (UTC)
 * I did not diverge from the topic. One of the proposals was to merge and redirect, and the question was which article to merge it into.  My comment was on that topic.  My comment was not about the validity of the theorem; I don't see how you find that in my comment. Michael Hardy (talk) 21:21, 25 September 2010 (UTC)
 * You DID deviate from the topic. Perhaps I was wrong in characterising your comment as pertaining to "validity of the theorem", but you continued babbling about other mathematical concepts that have no connection to this discussion. Even if you suggest a merge, the analysis above by JohnBlackburne, Extcetc, and you qualifies as original research, and we cannot merge on the basis of that. Protector of Wiki (talk) 22:37, 25 September 2010 (UTC)
 * My comment was on topic. If you fail to see its connection to this discussion, that is your failure to see, not my failure to be on topic. Michael Hardy (talk) 01:43, 26 September 2010 (UTC)
 * I agree with you on the content of your comment, but please avoid yelling at users with all caps and using this kind of tone. You are an editor like everyone else, you don't shout orders at us. -- Cycl o pia talk  19:42, 25 September 2010 (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.