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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 no consensus. The article was changed significantly in the middle of the AfD, so many of the earlier comments can't be properly applied to the article as it stands now. The comments surrounding the most recent version appear to be heading towards keeping the article, yet there was such amount of contention surrounding a few points (such as the relevance of WP:HOWTO) that make me uncomfortable with a keep closure. No consensus seems like an optimal closure as it satisfies the recent keep votes yet takes into account the unusual circumstances in regards to the significant improvement and the remaining concerns by those asking for deletion. \ Backslash Forwardslash / (talk) 12:43, 10 September 2009 (UTC)[reply]

Graphical methods of finding polynomial roots

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Graphical methods of finding polynomial roots (edit | talk | history | protect | delete | links | watch | logs | views) (delete) – (View log)
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Unsourced original research. Contested prod. A previous version of the article contained the sentence "Plotting the imaginary roots using empty circle in the Cartesian coordinate system is something new I am proposing" so was obviously OR. This sentence has been removed by subsequent edits, but contents of article have not been substantially changed and no sources have been provided to demonstrate it is not OR. Gandalf61 (talk) 09:14, 3 September 2009 (UTC)[reply]

Note that during this discussion the article was moved to Graphical methods of finding polynomial roots. Title, topic and contents are now completely different from the nominated version. The original (and still unsourced) contents of the article were moved to its talk page and so effectively removed from Wikipedia article space. Gandalf61 (talk) 10:18, 6 September 2009 (UTC)[reply]

  • Keep We have active discussions on the article's talk page by interested editors. The nomination seems to be forum shopping and/or forcing the issue in a disruptive way. There is no need for a 7-day deadline and so, per WP:BEFORE, ordinary methods of editing should be tried first. Note that I have provided multiple good sources which touch on this matter. The nominator disputes them but so it goes ... Colonel Warden (talk) 12:32, 3 September 2009 (UTC)[reply]
Comment Escalating to AfD when a prod tag is removed (and removed by you, let us note) is standard practice so I invite you to withdraw your unfounded accusations of forum shopping and disruption. I still see no sources that describe this specific method of visually finding complex roots of a quadratic equation. Gandalf61 (talk) 13:14, 3 September 2009 (UTC)[reply]
Comment WP:NOR: "To demonstrate that you are not presenting original research, you must cite reliable sources that are directly related to the topic of the article, and that directly support the information as it is presented". I see no such sources.Gandalf61 (talk) 13:14, 3 September 2009 (UTC)[reply]
Loads of potential sources (1) The American mathematical monthly, (2) ON-Math Spring 2003 | Volume 1, Number 3 "Connecting Complex Roots to a Parabola's Graph", (3) "Roots of Quadratic Equations from Parabola graph". Since this is a mere cursory look, hardly involving the digging that an expert could perform, the potential sources and possibility of article expansion here seem quite vast. An argument that there is a lack of sources doesn't hold up, falls foul of WP:BEFORE. --Firefly322 (talk) 21:37, 3 September 2009 (UTC)[reply]
Comment In fact WP:BEFORE reads "When nominating an article for deletion due to sourcing or notability concerns, make a good-faith attempt to confirm that such sources aren't likely to exist." I see ZERO effort on the part of the nominator to have been made. --Firefly322 (talk) 21:46, 3 September 2009 (UTC)[reply]
Comment Yeah, WP:OTHERSTUFF. Let's stick to the point. You (or any other editor) can preserve this article very simply - you just have to "cite reliable sources that are directly related to the topic of the article, and that directly support the information as it is presented". I still see no such sources. Gandalf61 (talk) 14:20, 3 September 2009 (UTC)[reply]
WP:OTHERSTUFF is a good argument when the precedents are valid - please read it. Your appeal to it is therefore a WP:VAGUEWAVE. As for sources, I've already made a good start and this fork in the discussion isn't helping as we are now diverted by tiresome AFD rhetoric rather than getting at the facts of the matter. Do you actually dispute the correctness of this mathematical method? I just took another quick look and soon found this paper which seems to apply the same idea to quintics. The topic is clearly not original and our task seems how best to present it rather than punishing a naive editor for his impudence contrary to WP:BITE. Colonel Warden (talk) 14:58, 3 September 2009 (UTC)[reply]
Comment The method is correct, but that is irrelevant. Unless it has been described in a reliable source it does not belong in Wikipedia - our benchmark is verifiability, not truth. A paper on finding real roots of quintics is not related to an article on finding complex roots of quadratics. I still see no sources. Gandalf61 (talk) 15:24, 3 September 2009 (UTC)[reply]
Comment Again if this is OR, then its original editor deserves a Fields medal. If one doesn't believe this editor deserves a Fields medal, then one must logically conclude that this OR-argument is false. --Firefly322 (talk) 21:20, 3 September 2009 (UTC)[reply]
FireFly, please stick to wikipedia reasons. Provie RS or stop going on about the Fields medal. If someone has won such an award for this, then provide the RS. I realise you've had problems understanding our guidelines in the past, but you've been here long enough now to know that these sorts of arguments aren't valid. Verbal chat 21:50, 3 September 2009 (UTC)[reply]
Comment There are seven points in WP:NOTHOWTO none of which mention mathematics articles. This is a specious argument that also falls foul of WP:BITE. Just as the argument labeling it WP:OR does. --Firefly322 (talk) 21:20, 3 September 2009 (UTC)[reply]
See point 4 and 6, for starters. The reference to "bite" is unsupportable. Verbal chat 21:53, 3 September 2009 (UTC)[reply]
Nonsense. Point 4 clearly wasn't written with math articles in mind. Using it here seriously distorts any semblance of right or wrong on wikipedia. Nearly all mathematics articles seem to violate point 4. But clearly math articles are wanted. As for point 6, how in the world does that apply? I don't see any relevance to this AFD debate. And WP:BITE does indeed apply. --Firefly322 (talk) 03:20, 4 September 2009 (UTC)[reply]
Not all math articles need be guides on how to perform certain mathematical operations, and even if many of them do, WP:WAX is not a good argument. Point 4 seems to clearly apply to this: as currently written, it is just like a textbook, and should therefore be put on wikibooks. I believe that the topic itself could be treated encyclopedically, but I think it would require major work to make it that way. — DroEsperanto (talk) 07:45, 6 September 2009 (UTC)[reply]
Changed to keep. Article has been effectively deleted and a new one made in its place. Still has how-to problems. Should be stubbed if nothing but the lede can be sourced. --Ronz (talk) 22:35, 6 September 2009 (UTC)[reply]
Comment When there are those here who claim to have Ph.D.'s in Math, but their comments don't really hold up to such a claim, using them to bolster arguments via per is naive at best. See Essjay controversy. --Firefly322 (talk) 03:14, 4 September 2009 (UTC)[reply]
Please don't resort to personal attacks, which have seen you blocked for very long periods quite recently. Verbal chat 18:12, 5 September 2009 (UTC)[reply]
Please don't threaten me with a past in which I called a spade a spade ([Orangemarlin stopped because he was about to get wiki-sensored or banned]). The fact that you continue to go to great lengths to defend an editor capable of such junk is not a good indicator of your judgement then or now. --Firefly322 (talk) 17:02, 7 September 2009 (UTC)[reply]
  • keep The basis of this nomination seems dubious at best. previous version of the article contained the sentence.... What a previous version of the article contained seems to be completely irrelevant. In fact I went and looked at the list of arguments not to use in a deletion discussion and was wondering if maybe I could find something along those lines already listed. I didn't find it, but maybe we should consider adding it. Finding the roots of a parabola is certainly a notable topic. I can pull books off my shelf that discuss the topic. The method is certainly verifiable, in the discussion on the discussion page, I pointed to at least one discussion of imaginary intersections, in Hamilton's Elements of Quaternions article 214, with the only problem being that this particular article discusses the imaginary intersections of lines and circles. A little digging would probably turn up parabolas as well, but if not found in that particular text, it seems pretty obvious that this topic has been discussed some place before.TeamQuaternion (talk) 05:03, 4 September 2009 (UTC)[reply]
  • For the sake of argument LOL, lets say that the current method being presented is original, and has never been proposed before. That is not really relevant, because if there exists any notable published graphical method for finding imaginary roots of a parabola then the article could be fixed by substituting that method, for the current method. Suppose that Gandalf61 could prove not only that this method is original, which I doubt, but also that no method of graphically finding the imaginary roots a parabola has ever been found up until the present article under discussion. If this were the case he could certainly find reliable sources stating this to be the case. If he wants to claim that this is indeed the case, I challenge him to find documentation for this remarkable fact. Yet that would still not be grounds for deleting the article as its contents should then read that there is no known graphical method for finding the roots of a parabola, citing the sources that Gandalf61 has provided. Of course if this were the case, this wonderful new method will soon be published in reliable sources, and we can then once again include it as well.TeamQuaternion (talk) 05:03, 4 September 2009 (UTC)[reply]
  • How about this? The method only works for the parabola given. Try 0.75(x – 7)2 + 5; the "visual method" gives about 7 ± 2.235i, but the actual roots are closer to 7 ± 2.582i. The problem is the choice of nothing but powers of two in the example in the article; 0.5(x – 4)2 + 2. Can any mathematicians check my work? I think I'm right. Abductive (reasoning) 07:41, 4 September 2009 (UTC)[reply]
If you have problems with the visual method, Abductive, put the image up for deletion, you don't delete an article because of the image in the article, wouldn't you agree? The image can be easily removed. Just like sources could have easily be found by the nominator, in which he neglected to do, in violation of WP:BEFORE and WP:PRESERVE Ikip (talk) 09:50, 6 September 2009 (UTC)[reply]
Response to Ikip: If it is so easy to find sources for the original article, then it is strange that the original article material remained completely unsourced right up to the point when you removed it all from the article. I see nothing in WP:BEFORE and WP:PRESERVE that requires a nominator to entirely rewrite an article, changing both its topic and its contents to fit an arbitrary list of available sources, as has been done here. Your ad hominen attacks on myself and other editors simply reveal the lack of substantive arguments for retaining any of the original material. Gandalf61 (talk) 12:40, 6 September 2009 (UTC)[reply]
I think the award for biggest personal attack goes to.....Hfran.[1] When I asked him to remove these personal attacks, he deleted my response.[2] Asking an editor to follow WP:BEFORE and WP:PRESERVE is not a personal attack.
Ummm. Grandlf61. There are 20 references now to the article. No amount of accusations against me change this. No amount of accusation against me change the fact that the original reason you wanted this deleted was, and I quote, "Unsourced original research." Sources are provided, substantive arguments are addressed, and now the reason for deletion changes by most those editors who want to delete. Ikip (talk) 14:57, 6 September 2009 (UTC)[reply]
Response to Ikip:... and not a single one of those references is about the very specific visual method of finding complex roots of a quadratic equation that was described in the original article. Not one. None. The text of the original article (i.e. the text that you removed to the talk page and that Spinningspark is now attempting to restore to the new article) is still completely unsourced. Gandalf61 (talk) 16:38, 6 September 2009 (UTC)[reply]
    • Just now I took a few seconds and drew the graph of Abductive's proposed example by hand on paper. Just eyeballing it, I'd read the answer as about 2.6 for the imaginary part. That is was algebra confirms. Quite aside from his advertising his inability to handle such a simple problem, his claim that by staring at the page he can come up with the thousandth's digit is astonishing. Even if you used a microscope, how would you draw the graph that accurately on a microscopic level with a pen and paper? Michael Hardy (talk) 18:54, 8 September 2009 (UTC)[reply]
  • Strong Keep This is well-sourced encyclopedic content on a notable topic that comes up in many math courses and is treated in a number of texts and journal articles. Nominator ignored WP:BEFORE guidelines and did not tag problem areas with tags such as {{Notability}} or {{Original research}} prior to nominating for deletion. Normal editing processes should be pursued to improve, and article has been substantially improved already.Math.geek3.1415926 (talk) 13:04, 8 September 2009 (UTC)[reply]
Response to Math.geek3.1415926: Strongly suggest you get your facts straight before lobbing round nasty little bad-faith accusations like that one. This version shows that the article was tagged (with {{Unreferenced}}) when I nominated it, and discussions on its talk page before nomination had failed to produce any relevant sources. Gandalf61 (talk) 14:24, 8 September 2009 (UTC)[reply]
The unreferenced tag was added a mere 45 hours before your proposed deletion. Why the rush to propose deletion without giving the normal editorial process time to improve the article? In isolation, "unreferenced" is not sufficient criteria for deletion IF the references exist to add them. However, tracking down references often takes some time and a trip to the library. Experienced editors should gently guide new editors toward more encyclopedic practices, not rush to justify throwing their contributions int the delete bin. The march toward possible deletion should be a slow one, giving editors ample opportunity to improve articles.Math.geek3.1415926 (talk) 15:45, 8 September 2009 (UTC)[reply]
Response to Math.geek3.1415926:You do not seem to realise that prodding and AfD nominations are part of the "normal editorial process". The original article was a rambling, unsourced, badly written, poorly illustrated "how to" manual for a trivial, non-notable method of finding approximate solutions to quadratic equations which any high school student can solve algebraically with far less effort. In the 4 weeks between 2 August when the original author last editted it and 30 August when I prod-ed it, it was editted twice; both edits were tags. Now in ten days it has been re-titled, re-focussed, sourced and entirely re-written, with input from numerous editors. Sometimes the "normal editorial process" needs a wake up call. Gandalf61 (talk) 16:30, 8 September 2009 (UTC)[reply]
This thinking is fallacious because it ignores the opportunity cost of this kafkaesque farrago. Our time and patience is limited and, by diverting us into unproductive bickering and bureaucracy, we are prevented from doing more useful work. When articles such as Graph of a function need improvement, we do not immediately start an AFD to start the clock ticking and stimulate activity. The proper process is to improve the article ourselves or, if we are incapable of that, to tag it for attention in an orderly manner by the relevant projects and interested editors. Moreover, by generating ill-will and strife, the deletion process tends to reduce the number of editors willing to exert themselves on behalf of the project. Please see WP:ZEAL for more details. Colonel Warden (talk) 17:28, 8 September 2009 (UTC)[reply]
Or, this could be taken as evidence that the Article Rescue Squadron needs to be more selective in the battles it chooses. Abductive (reasoning) 17:47, 8 September 2009 (UTC)[reply]

Editing break

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  • Comment Everyone can see that it's a clumsily written article, neglecting WP:MOSMATH at every opportunity (not to mention all the incorrectly capitalized initial letters in the article's title). But as I also pointed out on its talk page, the graphs are grossly incorrectly drawn in a way that causes secondary-school pupils to lose points. That doesn't encourage me to sympathize with its author very much, even if the remedy would be to clean it up rather than to delete it. But now to the content of the main point: that content is worth maybe a couple of paragraphs if an article is to be made of it. Michael Hardy (talk) 04:08, 5 September 2009 (UTC)[reply]
  • Delete. It looks like WP:OR, and appears to violate WP:NOTTEXTBOOK. One of the two supposed potential sources presented on the talk page does not verify the content of the article (indeed, it is about Cardano's solution of the cublic equation, which is a different though related matter). I cannot access the other suggested source, so I will not comment, but the editor who presented it also failed to indicate any details, merely stating that it is "another interesting angle". Verifiable material would, in any event, most likely be better covered in an article on quadratic equations since it seems very unlikely that a single method of visual would rise to the level of notability that a dedicated article must surely demand. Sławomir Biały (talk) 18:08, 5 September 2009 (UTC)[reply]
  • Merge some fraction into completing the square. It is kind of worth a graphic illustration there. Otherwise, frankly, it seems to be the sort of mathematics you leave for people to discover for themselves. Charles Matthews (talk) 20:58, 5 September 2009 (UTC)[reply]

I have requested input from WikiProject Mathematics for this discussion. - 2/0 (cont.) 03:07, 6 September 2009 (UTC)[reply]

  • That is a ridiculous suggestion - completing the square is not a graphical method, it is an analytic method, how can that be suitable target for a merge? Completing the square is relevant only to quadratics, how can that be a suitable target for an article about solutions to polynomials? Completing the square is only one method, how can that become an article about multiple methods? SpinningSpark 15:52, 6 September 2009 (UTC)[reply]
  • Comment I have developed the article to improve its structure. Numerous sources have been added including Graphical Solutions for Complex Roots of Quadratics, Cubics and Quartics (National Mathematics Magazine 17 (4): 147-150) and Graphing the Complex Roots of a Quadratic Equation (The College Mathematics Journal 16 (4): 257-261). These demonstrate the notability of the topic and rebut the complaints that sources are lacking. The only issue remaining is that the article might be a how-to but this is a stylistic issue rather than a reason to delete. To see how we present such matters generally, please see our category: Root-finding algorithms which contains numerous articles of a similar nature. Colonel Warden (talk) 08:52, 6 September 2009 (UTC)[reply]
    • These changes have not made the article any better and it's still a clear delete candidate. Verbal chat 08:59, 6 September 2009 (UTC)[reply]
    • Straw man, Colonel Warden. You have added a series of content-free one sentence sections as a coatrack for sources that are not related to the original material. No one has claimed that general graphical methods of finding roots of polynomial equations were not notable or could not be sourced. However, the original material, on a specific visual method of finding complex roots of a quadratic equation (which does not generalise to higher order polynomials) is still completely unsourced and should be deleted from Wikipedia. Gandalf61 (talk) 09:13, 6 September 2009 (UTC)[reply]
  • Per MOS:MATH, Most mathematical ideas are amenable to some form of generalization, and this seems the best way to go as I said at the outset. See our general editing policy, "Even poor articles, if they can be improved, are welcome. For instance, one person may start an article with an overview of a subject or a few random facts. Another may help standardize the article's formatting, or have additional facts and figures or a graphic to add. Yet another may bring better balance to the views represented in the article, and perform fact-checking and sourcing to existing content.". Colonel Warden (talk) 09:25, 6 September 2009 (UTC)[reply]
(ec) I understand if you would have made the claim that this article is unsourced 3 days ago, as many editors above did. But 35 minutes before you stated this page was unsourced (9:01), editors had finished adding 20 sources. There seems to be a real disconnect there. I would suggest striking this unsourced comment. Ikip (talk) 09:56, 6 September 2009 (UTC)[reply]
The text you mention Hrafn has now been removed from the page. So every section is now sourced. Nullifying 7 editors arguments here of OR and unsourced. Ikip (talk) 10:01, 6 September 2009 (UTC)[reply]
Revised basis for opinion: the article as of this latest version contains no substantive content. It amounts to little more to a slight and trivial elaboration on the statement that 'you can solve polynomials graphically'. HrafnTalkStalk(P) 10:11, 6 September 2009 (UTC)[reply]
LOL. No matter what happens to this article, you and other editors will always, always support deletion.[3] Where is the compromise, the give take, the ability to say, you know what good job editor, you really made that article get turned around. Nope. Ikip (talk) 10:18, 6 September 2009 (UTC)[reply]
Kindly keep your inane laughter to yourself. This article had no substantive, sourced content -- only a bunch of unsourced/WP:OR WP:HOWTO and a small amount of repeating the blindingly obious. After removal of the OR & the reptition, there is nothing substantive to keep, so little point in a "compromise" to preserve a non-informative stub. HrafnTalkStalk(P) 10:37, 6 September 2009 (UTC)[reply]
  • Strong keep exhaustively researched now (as of 6 September), making the nominators original "original research" arguments of nominator, User:Sławomir Biały, User talk:Ronz, User:Ozob, User talk:Verbal, User:Scjessey irrelevant. I have no idea why Hrafn wrote that it was unsourced though. This is how it will work now >> these same editors will come back and say the sources are not good enough, ignoring that their original justification for delete is now invalid. I agree with Colonel's arguments about sources above. Ikip (talk) 09:38, 6 September 2009 (UTC)[reply]
Exhaustively researched? You either tire easily, or missed out the fact that his research has failed to add references that support the content or the notability of the article, per nom and Hrafn. Verbal chat 10:00, 6 September 2009 (UTC)[reply]
Verbal's original argument: "Delete WP:OR due to lack of WP:RS, which also means it fails notability requirements." Verbal's arguments now: "his research has failed to add references that support the content or the notability of the article" Now we go into the inadequate reference phase, editors will name a reference, and the editors here can claim it is trivial or irrelevant. Ikip (talk) 10:11, 6 September 2009 (UTC)[reply]
  • Note to closing nominator since the nomination, this article has gone though extensive improvements, with an astounding 20 footnotes added.[4] Ikip (talk) 09:43, 6 September 2009 (UTC)[reply]
    • Further note These "improvements" are merely superficial and coatrack additions that do not serve to show notability or support the text. Verbal chat 10:00, 6 September 2009 (UTC)[reply]
      • "This is how it will work now >> these same editors will come back and say the sources are not good enough, ignoring that their original justification for delete is now invalid." Did I predict folks, did I predict it! Nevermind that verbal's original AFD argument is invalid now.Ikip (talk) 10:08, 6 September 2009 (UTC)[reply]
  • Keep. I think there's no reason to delete this article after it has been repurposed as Graphical methods of finding polynomial roots. There are enough sources for that topic, as evidenced by the 20 citations, and the quadratic equation is just a particular case. Sure, the quadratic section needs to be cleared of (potential) WP:OR by comparing, and potentially replacing its contents with what the sources say, but there's no reason to discard the contents that has been added to the article after this deletion nomination has been made. This new contents meets WP:V and WP:GNG. Pcap ping 12:19, 6 September 2009 (UTC)[reply]
  • Update. Delete link after article move, as the old name has nothing to do with, and no content in common with, the new article. Delete or Userfy new article anyway, as the only content is 3 unrelated well-sourced sentences, but still not related to the topic of the article. — Arthur Rubin (talk) 14:26, 6 September 2009 (UTC)[reply]
    • Trout for the person who renamed it, breaking links to the AfD from the article. — Arthur Rubin (talk) 14:27, 6 September 2009 (UTC)[reply]
      • That was verbal, he deleted several paragraphs,[5] and then argued that it be deleted because it is an "appalling stub".[6] Ikip (talk) 14:45, 6 September 2009 (UTC)[reply]
        • Could you please provide a diff to where this supposed deletion took place? These highly misleading comments are becoming disruptive. Please stop or I will take this further, which could result in a block or ban from AfD. What I see there is several identical sentences, except for one word. I removed the duplication. It could be argued that the repeated one sentence sections were a misleading attempt to make the article look like it had some actual content. It became an appalling stub as soon as you removed all the WP:OR. Verbal chat 15:55, 6 September 2009 (UTC)[reply]
          • Also, I didn't do the rename. Please strike. I also find your changes to comments, after they have been replied to, a misleading altering of the record. Please strike and then rephrase, do not hide the problem edits (usually). Verbal chat 15:58, 6 September 2009 (UTC)[reply]
  • I am going to restore the original article. It is ridiculous that the article has been stubbed in the middle of a deletion debate on the grounds that it is unsourced. Either the article is unsourcable and will be deleted at the end of the debate, or it is sourcable, in which case the text should be left in place while the sources are found. Besides, I suspect that the stub is innaccurate, or at least misleading while there does not appear to be anything actually wrong with the article. SpinningSpark 16:11, 6 September 2009 (UTC)[reply]
  • Unsourced has never, by itself, been a reason to delete. You are removing the very article this debate is discussing. The worthless stub you have left behind certainly deserves to be deleted, sourced or not. SpinningSpark 17:25, 6 September 2009 (UTC)[reply]
  • I fully agree. I don't think anyone has made the claim here that the article should be deleted merely because it is not sourced, and I agree that that once the unsupportable OR is removed what is left certainly deserves deletion. Perhaps you should change your !vote to reflect your new view? Verbal chat 17:29, 6 September 2009 (UTC)[reply]
  • Don't tell me what to do, I have said what I think and sarcasm won't change my mind. What I was going to do was to actually work on the article, but there is no fucking point if you are going to keep deleting it unless it is perfect. If you want to complain about my incivility you will now have to come to my talkpage as I am now unwatching both the article and this debate. SpinningSpark 18:05, 6 September 2009 (UTC)[reply]

Editing break 2

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  • Comment Are tactics like these even legal? I mean changing the topic of the discussion of an ADF this drastically? I feel bewildered. I am assuming good faith here, but I find this development really shocking and unexpected.TeamQuaternion (talk) 20:23, 6 September 2009 (UTC)[reply]
  • Keep article at its current state. The pruning and new diagram by Michael Hardy have given a very good result which conveys the point of the original in a comprehensible (and correct) manner. Johnuniq (talk) 01:29, 7 September 2009 (UTC)[reply]
  • Yowza! Above we have everything from an f-bombs to a photograph... To be totally honest, this discussion is difficult enough that were I an admin, I could not imagine closing as anything but "no consensus"; however, editors are making active good faith efforts at improvement and by and large we should give them further opportunity to do so beyond the week long AfD. Best, --A NobodyMy talk 02:03, 7 September 2009 (UTC)[reply]
  • Keep There is a good article in here trying to get out. Cardamon (talk) 18:18, 7 September 2009 (UTC)[reply]
  • Silliest edit summary in a while: "Removing OR. This "method" does not work for most parabolas. Try doing this with 0.75(x – 7)^2 + 5 and you will see that the roots can only be approximated. Prove me wrong". This is childish. To call a method "visual" or "graphical" is to say it's intended to give approximations, not exact answers. To say it "only approximates" the answers is to say that it works, not that it doesn't. Likewise to get the real x-intercepts in cases where they exist, by looking at the graph, is to get approximations. To use a calculator or a slide rule is to get approximations. (Even in cases where a calculator gives an exact answer, it doesn't tell you that that's what it is; you have to use your head.) This was by the same person who claimed this method in a certain case gives 7 ±0.235i. He claimed accuracy to the nearest thousandth! Childish. Michael Hardy (talk) 19:02, 7 September 2009 (UTC)[reply]
  • I made one mistake, using the method exactly as described. You keep repeating my one mistake, in an attempt to avoid confronting the very precise claims I have made about the sources not using visual methods to find imaginary roots. You still don't get what I am saying; the root is not some approximation, it is a number of the form a + bi, and once the parabola gets at all interesting, you can only estimate b (and poorly). Finding and estimating are not the same thing. If a student turned in a result like "about 2.6", would they receive points? No. A root is defined precisely; a root (or a zero) of a complex-valued function ƒ is a member x of the domain of ƒ such that ƒ(x) vanishes at Abductive (reasoning) 19:27, 8 September 2009 (UTC)[reply]
  • Comment I have now permanently laid to rest the "OR" worries. Could we now turn to the other issues? Michael Hardy (talk) 20:29, 7 September 2009 (UTC)[reply]
    • Utter falsehood. And how to you plan to overcome the plain fact that it is HOW TO? Abductive (reasoning) 01:35, 8 September 2009 (UTC)[reply]
      • There's nothing to overcome. It's clearly not a "how to". It identifies a mathematical fact. Like any mathematical fact, it can be used as a "how to". It can also used in other ways; it can be relied on in a proof. And how can you say it's an "utter falsehood" that the OR claim is laid to rest? The cited source describes exactly this content. Abductive, why does someone like you, who repeatedly loudly advertises his ineptitude at even routine secondary-school math, insist being so involved in this discussion? Michael Hardy (talk) 18:32, 8 September 2009 (UTC)[reply]
        • Because you keep insulting me. Because I am not as inept as you think. Because I am not the only one who has said this article is not appropriate. You have failed to address the problems here or on the talk page, and instead just keep repeating your claim that the OR issue is laid to rest. I, one the other hand, am making much more specific claims about the invalidity of using the sources provided, claims which you do not directly address. I have repeatedly asked anybody to use this method to find some roots for some every so slightly more comlicated parabolas, and nobody has risen to that challenge. If you are so good at math, how come you are using verbal methods to shout down my "pitiful" mathematical ones? Abductive (reasoning) 18:44, 8 September 2009 (UTC)[reply]
          • I did go through finding the roots in one of your examples, and reported the results on the talk page. I don't know what your "specific claims" about invalidity are. At one point you mentioned that they use algebra. Is that supposed to be a claim about invalidity? I can only offer guesses of that sort as to what you mean. Michael Hardy (talk) 21:31, 8 September 2009 (UTC)[reply]
            • A root is a number. This visual method does not give numbers, it gives guesses (in other words, an interval). If a student was told to find the roots, and responded with anything other than the exact numbers, they are just as wrong as somebody who says the answer is "cat" and "dog" are the roots. If you use algebra, the method is a roundabout way of using the quadratic. Picture progamming a computer to find the roots using the visual method. It would have to hunt in the interval, narrow the answer down, and then hunt again. This will require the same or more operators than just solving it algebraically. Abductive (reasoning) 23:14, 8 September 2009 (UTC)[reply]
              • Abductive, you are committing several errors: You say algebra will find an exact answer every time. That's not true: that holds only in cases where you know the coefficients exactly. If they are physical measurements, you don't. If you have only the graph, you can approximate the coefficients "visually", and then use algebra to find the roots (also approximately), but if you don't have the coefficients and can only approximate them based on the drawn graph, it's quicker to approximate the non-real roots "visually" using the method described here than to first approximate the coefficients and then use algebra. Secondly, you say students are not given credit for approximate answers. But that depends on what question was asked. Sometimes students are asked to get such approximations using graphs. If I assigned a problem like the ones contemplated here, I'd have students CAREFULLY draw the graphs, then use this method, then write a careful verbal explanation of what they did and how they did it. The next point you seem to miss is that this article explains the relationship between the roots and the graph, and that can be used for other things than numerical work. Michael Hardy (talk) 02:25, 9 September 2009 (UTC)[reply]
                • That seems to me to wander into the even less likely realm of having a graph but no equation. And it sounds HowTo-ish. But at least you are more understanding of my concerns. Abductive (reasoning) 02:41, 9 September 2009 (UTC)[reply]
                  • Um... if you're working from physical measurements, then you'll have a graph, consisting of data points, but no equation. Finding an equation that fits your data points is a big part of applied mathematics, you know. God doesn't tend to give us equations directly from His hand.

                    Why do you think your instincts about what's likely, or what's useful, are going to be better than the instincts of actual working mathematicians? How many absurd claims will you make before you start doing your homework on these topics?

                    The How-to issue is worth thinking about. However, your other claims... (1) The method does work. (2) The method is used by real mathematicians and real math students. (3) Complex solutions do have concrete physical meanings. (4) Obtaining approximate solutions is useful and does happen in both pure and applied contexts. (5) Having a graph without an equation is as common as dirt; it's how experimental science always works.

                    What are you going to claim next, Abductive? I recommend you stick to the "How-to" argument and stop pretending you know what goes on in mathematics. You've made it painfully and repeatedly clear that you don't. Start asking questions instead of making wrong assertions. -GTBacchus(talk) 08:39, 10 September 2009 (UTC)[reply]

  • Keep - I haven't been called nasty names in a while, and !voting "keep" here seems to be an efficient way to make that happen.

    Seriously, though, this discussion raises an interesting question. I've known this method of locating complex zeros since middle school - where did I learn it? It's not in the College Algebra textbook from which I teach today. Most books at that level that I've seen don't address any kind of geometric understanding of complex numbers; they're treated in an entirely algebraic manner, with no notion of a complex plane sticking out from the page. It's a shame really, because the visual approach probably would help a lot of students. I show fellow grad students this, though, and they've never seen it! Bizarre.

    I'd like to see the method extended to roots of cubics... -GTBacchus(talk) 20:38, 7 September 2009 (UTC)[reply]

    • Fellow grad students having never seen it supports the hypothesis that this is Original Research. Policy is that Wikipedia is not a publisher of original thought, point 1. Abductive (reasoning) 01:38, 8 September 2009 (UTC)[reply]
            • Abductive, let me help you by summarizing all of your comments on this page: Abductive hardly knows anything about mathematics. Since when are graduate students omniscient? On can also find people with Ph.D.s who've never heard of this. Therefore they shouldn't hear of it, by reading this article, you seem to tell us. The OR claim was silly from the outset and is dead. Leave it alone. Michael Hardy (talk) 18:02, 8 September 2009 (UTC)[reply]
              • On the talk page of the article I have made a case for why the method doesn't work, and so far you have not responded. I say this is because the method doesn't work without sneaking in some algebra. I have made a case that the sources are being misused, and nobody has responded. Nobody has reponded to the problem of avoiding How-To. Insulting me will not make me go away, but I again ask you to stop. Abductive (reasoning) 18:16, 8 September 2009 (UTC)[reply]
            • I did respond. I wrote out a detailed proof that the method works. Your "case for why the method doesn't work" is only a report that you tried it and you did it wrong. It's just a routine high-school homework problem, and you claim did it wrong, without specifics, and professional mathematicians tell you it works and write a proof that it works, and the proof is accessible at a secondary-school level, and you respond that you "have made a case for why the method doesn't work, and so far you have not responded". Michael Hardy (talk) 18:39, 8 September 2009 (UTC)[reply]
              • No, my case is that you can't seem to actually use the method to find some roots. I have given two example parabolas and asked for the roots; you have not responded with the roots. Why not? Isn't it easy? Abductive (reasoning) 18:48, 8 September 2009 (UTC)[reply]
                • Where are these example parabolas? I'd like to have a shot at it. -GTBacchus(talk) 08:02, 9 September 2009 (UTC)[reply]
                • Never mind, I found it, and solved the problem you posed. I only used a graph and my eyeballs, and I got 6.3 ± 2.3i. The trick was to find a nice, accurate graph - that's easy to do online. -GTBacchus(talk) 08:25, 9 September 2009 (UTC)[reply]
                    • I did it in less than one minute with no algebra, no calculator, no online or otherwise electronic help, just pen and paper, plotting just seven points and estimating the answer visually. For 0.83(x − 6.3)2 + 4.4, the imaginary part of the root appeared to be a bit more than 2. There you go. This is trivial. I was doing stuff like this when I was in 7th grade and so was everyone else (except those who don't care about things like this). Abductive, you keep pointing out that Norton & Lotto use algebra, as if that were an objection. Their algebra explains why it is possible to do this sort of visual stuff with no algebra. And if you couldn't, this article would still explain the geometric relationship between the parabola and the locations of the roots. That is the main point. Michael Hardy (talk) 11:42, 9 September 2009 (UTC)[reply]
                      • Your bold text won't steal my thunder. I got there first. :p -GTBacchus(talk) 14:39, 9 September 2009 (UTC) I'm joking[reply]
                        • My contention is that you aren't "finding" the roots, your're estimating them. If I plug in "a bit more than 2" or "6.3 + 2.3i" into the equation, do I get 0? No. A root is defined as a number x that makes f(x) = 0. Also, none of the sources talk about finding or estimating the roots in this way, and the article contains too much HowTo. Abductive (reasoning) 18:27, 9 September 2009 (UTC)[reply]
                        • I also note that we have gone from "this method is genius!" to "this method is trivially easy!" during the course of this debate. Abductive (reasoning) 18:27, 9 September 2009 (UTC)[reply]
                          • Yes. The article now states that the method is for approximation—for estimating roots—and not for finding exact ones. Everyone knows that, and nobody disagrees. As for whether someone thought it was "genius", that has nothing to do with anything, unless you're just looking for reasons to criticize people. Personally, I'm here to write an encyclopedia, and not to talk about other editors. -GTBacchus(talk) 19:21, 9 September 2009 (UTC)[reply]
        • You wouldn't believe how much mathematics my fellow grad students don't know. They're all younger than I, for one thing, and math education has been changing. The fact that I was taught it by a middle-school teacher inclines me to think it must be written down in a book somewhere. I suspect it's the newer textbooks that have cut a lot of material that used to be standard. I'm attending a mathematics conference right now, working with a researcher in complex analysis who went to school before I did. I'm going to ask him about this. -GTBacchus(talk) 09:18, 8 September 2009 (UTC)[reply]
The article is not OR because the first two external links show the method (the third may do as well, but I'm not sufficiently patient to read it all). Johnuniq (talk) 05:12, 8 September 2009 (UTC)[reply]
Indeed, the second source, but not the first, seem to resemble this visual method, with a crucial exception; the authors do not claim to be able to read the roots off the graph; they have to use regular algebraic methods to get the roots. The other sources rely on algebra also. Abductive (reasoning) 08:00, 8 September 2009 (UTC)[reply]
  • Keep Graphical methods of root finding is clearly a well covered subject, although one that possibly might be duplicated on Wikipedia. OR issues surrounding the finding of complex roots can be, should be and in fact are beeing hashed out as part of the ordinary editorial process. Taemyr (talk) 07:31, 8 September 2009 (UTC)[reply]
  • Keep Great work improving the article, though I generally preferred the original version. As Giano advises we should write articles as though we are addressing a bright 14 year old with no knowledge of the subject. Maths is best learnt by doing math, and to facilitate that we need a more beginner friendly presentation. FeydHuxtable (talk) 17:26, 8 September 2009 (UTC)[reply]
  • Comment on Abductive's edit summary "the even less likely realm of having a graph but no equation": That's not unlikely at all. Physical measurements give you a graph but no equation. Physical measurements happen all the time. Michael Hardy (talk) 11:47, 9 September 2009 (UTC)[reply]
    • Why whould you need the imaginary roots of a physical measurement? Abductive (reasoning) 18:19, 9 September 2009 (UTC)[reply]
      • Holy cow, are you seriously asking this question? Do you not know that imaginary solutions have extremely concrete physical meanings in, for example, electrical engineering? Do you not know that complex roots have extremely concrete physical meanings when talking about systems that display simple harmonic oscillation? Do you really imagine that complex roots are somehow apart from physical reality? Wow. No more, just: Wow.

        In parallel to your statement above, your argument has changed from "you can't actually use this method", to "What are complex (or as you call them, "imaginary", although none of the examples we've looked at have pure imaginary roots) good for, anyway?" Wow. I'm sorry, Abductive, but that's sad.

        Let me clue you in a bit: When a system of differential equations has as an eigenvalue (6.3 + 2.3i) that means the system evolves by growing at a rate of e^6.3, while oscillating at a rate of 2pi/2.3. I was kind of assuming you knew that — my bad. -GTBacchus(talk) 19:25, 9 September 2009 (UTC)[reply]

        • Well, excuse me for not knowing everything. Nevertheless, even if everything you have said is valid, I fail to see how it is not pure HowTo advice, and I would like to see a reliable source from the electrical engineering literature that suggests approximating roots in this way. Abductive (reasoning) 19:38, 9 September 2009 (UTC)[reply]
          • You're excused. Nobody's born knowing this stuff. I was just surprised, given your level of participation so far in this debate. Sorry for my presumption. Regarding the HowTo argument. I don't disagree. The only points I've made here are that the method does work, and that complex solutions do have physical meaning. I, like you, would like to see a book that details this method, partly just because I'm annoyed that it's not taught much these days. As a math teacher, I wish the textbooks covered it. -GTBacchus(talk) 20:31, 9 September 2009 (UTC)[reply]
        • I urge people to try and understand; Wikipedia articles are not built on truth, they are built on reliable sources. As I have stated, this article twists the sources on their heads to claim that they use graphical methods to approximate (not find) the roots, when the articles are only using the graphs to show why the roots are well-behaved. Abductive (reasoning) 19:38, 9 September 2009 (UTC)[reply]
  • Delete or at best smerge to whatever suitable article there maybe. Wikipedia is not a textbook. WP:GNG does not require us to keep every single article with at least two sources, or every single paragraph with at least two refs can become its own article. This is such an elementary exposition of an imprecise method (or methods) that I have difficulty believing that any student of mathematics will have any use for it. We are not writing for mathematicians, of course, but we are not writing for 12-year-olds, either. Tim Song (talk) 04:08, 10 September 2009 (UTC)[reply]
The article contains information that is not in the articles you mentioned because some of it would not be relevant there. The information is relevant to the title of this article, and it may be expanded. A large number of people have claimed that the material is OR and presumably have been unable to locate the concepts in textbooks. Yet, the material is sourced (and so is not OR). It's interesting to hear the article described as "elementary" after some previous comments that it was wrong, and mathematicians really do spend time considering graphical or geometrical solutions that may appear redundant given an algebraic alternative. Johnuniq (talk) 05:22, 10 September 2009 (UTC)[reply]
(ec) Notice that the title of the article is actually now Graphical methods of finding polynomial roots, and that some of its material would not fit under quadratic function. I'd like to comment on the accuracy of graphical methods like this. Typically, it would be 2 or 3 significant figures, if done on paper by a skilful person with some sort of drafting tools. With practice, using a method like this to guessitimate the answer just by looking at a graph might be accurate to about 10%. With a graphics program, this method could be accurate to many decimal places. Finally, yes we do write for intelligent 12 year olds, among others. Cardamon (talk) 05:51, 10 September 2009 (UTC)[reply]
I was responding to Michael Hardy's suggestion that this is a WP:COATRACK "for the purpose of explaining the geometric relationship between the parabola and the locations of the roots" (emphasis mine). My point is that we are not writing a kid's encyclopedia. But I guess I'm not the best judge for that. Tim Song (talk) 12:03, 10 September 2009 (UTC)[reply]
Tim: "I have difficulty believing that any student of mathematics will have any use for it" Have you ever taught algebra? This is an excellent method, and I teach it to algebra students. Approximating solutions by looking at a graph is an important skill that I personally use in my graduate study - quadratic equations come up in all sorts of contexts (differential equations, for example), and we often find ourselves looking at approximate graphs. Simply knowing the sign of the real and imaginary parts of a solution can yield important qualitative information about the nature of a solution - e.g., whether an oscillation will be damped, or grow exponentially! (When you're driving across the Tacoma Narrows Bridge in the famous video, this sort of thing matters.)

If you want to know whether a method will be useful for math students, why not ask some math teachers? -GTBacchus(talk) 07:50, 10 September 2009 (UTC)[reply]

Sure, it's useful. Heck, I know that, I even use it myself sometimes. Does not mean it is entitled to its own article. I've struck that part of the comment, happy? But the title is ..."of finding ... roots" (emphasis mine). Determining the sign or approximate value of the root does not sound like "finding" the root to me. Tim Song (talk) 12:03, 10 September 2009 (UTC)[reply]

Comment Moving away from this specific article, some uses of graphical methods are:

  1. For many people, seeing a problem and its solution helps the understanding.
  2. If for some reason analytical solutions or numerical methods are not available, graphical methods can be very useful. This was more important historically (before computers and handheld calculators became common) than it is now. Note: Wikipedia does care about history.
  3. They can be used for "sanity checks" if one suspects a malfunction, a bug in a program or a calculation error. In this regard, the ability to guesstimate a graphical method just by looking at a plot is useful in catching gross errors, because it can be fast. One way to gain such an ability is by learning graphical methods. Cardamon (talk) 05:51, 10 September 2009 (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.
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