Wikipedia:Articles for deletion/Rational trigonometry


 * 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. Good arguments have been made by both sides in this discussion, but there does not appear to be a firm consensus available at this time. &mdash; Coffee //  have a cup  //  beans  // 19:53, 3 December 2013 (UTC)

Rational trigonometry
AfDs for this article: 
 * – ( View AfD View log  Stats )

The issue with the page given over four years ago has not been fixed. Simply put, there are very few actual other sources not involving the creator of the theory, Norman Wildberger which actually support the majority of the article, because nearly no one else has created sources that can be used in this article. Most other sources were irrelevant parts of the article, but are no longer valid and have expired. Most third party sources which do exist talk only about his book.

For this reason this article passes deletion criteria 7 "Articles for which thorough attempts to find reliable sources to verify them have failed" and fails the notability guidelines. Clearly if there were any other decent resources on Rational Trigonometry they would have been found within the last four years.

Until this theory becomes more mainstream and others write papers which can be used as reliable third-party citations this page should be removed and a possibly section about it should be added to the trigonometry article, since at the moment this reads as an advertisement for Wildberger's book.


 * Automated comment: This AfD was not correctly transcluded to the log (step 3). I have transcluded it to Articles for deletion/Log/2013 November 24.  — cyberbot I  Notify Online 01:07, 24 November 2013 (UTC)
 * Comment. I have no clear opinion if this subject is notable or not, but I did note that several apparent sources were removed in an earlier edit  on the stated ground that those sources were "broken" and needed to be replaced by "newer" sources; it is unclear to me what "broken" was intended to mean in that context, or if that removal of sources was appropriate.  Also, note should be taken of Articles for deletion/Norman J. Wildberger in 2009 which resulted in the merger of that biographical article into this one. --Arxiloxos (talk) 06:05, 24 November 2013 (UTC)


 * Comment. @ Arx: The sources didn't exist ie the URLs linking to the "sources" must have changed, or the sources themselves just deleted. "new" sources refers to URLs that actually work. Sorry for the mixup. SohCahToaBruz (talk) 11:01, 24 November 2013 (UTC)
 * Sources should not be deleted solely because of URL problems. Sources are not required to exist online. Please see WP:LINKROT.   --Arxiloxos (talk) 17:49, 24 November 2013 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions. Northamerica1000(talk) 15:55, 24 November 2013 (UTC)


 * I see, I've added in what I can, but I don't believe that changes any of my criticisms of the article, see David E's post further below. Thanks for the help. SohCahToaBruz (talk) 06:33, 25 November 2013 (UTC)


 * Comment., in repeatedly reverting to an older version of the article without so much critical commentary against the topic, removed the AfD notice. I have reverted to the version with the notice and warned him not to do that. —David Eppstein (talk) 17:18, 24 November 2013 (UTC)


 * Delete. I'd agree with the deletion of this page - the article has had a lack of third party sources for years and it's never been fixed. More important is the fact that it really can't be fixed at all, as the only sources that exist are the one book published on the topic, so all sources would be from the one guy - incredibly biased. In contrast to this, multiple sources exist from mathematicians which dispute and even disprove the works contained within the book on which this article is based, which provides solid evidence for deletion. 14.200.41.164 (talk) 02:25, 25 November 2013 (UTC)
 * Independent sources do exist, as noted below, which establishes notability. And nobody has "disproved" Wildberger; the debate has been about the practical benefits of the approach. -- 101.119.15.209 (talk) 11:43, 25 November 2013 (UTC)
 * I find it far-fetched that anyone claims to have "disproved" any mathematics done by Wildberger, and if they've disputed some of Wildberger's views, I doubt that they've disputed any of his mathematical results. I challenge the anonymous poster above to demonstrate that that has happened. Michael Hardy (talk) 19:29, 25 November 2013 (UTC)


 * Weak delete. Contrary to the nomination statement, there *are* reliably published third party sources: The New Scientist article, and the MAA review. However, the sources are all about the event of the book's publication, their existence does not distinguish this book from an enormous number of other mathematics books, and our article is not actually focused on the book but on its contents. I think the most relevant guideline is WP:NOTNEWS: this theory made a brief popular media splash when it appeared, but has not been demonstrated to have the enduring notability required to make it an encyclopedic topic rather than a news topic. Incidentally, the idea of simplifying certain calculations by using squared distances rather than Euclidean distances is a very useful one, but is far older than Wildberger's work (e.g. Cayley wrote about squared distances in 1860), so the usefulness of this idea cannot be used as a justification for keeping an article focused on Wildberger's contributions: it's not his contribution, even if he briefly popularized it. —David Eppstein (talk) 03:41, 25 November 2013 (UTC)


 * You're right, I changed the wording slightly of the nomination statement in order for it to be more accurate. Thanks. SohCahToaBruz (talk) 07:00, 25 November 2013 (UTC)


 * Keep. Removing valid sources from the article and then claiming sources couldn't be found is extremely bad form by the nominator, who deserves a WP:TROUT. The deleted sources included a properly cited journal article (Olga Kosheleva, Geombinatorics, Vol. 1, No. 1, 2008, pp. 18–25), which I have restored to the article. Problems with the accompanying urls were no reason at all to delete the references (as has been noted). A quick Google books search also finds several mentions of Wildberger's ideas, e.g. in Shirali & Vasudeva (2010), Multivariable Analysis, Springer, pp 246-247; Harrison (2009), Handbook of Practical Logic and Automated Reasoning, Cambridge University Press, p. 414. Together with the New Scientist article, and the MAA book review, that puts it over the notability line in my view, and indicates an ongoing interest in Wildberger's (possibly nutty) ideas. His finitist approach is interesting particularly for computational mathematics and automated reasoning, however. -- 101.119.15.209 (talk) 11:31, 25 November 2013 (UTC)

− 1. Vinh, Le Anh A construction of 3-existentially closed graphs using quadrances. Australas. J. Combin. 51 (2011), 3–6. − 2. Kisil, Vladimir Erlangen program at large-1: geometry of invariants. SIGMA Symmetry Integrability Geom. Methods Appl. 6 (2010), Paper 076, 45 pp. − 3. Shparlinski, Igor E. On point sets in vector spaces over finite fields that determine only acute angle triangles. Bull. Aust. Math. Soc. 81 (2010),  no. 1, 114–120. − 4. Kurz, Sascha Integral point sets over finite fields. Australas. J. Combin. 43 (2009), 3–29. − While this isn't exactly overwhelming, it does go contrary to what was claimed above. Usually Google Scholar gives more citations than MathSciNet but I have not checked it. Tkuvho (talk) 11:38, 25 November 2013 (UTC)
 * Weak keep. I noticed a claim by one of the editors above that there are no sources citing Wildberger's book. I understand this is the book "Wildberger, N. J. Divine proportions. Rational trigonometry to universal geometry. Wild Egg, Kingsford, 2005. xx+300 pp. ISBN: 0-9757492-0-X . If so, MathSciNet lists at least four separate authors other than Wildberger himself who cite the book.  These are the papers that cite it (other than Wildberger's own papers):


 * Keep - the "Notability and Criticisms" section mentions four third-party reviews of the theory. They are not complementary complimentary, so the theory may well be nonsense - but it does seem to be notable nonsense. Gandalf61 (talk) 12:02, 25 November 2013 (UTC)
 * I think you mean "not complimentary". I don't think Wildberger's framework is "nonsense", even though I personally don't find it appealing. It may well be of limited utility. Tkuvho (talk) 16:10, 25 November 2013 (UTC)
 * Yes, indeed. Fixed above. Gandalf61 (talk) 17:14, 25 November 2013 (UTC)
 * The theory is not nonsense. Wildberger tends to grandiosity in his statements about it, but it makes sense.  It makes sense in some contexts to separate those parts of trigonometry that do not depend on the choice of a particular parametrization of the circle from those that do.  That's what Wildberger has done. Michael Hardy (talk) 17:54, 25 November 2013 (UTC)


 * Delete – This is clearly a fringe theory (this is acknowledged in the body of the article). This is almost WP:original research, as nobody has claimed that the theory has been useful for him or that it solves pre-existing problems. The content of the theory consists only in replacing the distance by its square (which is not new as quoted above) and the angles by the square of their sinus (which prevents to consider oriented and obtuse angles). Thus this theory is very similar to tau (2pi) proponent (consisting in replacing, for similar biased reasons, pi by 2pi), but it is much less notable. D.Lazard (talk) 17:20, 25 November 2013 (UTC)
 * It is not true that it consists ONLY in replacing the distance by its square and angles by the squares of their sines. Rather, in conventional trigonometry, one parametrizes the circle by arc length, whereas in rational trigonometry one does not rely on any particular parametrization of the circle.  And it's not "original research" in the sense intended in Wikipedia's policy, because it's not published for the first time in a Wikipedia article. Michael Hardy (talk) 17:56, 25 November 2013 (UTC)


 * Keep per the 56 sources returned by Google scholar for the search term "Rational trigonometry" wildberger -author:wildberger http://scholar.google.co.uk/scholar?q=%22Rational+trigonometry%22+wildberger+-author%3Awildberger — Preceding unsigned comment added by 2.97.19.189 (talk) 18:03, 25 November 2013 (UTC)


 * Delete - The scarcity of strong secondary source support suggests that it is at least "too early" for this topic to be in an encyclopedia. I think this topic will just have to wait until it catches on in more places. Rschwieb (talk) 18:33, 25 November 2013 (UTC)
 * You say ""too early" for this topic to be in an encyclopedia" and yet it appears in the "Encyclopedia of Distances" http://books.google.com/books?id=QxX2CX5OVMsC&pg=PA81 — Preceding unsigned comment added by 89.241.227.185 (talk) 18:59, 25 November 2013 (UTC)
 * Well, nice try, but I think it's clear from the context I mean "an encyclopedia like Wikipedia," not an obscure encyclopedia in which the topic is likely to occur. Rschwieb (talk) 11:46, 26 November 2013 (UTC)


 * Merge. A subsection in the trigonometry page stating the basic idea of the theory, with a link to an external website with more resources on the idea is appropriate. However, there's no way that this topic is notable enough for its own article at the moment. Most of the "sources" are reviews of the book, not actual sources for the article itself! Ijeusjb0 (talk) 04:05, 27 November 2013 (UTC)


 * Keep. Some confused ideas about what Wilberger has done appear above, so let's be clear about those:
 * In conventional trigonometry, one parametrizes the unit circle by arc length. What seems to me to be the essential idea of "rational trigonometry" is that one does not parametrize the circle at all.  Rational trigonometry comprises those parts of trigonometry that can be done without any choice of a parametrization of the circle.  One is not viewing functions of angles as functions of a parameter that maps to a point on the circle.  One is measuring triangles without measuring circles.  Measuring triangles by measuring circles goes back at least to Ptolemy's table of chords and permeates many fields of mathematics.  One couldn't do Fourier analysis without functions on a circle.  Wildberger separates from that the things that can be done without parametrizing circles.
 * This paper says Wildberger's "spread", a function of an angle that is not defined as a function of a point on a circle, "allow[s] the development of Euclidean geometry over any field". Wildberger's work on geometry over finite fields is part of the relevance of this subject.
 * Michael Hardy (talk) 19:29, 25 November 2013 (UTC)
 * I might be more impressed by this argument if I had some idea what it means. "Do geometry of triangles without using circles": well sure, just don't mention circles, but saying what something is *not* is not a helpful way of saying what it is. One can describe colors subtractively as well as additively but it doesn't work so well for mathematics. There are standard ways of doing projective geometry over any field (or even rings), but of course they don't have proper distances either. Is there a clean axiomatizable way of describing what this work *adds* to projective geometry? How would we go about recognizing a "Wildberger geometry" and what examples are there of these things that are not just standard pre-existing geometries with some of the details filed off? —David Eppstein (talk) 08:05, 26 November 2013 (UTC)
 * As to "what it means". Of course, you find that out from Wildberger's book, but here's a start.  Suppose you have lines through the origin in Euclidean space spanned by two vectors (x1,x2,x3) and (y1,y2,y3) (but the dimension need not be 3).  The square of the sine of the angle between them is a rational function that is homogeneous of degree 0, of the coordinates of the two vectors.  One defines that quantity, the "spread" between the two lines, directly without using the radian measure of the angle by parametrizing the circle by arc length, etc. Michael Hardy (talk) 17:51, 30 November 2013 (UTC)
 * Why is this review of the subject itself continuing here? The correctness of the work is not relevant at all. The issue is the weakness of citations. Rschwieb (talk) 11:46, 26 November 2013 (UTC)
 * Hi Rschwieb, you have already mentioned "scarcity", "obscurity", and "weakness", but I am still not sure what you are referring to. The book was published recently and already has over 50 citations by authors other than Wildberger. For a trig text that's not bad. Tkuvho (talk) 13:35, 26 November 2013 (UTC)
 * Dear @Tkuvho : If one were to take your sentence as "support", then it is scarce (only one) obscure (the Encyclopedia of Distances or Wildberger's book, whichever) and therefore weak. However, I suspect you did not intend that to be a complete support. Can you provide a statement summarizing the full support for the book? I've seen the Encyclopedia of Distances and four citations listed above (one of which, Shparlinski, appears to be a department colleague of Wildberger's) I would like to take a look at them. I would also appreciate knowing which book you're pointing to as having 50+ references. Thank you Rschwieb (talk) 17:53, 27 November 2013 (UTC)
 * @Rschwieb, the book in question is Wildberger's "divine proportions, etc". The google scholar link listing over 50 references was reproduced above.  One of them is the article by Kosheleva mentioned above.  this was not reviewed in MathSciNet possibly because it is not a mathematical journal. Tkuvho (talk) 18:35, 27 November 2013 (UTC)
 * I thought it was common sense that self-published books are considered poor references unless corroborated by other strong sources. Are there two or three other texts? Rschwieb (talk) 19:27, 27 November 2013 (UTC)
 * Why is this self-published? Kosheleva's article appeared in the journal Geomcombinatorics. There is also an article by Maurice Craig in the The Australian Mathematical Society Gazette. The google scholar list may be a bit padded but there are definitely published articles there. Tkuvho (talk) 19:33, 27 November 2013 (UTC)
 * Wildberger owns the publishing company that published "Divine Proportions". It's the only book that they have published. See http://wildegg.com/. SohCahToaBruz (talk) 20:58, 27 November 2013 (UTC)
 * I see, I didn't realize that. At any rate his latest piece is Wildberger, N. J. Universal hyperbolic geometry I: trigonometry. Geom. Dedicata 163  (2013), 215–274. Geometria Dedicata is certainly a reputable journal. Tkuvho (talk) 19:27, 28 November 2013 (UTC)
 * @Tkuvho : Hm, it still seems like you aren't on board with what is going on here. The number, recency, and journal reputation of publications by Wildberger are all irrelevant data. What is relevant is a substantial record of publications by other authors in secondary and tertiary sources about the topic. Rschwieb (talk) 15:04, 2 December 2013 (UTC)
 * @Rschwieb, my last comment was not a response to you but rather a response to User:SohCahToaBruz who found fault with the book being allegedly "self-published". As far as your request for articles that cite Wildberger, I gave some examples above. Further examples are mentioned at the parallel discussion of spread polynomials here.  My impression is that there is a record of secondary sources that is sufficient to establish notability in this case.  I am not particularly impressed by Wildberger's theory and his philosophical quest to eliminate infinity from mathematics, but this does not undermine the notability of his framework.  Tkuvho (talk) 16:37, 2 December 2013 (UTC)
 * I don't see how that addresses anything SCTB said, and also s/he was just spelling out my objection of self-publication, which anyone with two minutes and access to Google should have discovered: please forgive me for confusing it for a response to me/us. The articles listed above could be considered weak secondary support. I think it seems pretty common-sensical that support for the two articles shouldn't be balled together unless that article is merged as a subarticle of this one. Separate topics, separate citations. Rschwieb (talk) 18:06, 2 December 2013 (UTC)
 * The other page should be merged to rational trigonometry; I voted there accordingly. Tkuvho (talk) 18:51, 2 December 2013 (UTC)
 * This article isn't about a book! It's simply not relevant. Ijeusjb0 (talk) 04:05, 27 November 2013 (UTC)
 * Indeed. Rschwieb (talk) 17:53, 27 November 2013 (UTC)


 * Comment. See also Articles for deletion/Spread polynomials. —David Eppstein (talk) 01:10, 27 November 2013 (UTC)
 * Delete. Fringe theory, lack of sources supporting most of the article. 220.237.238.134 (talk) 15:47, 30 November 2013 (UTC)
 * Weak ... ummm, I'd vote to keep it is was shorter and meatier and made the point succinctly. I think that pedagogical reform is worth debating and having: too much grade-school math teaching is stuck in horrid, arcane 18th/19th century conceptions of math; perhaps the 'spread' could help fix some of this(?) So, for thease reasons, Micheal Hardy is correct in arguing for keep. But this article does not seem to be about pedagogy, its something else... My experience with fringe-theory articles is negative: they accumulate nutty cruft and crap and bizarre, incorrect claims over time, and can be real time-wasters to try to clean up. In such cases, its just simpler to delete. Which is why I recommend that this article be shortened, if it si to be kept. User:Linas (talk) 21:47, 30 November 2013 (UTC)


 * Strong Delete. I recommend that this article should be removed, and then remade if/when it meets the notability criteria, because it certainly doesn't yet. Especially since the book is essentially self published Themekenter (talk) 02:48, 1 December 2013 (UTC)
 * Keep. Enough coverage and mentions in other sources to suggest that it is at least a mildly notable fringe topic. The article could surely use editing to make it more readily understandable and probably shorter.  --Arxiloxos (talk) 15:36, 3 December 2013 (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.