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::::::* 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? [[User:Rschwieb|Rschwieb]] ([[User talk:Rschwieb|talk]]) 19:27, 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? [[User:Rschwieb|Rschwieb]] ([[User talk: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. [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 19:33, 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. [[User:Tkuvho|Tkuvho]] ([[User talk: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/. [[User:SohCahToaBruz|SohCahToaBruz]] ([[User talk:SohCahToaBruz|talk]]) 20:58, 27 November 2013 (UTC)
:::* This article isn't about a book! It's simply not relevant. [[User:Ijeusjb0|Ijeusjb0]] ([[User talk:Ijeusjb0|talk]]) 04:05, 27 November 2013 (UTC)
:::* This article isn't about a book! It's simply not relevant. [[User:Ijeusjb0|Ijeusjb0]] ([[User talk:Ijeusjb0|talk]]) 04:05, 27 November 2013 (UTC)
::::* Indeed. [[User:Rschwieb|Rschwieb]] ([[User talk:Rschwieb|talk]]) 17:53, 27 November 2013 (UTC)
::::* Indeed. [[User:Rschwieb|Rschwieb]] ([[User talk:Rschwieb|talk]]) 17:53, 27 November 2013 (UTC)

Revision as of 20:58, 27 November 2013

Rational trigonometry

AfDs for this article:
Rational_trigonometry (edit | talk | history | protect | delete | links | watch | logs | views) – (View log · Stats)
(Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL)

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.

  • 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)[reply]
Note: This debate has been included in the list of Science-related deletion discussions. Northamerica1000(talk) 15:55, 24 November 2013 (UTC)[reply]
  • 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)[reply]
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)[reply]
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)[reply]
  • 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)[reply]
  • 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)[reply]
  • 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):

− 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)[reply]

  • 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)[reply]
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)[reply]
Yes, indeed. Fixed above. Gandalf61 (talk) 17:14, 25 November 2013 (UTC)[reply]
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)[reply]
  • 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)[reply]
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)[reply]
  • 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)[reply]
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)[reply]
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)[reply]
  • 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)[reply]
  • 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)[reply]
  • 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)[reply]
  • 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)[reply]
  • 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)[reply]
  • @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)[reply]
  • 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)[reply]
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