Talk:Divine Proportions: Rational Trigonometry to Universal Geometry

message: I find this current article dubious in way of it essentially advertising a book from the UNSW University with all citations centered around a seemingly single source. I am unsure of the quality of any particularity new insights gained from this reformulations of trigonometry that may be necessarily inherited from such an approach nor the technical merit of thing being on Wikipedia as this currently stands. This article does not convey any particularly new knowledge, rather more a reflection of a minor in-print book, Wikipedia is not a minor book review service.  —Preceding unsigned comment added by 149.171.184.73 (talk) 09:44, 3 May 2011 (UTC)
replies: text: Nothing actually could be wrong here. These are just definitions of new terms upon which rational trigonometry could be built. I believe that this article is quite correct as it just describes an idea that stroke a mathematician elsewhere and references the page where further information may be obtained. As for me, I looked through the first chapter of the book and found nothing quite obviously delirious that would make deletion favorable. --ACrush217.23.131.98 09:52, 18 September 2005 (UTC)
thread_title:  Doubt 

message: I was reading through this article.  It make sense.  But it would have been easier for me to follow had there been more diagrams.  Val42 16:54, 4 February 2006 (UTC)
thread_title: Diagrams

message: I don't know if this is useful or anything, but given two connected collinear line segments with quadrances Q1 and Q2, you can obtain the quadrance of the combined line segment with the following formula:
Q_3 = Q_1 + Q_2 + 2\sqrt{Q_1Q_2}
Ubern00b 22:49, 5 April 2006 (UTC)
thread_title: "Adding" quadrance

message: :Could you tell me where to find the public discussions to which you refer? Michael Hardy 21:24, 13 April 2006 (UTC)
replies: text: See  my talk page for a response (briefly: Google). But there is also a review by one of Wildberger's colleagues to appear in the Intelligencer,  which should be seen by quite a few mathematicians. The publisher is Wild Egg Books, run by Norman Wildberger, and with one book published to date (according to my reading of the site). As they say: 'Wild Egg Books is delighted to offer the controversial new book DIVINE PROPORTIONS: Rational Trigonometry to Universal Geometry by N J Wildberger'.  I suggest people who are aware of reviews and other extended comments may wish to add to this section as they come across them (and also to the main page presumably, but the threshold here is much lower).  Abu Amaal 01:35, 14 April 2006 (UTC)
replies: text: The Drexel Mathforum site is relevant. This thread is a short one initiated by Wildberger. I imagine further discussion will accumulate on that site. Abu Amaal 19:40, 14 April 2006 (UTC)
thread_title:  References 

message: Are there any objections, or alternative suggestions, to starting a Divine Proportions: Rational Trigonometry to Universal Geometry article, to discuss the book, and the more controversial views presented therein by Wildberger?  --Piet Delport 03:06, 14 April 2006 (UTC)
replies: text: I somewhat prefer keeping the discussion brief and on this page. But your proposal may be more broadly acceptable at this time. I would suggest in that case making the title short: Divine Proportions and putting a link (otheruses4 I believe) to Divine Proportion at the top of the page.  I'm a little uneasy about the clash with a very different topic of major interest (if my short title is adopted) but it seems to me it can be handled cleanly. Abu Amaal 14:31, 14 April 2006 (UTC)
replies: text: Agreed. Rational trigonometry, Wildberger, and his book are so intermingled as topics, it seems unnecessary to split them (it's not like Stephen Wolfram and A New Kind of Science, where there's a huge amount of reportage and controversy, and the author and book have separate notability). I recommend creating redirects pointing to Rational trigonometry. Tearlach 14:53, 14 April 2006 (UTC)
thread_title:  Proposal: ''Divine Proportions'' article 

message: I'm tempted to put my hand to this article and try recasting it.  I'm thinking more in terms of shape than content, though I expect there would be consequences at the level of content too. Broadly speaking, this article has two pieces, namely, an introduction which has a lot of content in itself, in terms of setting context and so on (but which I think requires a close reading to pull it all out), and a second piece which gives some necessary items - definitions, in particular - and a variety of formulas. I have a clearer sense of why the first part looks the way it does than I have for the second part. Anyway I would keep this general shape but no doubt tilt things more toward the front end. While one can always revert afterwards, if people are attached to the status quo it would be good to know.  Abu Amaal 00:24, 16 April 2006 (UTC)
thread_title:  Proposal: reshape - on second thought 

message: I have now learned that Norman Wildberger thinks that what is controversial is not the content of the mathematics itself.  Not surprising, of course.  Michael Hardy 02:13, 16 April 2006 (UTC)
replies: text: Do you mean "not surprising that Wildberger thinks that", implying that he's mistaken?  --Piet Delport 23:25, 16 April 2006 (UTC)
replies: text: I meant (of course) it's not surprising that Wildberger thinks that, implying that he's obviously right (see my comments above!). Michael Hardy 01:09, 17 April 2006 (UTC)

text: I may add a section on the philosophical and pedagogical points Wilderberg is trying to make. Two points in particular give a rationale for rational geometry - his lack of belief in "non-computable decimal numbers" and his belief that the concept of "angle" is weak. Nick Connolly 19:43, 23 October 2007 (UTC)
thread_title: controversy?

message: With much discussion on Rational trigonometry, I was wondering how many have actually read ``Divine Proportions"?  Best regards, Dmaher 10:21, 1 June 2006 (UTC)
replies: text: I've read some parts of it.  Not the whole thing yet. Michael Hardy 21:50, 1 June 2006 (UTC)

text: Nearly finished it. Had a longish conversation with Wildberger a few weeks ago also.Nick Connolly 20:04, 23 October 2007 (UTC)
thread_title:  Anybody else read it? 

message: It's called rational trigonometry. Is it about a particular book or the mathematics in it? 
If it's the latter, it can include some references to earlier similar work, and if it is the former it should include something about the reactions to the book. As it stands, it seems entirely based on one source. Shreevatsa (talk) 00:57, 1 January 2009 (UTC)
replies: text: Furthermore, the article Norman J. Wildberger appears to derive its notability entirely from its subject's introduction of the notion of rational trigonometry.  Per WP:ONEEVENT, it seems likely that the latter article should be deleted and its relevant content merged here. siℓℓy rabbit (talk) 07:06, 1 January 2009 (UTC)
replies: text: I implemented the merge. —David Eppstein (talk) 03:13, 17 March 2009 (UTC)
thread_title:  What is this article about? 

message: Okay folks, I haven't yet read the book, but I've been enthralled since the moment I heard about the concept of rational geometry.  Not only does this theory fit better with my intuition about real numbers, it accomplishes its primary mission.  It truly is easier to grasp than traditional trigonometry; I remember my struggles from those days.  If I was asked to teach trigonometry, this technique would be my first choice.
What would like to see the article do a better job of, however, is explaining the connection this work has to Universal Geometry, as the book title suggests.  My sense is that it relates to the abstraction of the notions of quadrance and spread to other geometric domains, but this is at best implicit.  70.247.160.102 (talk) 19:48, 20 February 2010 (UTC)
thread_title:  Universal Geometry? 

message: Consider:
* Philip DeFranco -- whose videos I often enjoy.
* Fred Figglehorn / Lucas Cruikshank -- I used to laugh at Fred, but these days his oeuvre seems stale.
* Jared Lee Loughner -- looks like a One Eventer to me.
* Jenna Marbles -- who is sometimes clever and funny -- oh, wait, she is up for deletion, but with the following notice: "If you can address this concern by improving, copyediting, sourcing, renaming or merging the page, please edit this page and do so. You may remove this message if you improve the article or otherwise object to deletion for any reason." Wildberger gets no such courtesy. He is gone -- poof -- with no explanation on the page, only the speechless redirect.
Or consider the following mathematicians:
* Robin M. Williams
* K. S. Amur
* Tatomir Anđelić
* George Anderson (mathematician)
* Ben Andrews
For perspective, look at Wildberger's research page. He is not just all about rational trigonometry. 
Are certain editors guarding the gates here -- against repeated attempts to put this man in, as I did yesterday, only to have that deleted overnight? I have nothing to do with Mr. Wildberger, and only read about him yesterday via a tweet from a mathematics professor. I looked up his name and found this odd redirect.
Incidentally, if you want to question my impartiality in some other way, know that I dislike creationism, and that I agree that so far Wildberger is a one-trick pony in terms of the public eye, or among mathematicians. But so is Jared Loughner -- or is he actually famous for more than just that shooting spree? And get this: Kim Kardashian "is known for a sex tape with her former boyfriend Ray J as well as her E! reality series that she shares with her family, Keeping Up with the Kardashians." Now, if Norman Wildberger could possibly make a sex tape and put that up on Youtube along with his lectures, he'd stand a better chance of getting a page in WP. Dratman (talk) 23:18, 18 September 2011 (UTC)
replies: text: Despite all the wikidrama which comes up from time to time, WP:N isn't all that complicated, and can be roughly summarized as "if you think the article should be kept, find more reliable sources independent of the subject". Most of the above arguments seem like WP:OTHERSTUFF. Last time I looked for sources on this, I found more for rational trigonometry than for Wildberger (not unusual for academic topics), and I added a few to the article. Kingdon (talk) 14:49, 24 September 2011 (UTC)

text: A decade later, I think you could certainly come up with enough material in third-party sources to write a defensible Wikipedia article about Wildberger himself, independent from his book or specific topics. Plenty of the chatter about him is based on self promotion and artificially hyped controversy, but there are also enough independent "reliable sources" to fill out a short encyclopedic biography, if someone is willing to put in the work. –jacobolus (t) 22:54, 7 May 2023 (UTC)
thread_title:  Wildberger should have a biographical page 

message: If the underlying field has a square root of -1, then the line L with that slope is pathological.  (For example, in F_13, this would be a line x+5y=constant or x-5y=constant).  Any two points on L have quadrance 0, but are not identical.  The spread between L and any other line is infinite.  What does Wildberger say about this case?
The Pythagorean Theorem section states:
:The lines A1A3 (of quadrance Q1) and A2A3 (of quadrance Q2) are perpendicular (their spread is 1) if and only if:
:: Q_1 + Q_2 = Q_3.\,
but the proof only goes in one direction.  In fact the converse seems to be false: in a field of characteristic 2, all triangles are Pythagorean (Q_1 + Q_2 = Q_3), but not all spreads are 1.  Does the "iff" apply only when the characteristic is not 2?
Joule36e5 (talk) 11:11, 26 July 2012 (UTC)
thread_title:  Pathological cases 

message: Please, someone check if all links pointing here are indeed necessary. I have come here from Hyperbolic geometry, and spent a lot of (unhappy) time trying to understand this "theory" with no results. So I relied to Mathscinet and Zentrlablatt, which, at least, confirmed that I am not the only one who does not understand! As I have added to the page, there is a secondary source asserting that it is not clear what [the author's geometry] is.  The review (by Victor V. Pambuccian for Mathscinet) is in fact even cruder When using venerable names, such as "hyperbolic" and "geometry", one expects to find an axiom system... and a representation theorem for that axiom system, describing all models of it.... None of it is happening here, so we have no idea what precisely "universal hyperbolic geometry" is. And Anyone wanting to actually learn "universal" metric geometry should, instead of this paper, study Bachmann's book [Aufbau der Geometrie aus dem Spiegelungsbegriff, zweite ergänzte Auflage, Springer, Berlin, 1973;], a paper by Struve and Struve [H. Struve and R. Struve, Z. Math. Logik Grundlag. Math. 34 (1988), no. 1, 79-88] as well as their other paper [J. Geom. 98 (2010), no. 1-2, 151-170], R. Lingenberg's [Metric planes and metric vector spaces, John Wiley & Sons, New York, 1979], and R. Frank's [Geom. Dedicata 16 (1984), no. 2, 157-165; (which is what I am going to do, rather than staying here).
By the way, I believe that the page should be kept, provided it is clearly explicitly stated that, so far, professional reviewers have found the theory unclear. Indeed, Wildberger has also written a lot of other books and papers on important journals.--78.15.196.22 (talk) 17:03, 6 September 2013 (UTC)
replies: text: PS: to be clear, I do not mean that Wildberger's book contains errors, actually I do not think so. It simply appears that it contains just only a part (the simplest part) of trigonometry, and that it is really far from getting some kind of "Universal Geometry", whatever this means. This is also confirmed by Franklin's review, when he says "It is true that there is a need to retain the “circular” or “harmonic” functions to deal with circular motion, Fourier analysis and the like...". How this can be inserted into Wildberger framework I really do not understand. It looks like someone wanting to "simplify" the theory of the algebraic sums of integers just by considering only sums of positive numbers... Of course the resulting theory is simpler ;) but I call this a restriction, not a simplification!--78.15.196.22 (talk) 17:33, 6 September 2013 (UTC)
thread_title:  Too many links pointing here 

message: I think this article should be deleted, the only sources explaining how this theory works comes from Wildberger's book which surely cannot be a third party source. There are no other reasonable sources on the topic because the theory isn't actually used by anyone else, and thus is not notable enough for a wikipedia page.  — Preceding unsigned comment added by BBF3456789 (talk • contribs) 01:27, 12 November 2013 (UTC)
thread_title:  Deletion 

message: My impression is that Wildberger's main interest is not so much to simplify trigonometry as to eliminate infinity from mathematics. The page should make this clear. Tkuvho (talk) 12:07, 25 November 2013 (UTC)
thread_title:  Wildberger against infinity 

message: The Plimpton 322 tablet has recently been claimed to be a trigonomic table using the rational approach:
https://phys.org/news/2017-08-mathematical-mystery-ancient-babylonian-clay.html
207.224.80.52 (talk) 03:24, 25 August 2017 (UTC)
thread_title:  Babylonian precedent 

message: The page, as it is currently written, says "The laws of rational trigonometry, being algebraic and 'exact-valued'..." This is not correct. This phrase implies that rational numbers are "exact" and that irrational numbers are not. There is nothing "inexact" about irrational numbers or real numbers in general. For example, the exact solutions of  x^2 - x - 1 = 0  are the golden ratio and the silver ratio, two irrational numbers, for example. There is nothing approximate about them. Any solutions other than these two would be, at best, approximations to the actual solution. If you use a number system that does not permit irrational numbers, then the equation  x^2 - x - 1 = 0  has no exact solutions, just as the equation  x^2 + 1 = 0  has no solutions if you limit your number system to the real numbers. Matheducator22 (talk) 05:49, 1 May 2019 (UTC)
replies: text: WP:SOFIXIT .  –Deacon Vorbis (carbon • videos) 12:32, 1 May 2019 (UTC)

text: And if you approximate rational numbers as decimal or binary or floating point then the algebra becomes just as infinite. There is nothing special about rationality here. —David Eppstein (talk) 08:09, 5 May 2019 (UTC)
thread_title:  Erroneous conflation of "exact values" with rational numbers 

message: The article emphasizes the self-published nature of the book, which I think goes overboard in this case, and leads to UNDUE and BLP.   The implication of self-published, together with all the other criticism included in the article is that the book is a vanity publication, crackpotry or something that would not have passed review at an academic press or a peer-reviewd journal.   But that is not true here; the mathematics is undisputedly correct and competent, and any controversy or skeptical reviews concern the claims about advantages of Wildberger's approach compared to the traditional ones.
There are a quite a few mathematicians who have become publishers and sellers of their own books in the age of LaTeX and journal boycotts.  Nobody criticized Michael Spivak's books on differential geometry, or Thurston's notes on 3-manifolds, for being essentially self-published.  I don't think Wildberger's book has to be of that quality for him to not be cast as the operator of a vanity press. 73.89.25.252 (talk) 18:57, 31 December 2020 (UTC)
replies: text: It's only because I've been typically putting who wrote a book and how it was published into the lead for lack of a better place to put it. In this case it happens to be self-published. I don't think it ended up being important to how it was received — most self-published works and even many conventionally published books don't get this level of published book reviews — but it should be mentioned somewhere. Compare Adventures Among the Toroids, another article I wrote about a self-published book (where again I had no intention of implying crankery but self-published went into the lead for lack of a better place to put it). —David Eppstein (talk) 19:43, 31 December 2020 (UTC)
thread_title:  Undue weight on self-publication 

message: Cited is a review by Laura Wiswell, who is unknown to the Internet and appears to be Laura Wisewell, then a mathematician at Edinburgh, with the name misspelled in the source.  Since Ms. Wisewell has died it is hard to confirm this, and the document is listed under the misspelling, things could be left as they are with a note in the reference, but if there is sufficient confidence in the determination of the true author it would make sense to correct it throughout the article.  What sayeth thou, WP? 73.89.25.252 (talk) 21:08, 1 January 2021 (UTC)
replies: text: Thanks for catching this. It seems clear that they are the same person. I think we should just silently correct the typo. —David Eppstein (talk) 21:27, 1 January 2021 (UTC)
replies: text:  Changed now in the text, with a silent note on the misspelling in the reference, and the coding of the citations unchanged (to retain the name actually used in the journal). 73.89.25.252 (talk) 22:03, 1 January 2021 (UTC)
thread_title:  Wiswell is actually Wisewell, but... 

message: The redirect Pythagoras' theorem proof (rational trigonometry) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  1234qwer1234qwer4 19:33, 21 April 2023 (UTC)
thread_title:  "[[:Pythagoras' theorem proof (rational trigonometry)]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The redirect Coturn (rational trigonometry) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  1234qwer1234qwer4 19:34, 21 April 2023 (UTC)
thread_title:  "[[:Coturn (rational trigonometry)]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: I'm parking some more citations here, in roughly chronological order, in case they're useful to anyone trying to work on this article. (All of the citations in the current article are reviews published shortly after the book first came out.)
I tried to exclude anything either (a) directly by Wildberger or his students, or (b) that only mentioned his work incidentally (but I did include some articles that merely adopted the name "quadrance" for squared distance). Obviously most of these are not fit for inclusion in this article. But sifting through may help if anyone wants to write sections about influence, applications, etc. Feel to modify the below list if there's anything I missed. There are a lot of masters theses and conference papers here, but also a nontrivial number of journal papers. –jacobolus (t) 03:45, 8 May 2023 (UTC)
replies: text: I am not pushing this as a "breakthrough". But I also don't think it can be dismissed off-hand as trivial, even if Wildberger rubs you the wrong way for his polemical self promotion. Also, Stolfi's book is nice, though personally I think still not the best representation for my own uses. I like Stolfi, who is a Wikipedian, e.g. User:Jorge_Stolfi/DoW/Vogonization. –jacobolus (t) 13:20, 8 May 2023 (UTC)
thread_title:  Works citing Wildberger on rational trigonometry and related topics 

message: The redirect Pythagoras's theorem proof (rational trigonometry) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.   Jay 💬 05:00, 9 May 2023 (UTC)
thread_title:  "[[:Pythagoras's theorem proof (rational trigonometry)]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The redirect Pythagorean theorem proof (rational trigonometry) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.   Jay 💬 05:01, 9 May 2023 (UTC)
thread_title:  "[[:Pythagorean theorem proof (rational trigonometry)]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]