Talk:Pythagorean triple

message: Why does the section on Heronian triangle triples in the present article focus on Heronian triangles with distinct side lengths; that is with the property that no two lengths are equal?  This is not a focus of the main article on Heronian triangles.  —Quantling (talk | contribs) 23:29, 26 March 2021 (UTC)
replies: text: I have edited that section of the article so that the emphasis is not on distinct side lengths. —Quantling (talk | contribs) 17:35, 15 January 2022 (UTC)
thread_title:  Heronian triangle triples with distinct side lengths 

message: Should Pythagorean triples, primitive Pythagorean triples, and multiples of primitives, be defined only in the lead paragraph, as in this version A. Or should the extended definition be in the body of the article, and a less technical version reside in the lead paragraph, as in this version B.
Relevant guidelines are MOS:LEAD and WP:TECHNICAL.
LK (talk) 02:46, 12 April 2021 (UTC)
replies: text: * I do not appreciate your disparaging my motives. Kindly explain what an editor should do instead of starting an RfC if he gets into a dispute about content with an editor unwilling to budge? Be honest, D.Lazard – how likely was it that you would not have  reverted any further attempts of mine to edit the lead? Especially after brushing off my objections as nothing.  LK (talk) 02:59, 13 April 2021 (UTC)
thread_title:  RfC: Should an extended definition reside only in the lead? 

message: *I don't think primitive pythagorean triples should be in the first paragraph, but I believe we should still define them in the lede. Much of the article is about primitive pythagorean triples and isn't applicable to the general case. It seems that primitive pythagorean triples are of much greater interest than regular ones. Chess (talk) (please use  on reply) 04:42, 12 April 2021 (UTC)
replies: text: * I do not appreciate your disparaging my motives. Kindly explain what an editor should do instead of starting an RfC if he gets into a dispute about content with an editor unwilling to budge? Be honest, D.Lazard – how likely was it that you would not have  reverted any further attempts of mine to edit the lead? Especially after brushing off my objections as nothing.  LK (talk) 02:59, 13 April 2021 (UTC)
thread_title: Comments

message: Per the discussion above (RFCBEFORE), in relation to this article, is the peer reviewed paper  a primary source? Selfstudier (talk) 21:48, 8 August 2021 (UTC)
thread_title: RfC

message: *No Per WP:SCHOLARSHIP. The paper is also cited by reliable sources, WP:NEWSORG. Subject matter includes material re Plimpton 322 and Si.427 therefore notable.Selfstudier (talk) 21:52, 8 August 2021 (UTC)
thread_title: Discussion

message: For information, I added the following to the Babylonian mathematics article which has a section on Plimpton 322:
According to Dr.Daniel Mansfield, a researcher at UNSW Sydney, speaking about the "surveyor's tablet" Si.427 and its relationship with Plimpton 322, "The rectangles are perfect". The surveyor achieved this by using Pythagorean triples.
 Selfstudier (talk) 10:28, 9 August 2021 (UTC)
replies: text: Sorry, but 2 out of the 3 sources for the actual claim there are press release/churnalism. This looks undue for a broad survey article, which should only state the most essential and solidly established material about Plimpton 322. It's also not particularly informative: what are we supposed to get out of "The rectangles are perfect"? It's a dramatic statement, but not an educational one. XOR'easter (talk) 16:50, 9 August 2021 (UTC)
replies: text: No need to apologize.Selfstudier (talk) 16:53, 9 August 2021 (UTC)

text: The article begins with an extensive summary of the relevant scholarship to date, and is properly sourced (obviously, or it would not have passed peer review). It might therefore make a decent secondary source about the current state of scholarship (excluding the new hypothesis). But even then we should probably wait to see if other scholars use it at such by citing it approvingly. Martijn Meijering (talk) 19:02, 10 August 2021 (UTC)

text: The sentence "The surveyor achieved this by using Pythagorean triples." is stated by NS in their voice and separately from a quote by Mansfield. I am not given to source misrepresentation.Selfstudier (talk) 22:11, 10 August 2021 (UTC)

text: Another respectable RS, Deutsche Welle (DW) Thank the Babylonians not Pythagoras for trigonometry Selfstudier (talk) 22:17, 10 August 2021 (UTC)
replies: text: Why are you still citing press-release churnalism rather than proper scholarship, and calling it "respectable"? —David Eppstein (talk) 22:24, 10 August 2021 (UTC)

text:  Like every other "news" source provided so far, that one quotes no one but Mansfield. It's PR, all the way down. It also makes statements that are downright nonsensical, like  How are trigonometric functions not "numerical relationships"? What is that even trying to say? Who knows? It also implicitly gives Mansfield credit for the discovery that the Babylonians knew about Pythagorean triples, and the interpretation of them as trigonometric; needless to say, that interpretation is decades old. It also says,  The Greek credited as the "father of trigonometry" is Hipparchus; no serious historian of mathematics would make a definitive statement about what Pythagoras did or didn't do, given that exactly zero writings by the man himself survive, and the later sources contradict one another. Let's let the wave of publicity pass and wait for serious commentaries to be written. XOR'easter (talk) 22:38, 10 August 2021 (UTC)
replies: text: I have cited the scholarship that there is (a primary source about a primary source), you just don't like it? If there were any thing else worth citing I would cite that too, it's in the Daily Mail, I left that one out. If there's an RS with something criticizing the article I am sure we will hear all about it in short order.Selfstudier (talk) 22:45, 10 August 2021 (UTC)
replies: text: The problem isn't that I "just don't like it"; the problem is that it's not scholarship. It's clickbait. This is what you get when news media, who can be serious on other topics, get a slick press package about a subject where they have no in-house experience and don't care enough to call around for commentary. XOR'easter (talk) 22:55, 10 August 2021 (UTC)
replies: text: You learn something every day.Selfstudier (talk) 22:59, 10 August 2021 (UTC)

text: Attributing the invention of trigonometry to Pythagoras??? You would think history of mathematics coverage in the press couldn't get any worse; then it hits a new low. Will Orrick (talk) 12:08, 12 August 2021 (UTC)
thread_title:  Babylonian mathematics 

message: *Yes Per WP:SCHOLARSHIP. The paper is also cited by reliable sources, WP:NEWSORG. Subject matter includes material re Plimpton 322 and Si.427 therefore notable. I have not been able to locate criticism of the paper in any reliable source. Should any emerge, it can be added. Two short sentences in the article, which already references Plimpton 322 in its lead, does not seem undue.Selfstudier (talk) 09:16, 10 August 2021 (UTC)
replies: text: The article begins with an extensive summary of the relevant scholarship to date, and is properly sourced (obviously, or it would not have passed peer review). It might therefore make a decent secondary source about the current state of scholarship (excluding the new hypothesis). But even then we should probably wait to see if other scholars use it at such by citing it approvingly. Martijn Meijering (talk) 19:02, 10 August 2021 (UTC)
replies: text: The sentence "The surveyor achieved this by using Pythagorean triples." is stated by NS in their voice and separately from a quote by Mansfield. I am not given to source misrepresentation.Selfstudier (talk) 22:11, 10 August 2021 (UTC)

text: Another respectable RS, Deutsche Welle (DW) Thank the Babylonians not Pythagoras for trigonometry Selfstudier (talk) 22:17, 10 August 2021 (UTC)
replies: text: Why are you still citing press-release churnalism rather than proper scholarship, and calling it "respectable"? —David Eppstein (talk) 22:24, 10 August 2021 (UTC)

text:  Like every other "news" source provided so far, that one quotes no one but Mansfield. It's PR, all the way down. It also makes statements that are downright nonsensical, like  How are trigonometric functions not "numerical relationships"? What is that even trying to say? Who knows? It also implicitly gives Mansfield credit for the discovery that the Babylonians knew about Pythagorean triples, and the interpretation of them as trigonometric; needless to say, that interpretation is decades old. It also says,  The Greek credited as the "father of trigonometry" is Hipparchus; no serious historian of mathematics would make a definitive statement about what Pythagoras did or didn't do, given that exactly zero writings by the man himself survive, and the later sources contradict one another. Let's let the wave of publicity pass and wait for serious commentaries to be written. XOR'easter (talk) 22:38, 10 August 2021 (UTC)
replies: text: I have cited the scholarship that there is (a primary source about a primary source), you just don't like it? If there were any thing else worth citing I would cite that too, it's in the Daily Mail, I left that one out. If there's an RS with something criticizing the article I am sure we will hear all about it in short order.Selfstudier (talk) 22:45, 10 August 2021 (UTC)
replies: text: The problem isn't that I "just don't like it"; the problem is that it's not scholarship. It's clickbait. This is what you get when news media, who can be serious on other topics, get a slick press package about a subject where they have no in-house experience and don't care enough to call around for commentary. XOR'easter (talk) 22:55, 10 August 2021 (UTC)
replies: text: You learn something every day.Selfstudier (talk) 22:59, 10 August 2021 (UTC)

text: Attributing the invention of trigonometry to Pythagoras??? You would think history of mathematics coverage in the press couldn't get any worse; then it hits a new low. Will Orrick (talk) 12:08, 12 August 2021 (UTC)
thread_title: Discussion

message: I just glanced at all of the "Pythagorean Triplets" sites that came up.  I was surprised that Euclid's Formula seems to be the latest word on this topic.  The most innovative switched the parameters 'm' and 'n' to some other letters!
In sum, the sites all repeated the same stuff.  [ljc -- So, nothing new in three millennia.]
I don't have time to write an update of this site now -- based on my look at this problem years ago -- as it would take hours and my notes are not in draft form.  [Don't take this as a 'note on the margin of the page' like a comment about a solution to one famous problem; which solution was never found in that mathematician's papers.]
Further, and more importantly, I got nowhere in trying to add to the "Axonometric Projections" topic-- except for my comments at the end of the 'Talk' section; so won't make an effort here unless I here that someone is interested.  (I couldn't change that article without citing a source, but my own article in 1989 was the source.  You will now find that a DOI for my correction in APA style is included in that comment section; which DOI was issued by the original journal: Engineering Design Graphics Journal.
It isn't hard to generate a table of solutions, based on two parameters.  I initially mentioned my idea to H. Martyn Cundy in private correspondence decades ago.  He was not impressed.  However, I'm sure it's at least as good as Euclid's Formula; upon which it was based.  So I not claim a major breakthrough in Number Theory.  That is to say, it did not impress a famous mathematician (i.e. of "Cundy & Rollett"), but is better than the stuff currently universally offered at the high school level.  Lemchastain (talk) 16:30, 13 January 2022 (UTC)
replies: text: Thanks for your comments. However, Wikipedia policy is that original research is strictly forbidden in Wikipedia, and, on such a topic, everything must have been published in  textbooks. So, your personal notes are useless here. D.Lazard (talk) 18:45, 13 January 2022 (UTC)
replies: text: There is a whole article devoted to Formulas for generating Pythagorean triples.  Perhaps the approach you are looking for is listed there?  —Quantling (talk | contribs) 23:53, 13 January 2022 (UTC)

text: Please read WP:Original research. Publishing your own research in Wikipedia is strictly forbidden per WP:OR, and also WP:COI. D.Lazard (talk) 19:03, 15 January 2022 (UTC)

text: I removed it again, because it was already in the footnotes (in the Dover edition) and your addition made a duplicate reference. —David Eppstein (talk) 00:47, 8 February 2022 (UTC)
replies: text:    This does not surprise me -- although it took you almost a quarter of an hour.  However, I would like to raise a couple of points:  1. You use the word 'again'.  I do not recall trying to list Sierpinski prior to this.  Others may find in the records that I did; or perhaps someone else did.  2.  You speak of "footnotes".  I do not see that term listed in the articles index.  I have searched the references, and no Sierpinski.  In "Notes", #13 does list his name, but only pp. 4-6.   I was trying to list his entire book.  How would you like a 'reference' to Sierpinski(1962), pp. 1-3, and 7-107?   Surely, someone interested enough in this topic to start going through the 'references', 'notes', and 'See also' might well want to know what was written in 1954, and which to a good extent is just being repeated without citation on several Internet sites.  To carry this a bit further, since Euclid is cited (in the Heath translation), why not just 'revert' most of the other repetitive citations.   Also, note 13, does not say explicitly what bit of Sierpinski's writing to which it refers.  He must have written at least 4 other pages on something else at some point.  If anything should be 'reverted' it is such a vague citation as note 13. (talk) Ljc 16:57, 8 February 2022 (UTC)

text: To say nothing (almost) of the difficulty in finding a reference in the 'Notes' section; due to it not being in an alphabetical order and being a bit long.— Preceding unsigned comment added by Lemchastain (talk • contribs) 15:29, 8 February 2022 (UTC)
thread_title:  Lem Chastain comments 

message: Under "Euclid's formula":
An early sentence has "and not both odd" (referring to m and n).
The next sentence has "one of which is even" (referring to same).
I would think it better to use the latter expression in both sentences.
Dave C (talk) 16:50, 11 March 2022 (UTC)
replies: text: I agree, it’s simpler.  I’ve made the change. —JBL (talk) 17:16, 11 March 2022 (UTC)
thread_title:  very minor suggestion 

message: Title: Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
Author: Amnon Yekutieli
Ref: 
American Mathematical Monthly, online open access, 
https://doi.org/10.1080/00029890.2023.2176114
Amyekut (talk) 10:46, 11 March 2023 (UTC)
thread_title:  New paper on this subject 

message: Please update the reference [26]
https://en.m.wikipedia.org/wiki/Pythagorean_triple#cite_note-Yekutieli-26
to the published version of the paper:
Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
Amnon Yekutieli
The American Mathematical Monthly 
Volume 130, 2023 - Issue 4
https://doi.org/10.1080/00029890.2023.2176114
 
https://en.m.wikipedia.org/wiki/Pythagorean_triple#cite_note-Yekutieli-26 Amyekut (talk) 13:50, 6 May 2023 (UTC)
replies: text: —David Eppstein (talk) 18:15, 6 May 2023 (UTC)
thread_title:  Update reference