Talk:Arithmetic billiards

I am not a math expert, but I think I understood this enough to edit. Please let me know if I changed something important to the content. SilkPyjamas (talk) 23:30, 28 January 2025 (UTC)

Nominator: Lee Vilenski (talk · contribs) 12:58, 1 January 2026 (UTC)

GA review

This review is transcluded from Talk:Arithmetic billiards/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Dedhert.Jr (talk · contribs) 10:06, 5 January 2026 (UTC)

@Lee Vilenski. I'll try to review this article, but I need a second opinion if necessary. For now, I'll give quick comments below:

• Avoid "we" per MOS:MATH#NOWE.
  • Oh, very good. I think I've removed all. Lee Vilenski ^{(talk • contribs)} 10:36, 5 January 2026 (UTC)
• Is the generalization proof under WP:CALC or basically unsourced? The fact that GA nowadays is strictly problematic for providing no citation, AFAIK.
  • I've added a source to where it was presumably brought from. Lee Vilenski ^{(talk • contribs)} 20:17, 5 January 2026 (UTC)
• I see that plus.maths.org is a magazine paper originating from the University of Cambridge. So I am surprised.

Dedhert.Jr (talk) 10:06, 5 January 2026 (UTC)

• • Is that bad? Magazines can be reliable. Lee Vilenski ^{(talk • contribs)} 20:17, 5 January 2026 (UTC)

    It is not that bad or good. I actually admonished myself that a magazine can be reliable like The Aperiodical in the article Herschel graph. Dedhert.Jr (talk) 23:46, 5 January 2026 (UTC)

Hi Dedhert, full disclosure. I do have some knowledge of maths, but I don't regularly edit in that area, so there may well be some local formatting that I'm unaware of.

Looking forward to more of your thoughts Lee Vilenski ^{(talk • contribs)} 10:27, 5 January 2026 (UTC)

Some comments:

It would be better to wikilink Recreational mathematics instead of Mathematics.

Sure, done Lee Vilenski ^{(talk • contribs)} 09:34, 6 January 2026 (UTC)

I am worried that the source of Arithmetic billiard by Antonella Perucca, Joe Reguengo De Sousa, and Sebastiano Tronto in 2022 leads to WP:CIRC because of using Wikipedia as its source.

I can't see Wikipedia listed in the sources on that page. Am I being blind? Lee Vilenski ^{(talk • contribs)} 09:34, 6 January 2026 (UTC)

Type "[Wik]" or "wikipedia" through Ctrl+F, then you see the feature. Dedhert.Jr (talk) 02:04, 7 January 2026 (UTC)

Yeah, that's what I've been doing, I get 0/0 entries. Lee Vilenski ^{(talk • contribs)} 21:09, 8 January 2026 (UTC)

Huh. Weird. You can't see, yet I can see. Nevermind about this. Dedhert.Jr (talk) 01:22, 12 January 2026 (UTC)

You have to click on the button labeled “references” before it displays on the page.

Dedhert.Jr also started a conversation on the reliable sources noticeboard here. Mitchsavl (talk) 11:37, 19 January 2026 (UTC)

Checking from the oldid 1331326444, it appears that the first and fourth sources are in common.

Merged. Lee Vilenski ^{(talk • contribs)} 09:45, 6 January 2026 (UTC)

"Time reversible" sounds like WP:NEO.

Removed Lee Vilenski ^{(talk • contribs)} 09:41, 6 January 2026 (UTC)

Have we heard about the theorem, lemma, or statement that generally requires a proof?

I'm not sure what you mean. Lee Vilenski ^{(talk • contribs)} 09:41, 6 January 2026 (UTC)

Basically, when I was looking at the section of "Proof", what statement are you trying to prove? Dedhert.Jr (talk) 01:52, 7 January 2026 (UTC)

I guess it's not really a proof. I've changed it to "mirror images" as that is what the section is talking about. As it's geometry, it's not really to be proved, rather it's a way of displaying lcm, etc. Lee Vilenski ^{(talk • contribs)} 21:07, 8 January 2026 (UTC)

Hit by Google Scholar, maybe you can add the different approach from different authorship, connection with pseudo-arithmetic billiards , the generalization of three-dimensional arithmetic billiards, and ${\displaystyle n}$-dimensional arithmetic billiards . Interestingly, the latter source gives the open problem. See more .

I'll take a look at these. Lee Vilenski ^{(talk • contribs)} 09:45, 6 January 2026 (UTC)

I had a look, and I think the math behind some of this is a bit beyond me. I am pretty confident with the information as it is, but I'm not sure how much this needs adding into further thought processes. Lee Vilenski ^{(talk • contribs)} 19:58, 10 January 2026 (UTC)

@Lee Vilenski. I could only think of renaming the "Usage" section as "Further information", which can provide a brief on its generalization in higher dimensions, a different approach, and open problems, although the proposal name is somewhat ambiguous. Adding template {{Unsolved}} might attract audience and editors in List of unsolved problems in mathematics, but AFAIK, the open problem might require multiple sources per WP:NOTABILITY, cmiiw. If you have a better idea, let me know. Dedhert.Jr (talk) 06:49, 11 January 2026 (UTC)

Yeah, we can do that. I do think we'd need more sources that talk about the open problem for it to be notable enough for inclusion, rather than a thought problem that was created by one. I'll change the section head. Lee Vilenski ^{(talk • contribs)} 11:44, 11 January 2026 (UTC)

One more, since we have three images of examples in arithmetic billiards, how about taking one of those three, explaining the LCM and GCD altogether, and explaining the number of bouncing points of a rectangle with a given length?

• • I've added a piece in the lede image explaining the basics of LCM and GCD. And I've explained one of the other images about the bouncing points. Lee Vilenski ^{(talk • contribs)} 19:54, 10 January 2026 (UTC)

Overall, the article meets GACR of 1, 2, 4, and 5. This remains the GACR 2b, 3, and 6. But it seems that the article has 26.5% of plagiarism from Plus Magazine . Dedhert.Jr (talk) 02:31, 6 January 2026 (UTC)

Personally, I think the EarWig stuff is mostly WP:LIMITED, but we can make a couple of word changes to make it lower. It doesn't look too bad to me. Lee Vilenski ^{(talk • contribs)} 09:44, 6 January 2026 (UTC)

GACR 6 seems ok in my opinion, illustrations seem appropriate enough Crystalite13 (talk) 18:49, 23 February 2026 (UTC)

Update: I cannot prolong the time of reviewing this, and I am not going to fail this nomination. To be more precise, I have no opinion regarding the WP:CIRCULAR source, which means I need to get it from another. Anyone can review the content in more detail than mine, who can pass or fail the nomination. Dedhert.Jr (talk) 01:50, 20 February 2026 (UTC)

If this is regarding Plus Magazine, it is fairly well regarded in mathematics. That particular article was written by Antonella Perucca, an associate professor in mathematics from the University of Luxembourg. The EarWig detection seems primarily focused on the definition itself and I agree with Lee that it is a case of LIMITED. The only way to alter it without convoluting the phrasing is to use uncommon names for LCM, GCD, and natural numbers. MB2437 09:06, 23 February 2026 (UTC)

A note on Perucca after digging further. This appears an instance of WP:SELFCITE. She seemingly wrote both the article in question and is the largest contributor to this article's content under the username "Antonellaper" (her final version in December 2018, eight months after her article was published). I would definitely add a second source to ease the COI concerns. MB2437 09:50, 23 February 2026 (UTC)

I don't mind helping! Crystalite13 (talk) 18:40, 23 February 2026 (UTC)

Some general notes are MOS:CAPFRAG in the second and fifth images; a fair few instances of WP:4THWALL i.e. instructing the reader to "give", "suppose", "consider", etc. although MOS:MATH#TONE is relatively neutral on the matter; and no WP:ALTTEXT for the images.

I have some concerns over 3a (broadness). There is no history of the method. Who theorised it and when? When did it first appear in academic literature? Is it closely related to other methods? There is no mention of alternative/historical methods, if there are any. The article discusses the method itself, but nothing else surrounding it besides citing some further information, which would be better as a list after references.

The physical contrast with billiards should probably be expanded—i.e. weightless ball on a smooth surface with elastic collisions—given its prevalence in education of the method. MB2437 09:39, 23 February 2026 (UTC)

Agree with this: 3a could use some work. Crystalite13 (talk) 18:51, 23 February 2026 (UTC)