Wikipedia talk:WikiProject Mathematics

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Idempotency of entailment

I'm lost. I only got to Stats 3. Please help to source this stub and explain it in an educated layperson's perspective. Bearian (talk) 11:56, 7 March 2025 (UTC)

This article was clearly written for people who already know the subject. It is now a redirect. D.Lazard (talk) 15:25, 7 March 2025 (UTC)

That is sadly true of many math articles. —Tamfang (talk) 19:42, 7 March 2025 (UTC)

Not all mathematics topics have its own article, I suppose. WP:NEED? Dedhert.Jr (talk) 07:02, 10 March 2025 (UTC)

@Tamfang: I doubt it's true that most math articles are written for people already aware of the article's topic. It is true that most are written for people with expertise in the field, though. Michael Hardy (talk) 23:13, 24 March 2025 (UTC)

Trapezoid article's problem

Apparently the Trapezoid's American English writes differently than the British trapezium, and I'm having trouble with the content including the characteristics while I'm trying to improve it, and even to understand it;WP:UNDUE???. Yet, the remainder of the article seems to talk about inclusive definition, rather than exclusive; so what happens if the article contains both definitions? Dedhert.Jr (talk) 06:45, 10 March 2025 (UTC)

Mathematics texts should try to always use the inclusive definitions in this and similar cases. The exclusive definitions are historical relics that are confusing and lead to a proliferation of ugly case analyses. However, it is essential to explain the difference at the top of an article like this, because both versions are commonly found. –jacobolus (t) 07:13, 10 March 2025 (UTC)

While we're at it, Rhomboid should probably be merged into Parallelogram. The slight variation of definition isn't sufficient basis for an independent encyclopedia article. –jacobolus (t) 07:29, 10 March 2025 (UTC)

I agree and have tagged them for a proposed merge. Interested editors are invited to participate in a discussion at Talk:Parallelogram#Proposed merge from Rhomboid. —David Eppstein (talk) 07:56, 10 March 2025 (UTC)

Indeterminate equation

Is this really a thing? The article was created by Jagged 85, which is one point of suspicion, and the sources are very poor, disagree with each other, and don't support any of the article content. 100.36.106.199 (talk) 01:42, 14 March 2025 (UTC)

It's a pretty well-ramified concept in algebra, to answer your question. Remsense ‥ 论 01:47, 14 March 2025 (UTC)

Maybe merge (redirect) to Diophantine equation

In the third century Diophantus attempted a systematic study and in fact nowadays indeterminate equations are often called Diophantine equations.

• Keng, Hua Loo, and Hua Loo Keng. "Indeterminate equations." Introduction to Number Theory (1982): 276-299.

Johnjbarton (talk) 01:55, 14 March 2025 (UTC)

This suggests that it's a thing, although not either the thing the sources say nor the thing that occupies most of the text ... 100.36.106.199 (talk) 02:00, 14 March 2025 (UTC)

Huh? "Indeterminate equations" are a notable topic covered in Diophantine equation. Johnjbarton (talk) 02:03, 14 March 2025 (UTC)

I can't find any mention of "indeterminate equation" in the article Diophantine equation. Maybe I misunderstand you.

Is the definition given at Indeterminate equation (an equation having more than one solution) even correct? The source cited is not obviously reliable to me. Mgnbar (talk) 02:33, 14 March 2025 (UTC)

The source discusses plural "Indeterminate equations" and says they are equivalent to Diophantine equations. I added the ref to Diophantine equations. The singular form "indeterminate equation" would, I suppose, have to be a single equation with have 2 or more unknowns and addition constraints (eg integers only). Thus it would be a "Diophantine equation", an exact match to Diophantine equation.

The definition "an equation having more than one solution" is not correct: it is incomplete per the above source:

• By indeterminate equations we mean equations in which the number of unknowns occurring exceed the number of equations given, and that these unknowns are subject to further constraints such as being integers, or positive integers, or rationals etc.

At least in my opinion a book published by Springer with >1500 citations should count as a reliable source.

Also in my opinion you should boldly redirect the article with two lame web cite sources to Diophantine equation. Johnjbarton (talk) 03:03, 14 March 2025 (UTC)

Redirecting or merging Indeterminate equation into Diophantine equation is blatantly non sensical:

• in the context to Diophantine equations, the phrase "indeterminate equation" is never used.
• the phrase "indeterminate equation" is used only for equations for which the real or complex solutions are sought.
• The equation ⁠$\sin x=e^{y}$⁠ is clearly indeterminate, but has nothing to do with Diophantine equations.

The only relationship between the two concepts is that Diophantine equations become indeterminate equations when considered as equations over the real or complex numbers. D.Lazard (talk) 09:46, 14 March 2025 (UTC)

Neveertheless, the article Indeterminate equation is very poor. I suggest to merge it into Underdetermined system, the correct name for the concept. D.Lazard (talk) 10:01, 14 March 2025 (UTC)

Johnjbarton, both my second comment and Mgnbar's comment are about the Wikipedia article Indeterminate equation and the sources therein. 100.36.106.199 (talk) 10:26, 14 March 2025 (UTC)

The two sources of the Wikipediaarticle Indeterminate equation are clearly unreliable, per WP:reliable sources. Moreover most of the content of the article is not supported by these sources, and is blatant WP:Original research, for example, when asserting that quadratic equations are indeterminate equations. So, I'll redirect the article to underdetermined system, and adding there a definition of the phrase "indetermined system". D.Lazard (talk) 11:26, 14 March 2025 (UTC)

@D.Lazard can you explain why you reverted my edit on Diophantine equation? Are you claiming that the source is unreliable? On what basis? Are you claiming that my edit which simply asserted

Diophantine problems or "indeterminate equations" have fewer equations than unknowns and involve finding integers that solve simultaneously all equations.

is an incorrect summary of the source which says:

In the third century Diophantus attempted a systematic study and in fact nowadays indeterminate equations are often called Diophantine equations.

? Do you have any source that backs your claim that "Indeterminate equation" should redirect to "underdetermined system"? Johnjbarton (talk) 15:57, 14 March 2025 (UTC)

Do you have a better target for a redirect? Do you have a source supporting that the concept is notable enough for having its own Wikipedia article? Do you have a better way to respect Wikipedia policies and guidelines? D.Lazard (talk) 16:19, 14 March 2025 (UTC)

• "Do you have a better target for a redirect?" Yes, as I have already explained and sourced per WP:Verify, Diophantine equation.
• "Do you have a source supporting that the concept is notable enough for having its own Wikipedia article?" I made no such claim, nor is there any reason to do so. The reliable source says directly that the concept of "indeterminate equations are often called Diophantine equations". All we need is a redirect and a sourced equivalence in the article Diophantine equations.
• "Do you have a better way to respect Wikipedia policies and guidelines?" Yes, put my well-sourced edit back unless you have evidence it is incorrect.

Johnjbarton (talk) 16:46, 14 March 2025 (UTC)

Your edit is blatantly incorrect since the equation ⁠$\sin x=e^{y}$⁠ is a indeterminate equation that cannot be viewed as a Diophantine equation.

Also, the definition given in your source is By indeterminate equations we mean equations in which the number of unknowns occurring exceed the number of equations given, and this matches exactly the definition given in Underdetermined system. D.Lazard (talk) 16:58, 14 March 2025 (UTC)

Please give a source for your claim that "⁠$\sin x=e^{y}$⁠ is clearly indeterminate".

You are misquoting the source, which says, as I quoted above:

• By indeterminate equations we mean equations in which the number of unknowns occurring exceed the number of equations given, and that these unknowns are subject to further constraints such as being integers, or positive integers, or rationals etc.

This does not match Underdetermined system. As explained in the intro to that article, the extra constraints make all of the difference. Johnjbarton (talk) 17:18, 14 March 2025 (UTC)

@Johnjbarton This "extra constraints" you mention is a red herring. I have to agree with @D.Lazard that the previous article on "Indeterminate equation" was close to useless (not properly sourced, not a notable concept, etc, etc).

Someone just changed the redirect from Underdetermined system to Indeterminate system, which seems an even better solution. (And note that a single equation can also be considered a "system" of equations, with a single equation.) One limitation of this last article is that it mentions in the lead that it covers any type of equations; but then the rest of article is focused on linear equations exclusively. It would benefit from a non-linear example. Maybe even the equation $\sin x=e^{y}$ for example. PatrickR2 (talk) 20:11, 14 March 2025 (UTC)

You folks are just making stuff up. Do you have a reference for any claim you make?

I completely agree that the article that started this discussion was junk. But indeterminate equations are diophantine. More sources:

• Calinger, R. (1996). Vita Mathematica: Historical Research and Integration with Teaching. United Kingdom: Mathematical Association of America. Page 174, an outline of Algebraic analysis, "Indeterminate or diophantine analysis, which may be view as the second main part of algebra".
• Mordell, L. J. "Indeterminate equations of the third degree." Science Progress in the Twentieth Century (1919-1933) 18.69 (1923): 39-55. "In the meantime more communications, mostly unimportant, have been published upon Diophantine Analysis than upon perhaps any other branch of mathematics"
• Bashmakova, I. G. (2019). Diophantus and Diophantine Equations. United States: American Mathematical Society.

Johnjbarton (talk) 21:51, 14 March 2025 (UTC)

I'll just note that the entirety of volume 2 of Dicksons "History of the theory of numbers" concerns "indeterminate equations" (which is apparently synonymous with what we nowadays call diophantine equations). Tito Omburo (talk) 22:49, 14 March 2025 (UTC)

Maybe "indeterminate equation" was used historically with the meaning of "diophantine equation". But this is not the case nowadays anymore. And therefore, there should not be a separate article about it. The most we could do is mention that term as an old synonym in Diophantine equation. PatrickR2 (talk) 22:59, 14 March 2025 (UTC)

Yeah, its a problem traditionally solved by some kind of disambiguation. Tito Omburo (talk) 23:06, 14 March 2025 (UTC)

• "The most we could do is mention that term as an old synonym in Diophantine equation."

That is exactly what I did. I am asking you kindly put my content back.

Your understanding of the history may or may not be widely agreed. We would know if you had a source. My theory is that "indeterminate" is more widely used when authors are aware of the historical work in China on this topic which was independent of Diophantus. Whether this has worn off since 1982 I do not know. Johnjbarton (talk) 00:53, 15 March 2025 (UTC)

Fwiw, that was me. I don't have any opinion other than it's the natural redirect target for articles that exist at present (a merge or other reconfiguration of content may or may not be appropriate). It seems like indeterminate system (a statement on the space of solutions) is different than underdetermined system (a statement on the number of variables), but I haven't studied any sources so ymmv. Tito Omburo (talk) 20:46, 14 March 2025 (UTC)

The issue here is that the last version of indeterminate equation was pleasant and approachable for high-school students interested in the topic. By contrast, indeterminate system is obtuse and stultifying. At first, do no harm: this is a high-school math topic. Open the doors to the intended audience. This is not about some cutting-edge unsolved conjecture. 67.198.37.16 (talk) 21:59, 14 March 2025 (UTC)

I agree. Tito Omburo (talk) 22:38, 14 March 2025 (UTC)

Being "pleasant and approachable for high-school students" is a good thing, but misleading high-school students is not acceptable. This is what is done by asserting that the examples given are "indeterminate equation", when no common textbook uses this phrase for referring to any of these equations. Also, "multiple solutions" is used in a sense that is the exact opposite of the common mathematical sense: the equation ⁠$(x-1)^{n}=0$⁠ has a single multiple solution. D.Lazard (talk) 09:16, 15 March 2025 (UTC)

Compound of two tetrahedra

• Compound of two tetrahedra → Stellated octahedron  (talk · links · history · stats)     [ Closure: keep/retarget/delete ] 

Compound of two tetrahedra may also be considered as the stellated octahedron, and most sources in Google Books mentions the same. Dedhert.Jr (talk) 05:53, 14 March 2025 (UTC)

Extended content

Comment: @Dedhert.Jr Since Compound of two tetrahedra is not a redirect, this likely belongs at WP:AFD. Plant🌱man (talk) 06:27, 14 March 2025 (UTC) @Plantman I don't think this should be in AfD. The reason is some sources mentions the stella octangula as "compound of two tetrahedra". The problem is the article has no provided sources for many different type of compounds other than stella octangula itself. Dedhert.Jr (talk) 06:35, 14 March 2025 (UTC) @Dedhert.Jr Actually we were both wrong, lol. RfD is only for those pages that are already redirects, not for things that are articles. If Compound of two tetrahedra was a redirect, yes, you'd be correct to put it here. But AFD isn't exactly appropriate either. I think you're looking for Wikipedia:Proposed article mergers. (Anyone - if I'm wrong feel free to correct me). Plant🌱man (talk) 06:44, 14 March 2025 (UTC) @Plantman Oh yeah. How can I forget that. I'm so silly. Dedhert.Jr (talk) 06:45, 14 March 2025 (UTC) @Dedhert.Jr Nah, you're good Plant🌱man (talk) 06:46, 14 March 2025 (UTC) @Plantman Nevermind. Just move out to the WT:WPM instead. Dedhert.Jr (talk) 06:46, 14 March 2025 (UTC) @Dedhert.Jr Well, since you're an expert in that and not me + you proposed this, I'd rather you do it. Plant🌱man (talk) 06:47, 14 March 2025 (UTC)

Members are welcome to discuss. Dedhert.Jr (talk) 06:53, 14 March 2025 (UTC)

• Support merge or maybe just a redirect. I don't think there is any sourceable content at compound of two tetrahedra worth saving and merging. There is a technical difference between a stellation and a compound (the stellation has non-crossing faces with holes in the same planes where the compound has crossing triangular faces) but I don't think it's an important enough difference to have two separate articles. —David Eppstein (talk) 17:40, 14 March 2025 (UTC)

  Merge done. Dedhert.Jr (talk) 03:18, 24 March 2025 (UTC)

Superfluous whitespace caused by math tags inside a blockquote

I noticed that the blockquote in Eadie–Hofstee diagram is rendered with linebreaks after each math tag, creating lots of superfluous whitespace. I tried to fix this in three ways: (i) with displaystyle inside the math tags, (ii) with span tags around the math tags, (iii) by enclosing the math tags inside a table tag inside the blockquote. The first two options did not have any noteworthy effect, while the third one looks like it might be tweaked such that it works for a particular browser setting, yet in a way that would likely not work across various platform/ browser settings. I am thus inviting the collective wisdom here to see whether we can find a workable solution. Thanks for any insights! Daniel Mietchen (talk) 18:19, 14 March 2025 (UTC)

I am not seeing the issue, beyond what looks like "normal" rendering. Tito Omburo (talk) 18:23, 14 March 2025 (UTC)

I also do not see any extra linebreaks in the blockquote, neither on a web browser (Firefox/MacOS/Vector2022) nor on the android app. @Daniel Mietchen: perhaps you can be more specific about the viewing preferences that are causing this problem for you. —David Eppstein (talk) 18:29, 14 March 2025 (UTC)

Thanks for the quick checks. I have posted a screenshot, and in my user preferences, I am using the experimental MathML rendering. -- Daniel Mietchen (talk) 19:04, 14 March 2025 (UTC)

Ok, so post this as a bug wherever it will gain the attention of the people who maintain the experimental mathml rendering. Pinging some of the participants of the most recent discussion on this issue, Wikipedia talk:WikiProject Mathematics/Archive/2024/Oct § Transition to MathML rendering as default, who might know better where to report this: User:Salix alba, User:Tercer, User:Physikerwelt. —David Eppstein (talk) 20:48, 14 March 2025 (UTC)

PS maybe [1] is the right place to report this? —David Eppstein (talk) 00:58, 15 March 2025 (UTC)

I believe it's best to report problems as individual bug reports, e.g. T376546. The task you linked to, T271001 is an umbrella task to keep track of the transition to MathML. Individual bug reports can then be linked in it as subtasks. I wend ahead and created the bug report myself: T389021. Tercer (talk) 21:35, 16 March 2025 (UTC)

Thanks! I was hesitant to do this not having seen the bug myself (because I don't use the experimental mathml rendering) and not knowing whether it might just be a dup. —David Eppstein (talk) 22:23, 16 March 2025 (UTC)

The experimental MathML rendering is nowhere close to ready, and I would not recommend using it to read Wikipedia articles (unless your goal is to test the feature specifically). The maintainers keep threatening to make it the default for poorly motivated/explained reasons, which I sure hope doesn't happen any time in the foreseeable future. –jacobolus (t) 03:49, 15 March 2025 (UTC)

You should try to replace "<math>" with "<math display=inline>" or use {{tmath}} instead of "<math>...</math>". D.Lazard (talk) 21:57, 14 March 2025 (UTC)

Thanks for the suggestion — I tried both, and neither got rid of the line breaks. -- Daniel Mietchen (talk) 23:36, 14 March 2025 (UTC)

@David Eppstein: I've seen similar behaviour with maths formatting inside block quotes. There is a preexisting bug T382267 which covers a similar case. This was caused by the same problem at Dijkstra%27s_algorithm. The bug is medium priority but still unfixed. A workaround used at Dijkstra's was to change <math> to {{mvar}}, not ideal.

The problem seems to be that some part of the system inserts extra <p>...</p> tags, with the closing tag before each <math> tag. I'm not sure what changed with the system, it may not actually be the math component that caused the problem.

It might be an idea to add all pages we see this occuring on to the T382267 bug, so we can keep track of affected pages.--Salix alba (talk): 23:12, 17 March 2025 (UTC)

Confused regarding the origin and the first text on calculus

The debate centers on whether the works of Newton and Leibniz should be considered the first texts on calculus or whether *Yuktibhāṣā* qualifies as such, given its discussion of Taylor series and infinite series expansions of certain trigonometric functions—an argument recently introduced in edits to the Kerala article.It is sometimes said that kerala school work involved early ideas of differentiation and integration like using Infinitesimal as kim pfloker said although they didn't developed the concept of integral and derivative and these ideas were developed by greek and islamic mathematics centuries before kerala school like infinite series and method of exhaution can be considered as calculus. My major question is that whether the first text on calculus should be attributed to the works of Newton and Lebiniz nor it is attributed to yuktibhasa nor it should be attributed to greek mathematician Archimedes. Myuoh kaka roi (talk) 10:44, 16 March 2025 (UTC)

IMHO, the question of what is "the first text on calculus" is nonsensical. Calculus is a corpus of knowledge that has been elaborated upon the time. The great contribution of Newton and Lebiniz was to make it a systematic method of study. Yuktibhāṣā's results may be seen as precursors of calculus, as well as the Greek method of exhaustion and Fermat's method of adequality. There are many other mathematical work that can be seen as precursor of calculus or may be, nowadays, considered as belonging to calculus. Saying that "they are texts on calculus" is pure anachronism. D.Lazard (talk) 11:55, 16 March 2025 (UTC)

Deletion discussion for Differentiable vector–valued functions from Euclidean space

I nominated Differentiable vector–valued functions from Euclidean space for deletion; discussion here. ByVarying | talk 02:54, 24 March 2025 (UTC)

Possible COI editing on Chaos theory and Lorenz system

There was a user who was blocked for a separate reason, but suspected of COI editing. That user (and a sock) seem to have included a number of papers by Bo-Wen Shen on the pages for Chaos theory and Lorenz system, which may constitute COI editing. Could somebody verify that these papers are appropriate for these pages? It's not that I doubt the validity of these papers, but they may be too specific and technical for a wikipedia page. I'm not familiar with these subjects myself.

I'll also post this to WikiProject Physics. Truthnope (talk) 23:36, 24 March 2025 (UTC)

Symmetries of a square

Over on Talk:Square, discussion between User:Jacobolus and myself over the subsection on symmetry (which is, per WP:Summary style, a summary of Symmetry group of a square), has gotten somewhat heated, and additional inputs may be helpful to resolve the discussion. The discussion is long so let me try to summarize more briefly here. From my point of view, the basic disputes are:

• This section of the article currently places more focus on the symmetries themselves and how they act on the square, and only discusses more briefly the fact that composition of symmetries gives them the structure of a group. This was a deliberate editing decision on my part, because I think that is more salient for the square article (the opposite would be true for the symmetry group of a square article) but one that Jacobolus appears to disagree with.
• Jacobolus wants to describe the group multiplication structure by a group multiplication table, in the square article. (There should certainly be such a table in the symmetry group of the square article, and in fact there are three copies of it.) My position is that a table is a form of case analysis that provides no useful information about how each of the cases (64 of them in this instance) were calculated, and that readers of the square article who might actually want to compute compositions of symmetry operations are likely to follow the link to the symmetry group of a square article, so it should not be included here.
• In a (failed) attempt to satisfy Jacobolus's request for more about the group and its multiplication operation, and in an attempt to describe the group in a way that conveys some conceptual understanding rather than an understanding-free case analysis of 64 cases, I added a paragraph [2] on representing the group elements by signed permutation matrices, the group action on the plane by multiplying these matrices with coordinate vectors, and the group operation by matrix multiplication. Jacobolus hates this paragraph and wants this addition reverted.
• Jacobolus appears to think that abstract group theory is a secondary-school level topic; I think it is a sophomore mathematics-major university-level topic. I think we both agree that the matrix representation is also at an undergraduate university level but I think the additional technicality is worthwhile because it conveys some understanding of what the symmetries are and how to generalize them to higher dimensions; Jacobolus disagrees. (I would actually prefer signed permutations to signed permutation matrices but I think that is even more technical.) I think the technicality of abstract groups is not worthwhile in the context of the square article (although it is certainly very valuable elsewhere) because I do not see what understanding it brings; Jacobolus disagrees.

Anyway, additional input to the discussion to stop it from merely being a back-and-forth between the two of us would be welcome. —David Eppstein (talk) 06:42, 27 March 2025 (UTC)

This seems like an exaggerated and emotionally loaded summary, in keeping with what I have found to be heavily hyperbolic discussion on the talk page, so yes, some more eyeballs would be helpful. Anyway, no I don't think it's a secondary-school topic; that's too advanced. This can be explained to primary school students, as was e.g. done by Zoltán Dienes (in multiple different ways, e.g. via physical dancing). It most certainly does not take several years of undergraduate-level mathematics coursework to figure out that e.g. rotating a square by a half turn and then reflecting it vertically is equivalent to a horizontal reflection. –jacobolus (t) 06:51, 27 March 2025 (UTC)

So summarize it yourself. I have tried to describe the dispute as neutrally as I can, to the extent I understand it. If there are parts of the summary with which you disagree, then the point of disagreement would be helpful information. But your bad faith assumptions and tone-policing are not a helpful contribution to this request for additional opinions. —David Eppstein (talk) 06:58, 27 March 2025 (UTC)

I feel like you are being consistently rude, first in our discussion at talk:Square, and now continuing here, and it's starting to really grate. Instead of accusing me of "bad faith" and complaining about "tone policing", I'd appreciate if you tried to cool the rhetoric closer to room temperature. You can easily make the same claims without sarcasm or declarations about what I "hate". (For the record: I do not "hate" your new paragraph; I just think it is distracting and out of place in this context, and would be fit better at Dihedral group of order 8.) –jacobolus (t) 07:11, 27 March 2025 (UTC)

"exaggerated" "emotionally loaded" "heavily hyperbolic" "consistently rude". Who is heating up the rhetoric? —David Eppstein (talk) 07:29, 27 March 2025 (UTC)

Classification of quadrilaterals by their symmetry subgroups. The 8-fold symmetry of the square is labeled as r8, at the top of the image. The "gyrational square" below it corresponds to the subgroup of four orientation-preserving symmetries of a square, using rotations but not reflections.

Let me try to summarize briefly. I proposed we try to add some kind of graphical picture showing the symmetries of the square, which is currently missing from Square, as a more directly relevant and more legible image to illustrate the section § Symmetry than the previous image about quadrilaterals (shown with its caption to the right). My proposal was that we might try to make an interactive diagram using the new "calculator" feature, with some buttons which when clicked would apply the chosen transformation to an image of a square (marked some way so readers could keep track), possibly even with animated rotation or reflection, if the calculator feature can invoke CSS transformations. David Eppstein pointed out that the "calculator" feature seems to have some accessibility issues on mobile devices, so I was trying to figure out if we could make a static image instead, alongside a table showing the compositions of various reflections and rotations, so that readers could try to look at the picture and imagine how different symmetry transformations would compose. David really doesn't like the idea of having an 8x8 table, and made comparisons which I found to be absurdly exaggerated (for example to "big books of log tables" and "going into detail about real analysis" in discussing the definition of side length), as well as dismissing the proposal as a "failure" with "no explanatory value", and suggesting that to describe the composition of two symmetry transformations would necessarily require readers to understand "group homomorphisms, etc etc". I continue to maintain that including a floating image showing the symmetries more clearly above a table of compositions of symmetry transformations would be helpful to readers, and out of the flow of the text enough to not distract others. I proposed such a table is comparable in character to explicitly showing the first several rows of Pascal's triangle as an illustration (which we do on a surprisingly large range of Wikipedia articles), and David compared this to "[making] copies of Pascal's triangle within every Wikipedia article that happens to use a binomial coefficient somewhere", another comparison I found to be very exaggerated. For reasons I can't quite figure out, David interpreted my request for a better graphical depiction of the symmetries of the square and their composition to be a request for additional abstraction or rigor, and added a new paragraph full of explicit matrices. I don't think this new paragraph is helpful in context; I think it makes the section harder to read, requires unnecessary extra prerequisites beyond many of the intended readers of the page, and still doesn't show explicitly how transformations compose (now readers are supposed to work out the composition themselves by performing matrix multiplications). –jacobolus (t) 07:40, 27 March 2025 (UTC)

Perhaps you could explain because I still don't get it: why do you think it is important that readers of the square article be shown the result of composing each pair of symmetries, but that they not be shown any principled way of calculating that composition themselves? What are they going to do with that information? —David Eppstein (talk) 07:47, 27 March 2025 (UTC)

I believe the simplest "principled way of calculating that composition" is to take a graphical square, e.g. a square piece of paper with the same marking on both sides, and try turning it about in one's hands. (Or doing the same in one's mind's eye.) Giving readers a list of matrices and telling them to multiply them with pen and paper is not any more principled, but it does seem significantly more difficult with a dramatically sharper conceptual barrier.

As for what people will do with that information: I suppose that rather depends on whether they are artists, chemists, electrical engineers, video game designers, school mathematics teachers, cryptographers, or group theorists (etc.). This is basic information about the inherent structure of a single square, which is the type of thing I imagine someone going to read an article called Square might be interested in. What will readers do with any of the information in any of our articles? I can only speculate. I can tell you personally I have used this type of information in the past in writing code to generate mathematical sculptures and in writing code to solve and generate puzzles, but I can't pretend other people will have the same interests. –jacobolus (t) 07:57, 27 March 2025 (UTC)

To me the group action is the basic information about a square and the group composition law is secondary. But also, to me, a principled method of calculation is something one could implement in software. "Play with a piece of paper" is not that. The human visual system is very powerful but because of that, things that appear obvious through vision can actually be quite tricky to formalize. That's why I think the matrix representation is a helpful way to go. And it is because the group action, and not merely the group composition law, can be described directly using the matrix representation that I think it is relevant for the square article. Again, I think the square article should focus on the group action, and that the focus on the group composition law is better made in the article on the symmetry group of the square. Representing a group as abstract elements with a composition law is a very powerful idea but one that divorces the group from its action, and I don't think that divorce is helpful in the context of the square article. —David Eppstein (talk) 08:11, 27 March 2025 (UTC)

Both the discussion of group actions and group composition laws and the assumption of a significant fluency with matrix arithmetic and its application to geometric vectors seems out of scope for the early sections of this article, whose readership substantially consists of laypeople. The article Square should be as concrete and explicit as possible, and should aim for less reliance on advanced abstractions and jargon. Giving symmetry transformations names like "horizontal reflection" or "half-turn rotation" and then describing how those compose is not the same as "Representing a group as abstract elements with a composition law". What I am talking about is not "abstract" or "divorced" from symmetry transformations; it is rather extremely concrete, tangible, and immediate. There's no need to dismissively characterize geometric reasoning as "playing" (presumably contrasted with computing sums and products of numbers as real work). It's also not the case that computers cannot be programmed geometrically. Someone can use e.g. Geogebra to program these symmetry transformations explicitly using a graphical tool, with no need to interact with numbers. Mathematicians can also analyze them geometrically with whatever level of rigor they like; the use of numbers everywhere can be a convenience in many contexts, but it's in my opinion mostly an off-topic digression into implementation details better left to some other source, not all that dissimilar from putting a code listing in the same place. –jacobolus (t) 08:22, 27 March 2025 (UTC)

I do not understand well the subject of the dispute. Looking at section § Symmetries, I got several remarks that I tryed to fix:

• The way of saying that the group is transitive on vertices and edges was, at least, very confusing
• The fact that the group is simply transitive on pairs of a vertex and an adjacent edge was not stated.
• The section was pedantic by using uncommon terminology (for example "congruence transformation") and linking to too specialized articles.
• Pedantry occured also by parenthetical links to minor generalizations whose only effect was to distract reading.

As it is presently, the state of the section seems correct to me. If some change is needed, it must be requested clearly. Otherwise, the discussion cannot be conclusive D.Lazard (talk) 12:27, 27 March 2025 (UTC)