Wikipedia talk:WikiProject Mathematics/Archive/2022/Mar

Meaning of "nodes" as special points in interpolation.
There are 172 articles containing node interpolation except, however, Interpolation itself. Interpolation could read:
 * Interpolation provides a means of estimating the function between and beyond the nodes, for example, at $$x=2.5.$$

(as opposed to at intermediate points ).

I am in doubt, because --Rainald62 (talk) 18:40, 1 March 2022 (UTC)
 * I cannot find a matching entry for this meaning of "node" in Node. If there are other uses of "node" with this meaning (in numerical integration?), which article should the new entry link to?
 * There are only two interwiki links in Stützstelle.

Draft of Analysis of vector-valued curves
User:MarkH21 moved Analysis of vector-valued curves into draftspace in June 2020. It's since been changed substantially and is now at User:Mgkrupa/Analysis of vector-valued curves. Editing of the draft seems to have stalled. I was going to return this back to being an article so it won't be forgotten, but I wanted to give folks a chance to do further cleanup or trim any parts that were unacceptable. Does anyone want to do that in the next few days, or is it good to go now? -- Beland (talk) 21:21, 1 March 2022 (UTC)


 * The problem with that draft is that it looks a bit original research. The article title "Analysis of vector-valued curves" doesn't seem a standard topic name in literature (The Google search returns none). I think it's more of a part of calculus on a topological vector space. Maybe we just need to rename the draft to something like that. (The materials in the draft look legit so there is no need for deletion.) -- Taku (talk) 08:06, 2 March 2022 (UTC)

Draft:Ruler function
Via this deletion discussion, I noticed Draft:Ruler function and did some basic tidying-up and referencing. I think it would stand on its own in mainspace now, but it would have to be moved over a redirect. XOR&#39;easter (talk) 22:55, 1 March 2022 (UTC)


 * I have requested the move at Requested_moves/Technical_requests. (Now that it has more refs, it should be able to survive in mainspace.) -- Taku (talk) 08:09, 2 March 2022 (UTC)
 * Never mind, actually I was able to move it myself: Ruler function. -- Taku (talk) 08:11, 2 March 2022 (UTC)

Schwarz triangle function
Asking for help with this one. The original author was, but he stopped editing the article in February of 2017, leaving it unfinished. From this discussion on his usertalk page, it appears he suffered a stroke sometime in 2017. He's still active, but seemingly in a reduced capacity.

The unfinished article has two major problems. The first is that much of its content is redundant to other articles on Wikipedia such as Schwarz triangle. This content appears to me to be introductory preliminaries that would make sense to move elsewhere. The second is that he stopped right before the section where he talks about the Schwarz triangle function itself, instead of those preliminaries. So it seems to me that aside from a small amount of text I added, this article in its present state fails to address its topic at all!

I am not an expert on this topic and I'm reluctant to radically rework the article without consensus. Mathsci expressed disagreement with me on the article talk page, although has not started working on it again (and may not be able to given the medical issues mentioned earlier). I would really appreciate another editor's view. Apocheir (talk) 01:05, 25 February 2022 (UTC)


 * the page title has been moved to Schwarz triangle tessellation and the application to Schwarz triangle function, as a special case of uniformization, will be added be me (see below). As in the paper of Schwarz, the tessellation and uniformization have never been regarded as separate.


 * The theory concerns the 2 x 2 complex ordinary differential system $$f^\prime(z) = z^{-1}Af + (z-1)^{-1}Bf$$ with regular singular points at 0, 1 and ∞. There are several aspects: (a) the reduction to a 2nd order ODE, Euler integrals, hypergeometric power series and monodromy (Ince); (b) the geometric interpretation using the Schwarzian derivative, Schwarz triangle tessellation and automorphic forms (Caratheodory, Nehari, Hille); (c) the limiting case of the Farey tessellation, modular lambda function and theta constants (Ahlfors, Chandrasekharan, Hardy & Wright).


 * On wikipedia, many things are left incomplete. Concerti grossi, Op. 6 (Handel) [stable]]--> Concerti grossi, Op. 3 (Handel) [unfinished]; Clavier-Übung III [stable] --> Clavier-Übung I [unfinished]. Similarly here, sources have already been listed and specific page references are easy to add. New content mentioned above is easy to summarise; but the explicit formulas with quotients of hypergeometric formulas need more care; similarly the Kummer case of the Riemann sphere and finite groups. It's not clear whether Stillwell's "Papers on Fuchsian Functions by Henri Poincaré" are available online — the reference is good for further reading/commentary. Mathsci (talk) 14:24, 25 February 2022 (UTC)


 * I looked at the article and the one on Schwarz triangles. I was surprised not to see any images of (4,4,4), a tessellation by equilateral triangles with eight meeting at each vertex. It seems to be the most symmetrical (regular) tessellation of the hyperbolic plane. Do we not have any? Nor have I seen any of the related tiling by triangles with angles &pi;/2, &pi;/3, and &pi;/8. Six of these make up one of the equilateral triangles. JRSpriggs (talk) 21:48, 26 February 2022 (UTC)
 * You'd have to look at Commons to find relevant images. I think I spent some time looking for examples. Mathsci (talk) 21:25, 25 February 2022 (UTC)
 * The image was already added to the article yesterday. The equilateral triangles with angle $\pi$/$n$ are important because in the limit they tend to the ideal triangle. If you want images for Schwarz triangle, please look for them on Commons. Mathsci (talk) 22:07, 26 February 2022 (UTC)
 * To Mathsci: Thank you for adding the missing image of (4,4,4). JRSpriggs (talk) 22:18, 26 February 2022 (UTC)
 * I strongly agree with Apocheir's suggestions for reworking the page (same comment left at talk page) Gumshoe2 (talk) 18:58, 25 February 2022 (UTC)


 * Above I mentioned a matrix-valued ODE with regular singular points at 0, 1 and ∞. In 2008, I wrote content on the Knizhnik-Zamolodchikov equations and vertex algebra formalism; by SL(2,C)-invariance of "four-point functions", this reduces to a matrix-valued ODE and its monodromy properties, part of my expertise. Mathsci (talk) 22:14, 25 February 2022 (UTC)

I strongly oppose this move. The definition of Schwarz triangle is a triangle that can be used to tesselate a sphere, the plane, or hyperbolic space. Having a page called Schwarz triangle tessellation is redundant and amounts to a WP:CFORK. -Apocheir (talk) 23:04, 25 February 2022 (UTC)
 * I strongly agree with Apocheir about Mathsci's move of the page Gumshoe2 (talk) 23:06, 25 February 2022 (UTC)
 * you have stated that you know nothing about the area. But you have made a false assertion that is true by definition that any Schwarz triangle automatically defines a tessellation. Caratheodory spends eight pages showing that the tessellation can be constructed in an elementary way, using a convexity argument. Wilhelm Magnus, an expert of tessellation, then just quotes Catheodory. So there is an elementary but slightly lengthy proof; but no rabbit-out-of-the-hat easy proof. Mathsci (talk) 02:46, 26 February 2022 (UTC)
 * I didn't say I know nothing. I said I am not an expert. If I accidentally misstated the definition of a Schwarz triangle somewhat, that does not change the fact that the page currently titled Schwarz triangle tessellation covers much of the same material as Schwarz triangle.
 * I am growing increasingly frustrated with your obstructiveness and unwillingness to cooperate with other editors on this topic. Apocheir (talk) 19:58, 27 February 2022 (UTC)


 * Bourbaki's "Groupes et Algèbres de Lie", Chapters IV & V, is one of the classic sources for "hyperbolic reflection groups", following Tits (and Vinberg). Care has to be taken not to confuse a list (Coxeter-type diagrams) and a proof (triangle/polygon tessellation theorem). The new material on Tits' theorem on fundamental domains follows the standard pattern of editing wikipedia: there is WP:NORUSH. Please see also John Stillwell's English-language "Henri Poincaré: Papers on Fuchsian functions", which contains an excellent historical survey. Thanks, Mathsci (talk) 16:11, 2 March 2022 (UTC)

Draft:Flag algebra
Can a member here take a look at Draft:Flag algebra and help to evaluate if it can go on to the mainspace? There at least three editors (including me, and the other two who have commented on the article directly) passing on evaluating the draft. Thanks! – robertsky (talk) 08:05, 6 March 2022 (UTC)
 * This is about graph theory (not sure that this is immediately clear, even for graph theorists). D.Lazard (talk) 09:31, 6 March 2022 (UTC)
 * Although I don’t have a background in this area, the notability seems ok. There are also enough refs. As Lazard points out, the intro can be improved to give a better context. I would say it’s fine to move it to mainspace. —- Taku (talk) 04:45, 7 March 2022 (UTC)

merge ?
I would like to suggest merging Cantor's theorem (disambiguation) into Draft:List of things named after Georg Cantor, but I'm wondering if the former can be merged into an article that didn't pass AfC. --SilverMatsu (talk) 02:40, 7 March 2022 (UTC)


 * I have moved the draft to mainspace (the afc judgment was wrong in my opinion). The disambig page isn’t really an encyclopedia article; it’s more of a navigation page. So, I don’t know if it is a good idea to merge the two pages. —- Taku (talk) 04:40, 7 March 2022 (UTC)
 * Thank you your reply. When I added the "Cantor's theorem" to this page, the edit history was tagged as "Tag: Disambiguation links added", which seems useful when I accidentally type only with "Cantor's theorem". So, it might be better not to merge, because I missed it. Also, I agree with moving the draft to the mainspace. --SilverMatsu (talk) 07:28, 7 March 2022 (UTC)


 * By the way, can Draft:List of things named after Henri Lebesgue and Draft:List of things named after René Descartes be also move to the mainspace ? --SilverMatsu (talk) 23:40, 7 March 2022 (UTC)


 * I have moved them to mainspace. But please know you can also move them to mainspace; any editor with some editing history can. —- Taku (talk) 07:07, 10 March 2022 (UTC)


 * Remind me again, what's the advantage of having these lists in separate articles versus having these as sections in the respective articles about Lebesgue/Descartes/Cantor (where it seems they would be more likely to be accessed from anyway)? PatrickR2 (talk) 19:09, 10 March 2022 (UTC)
 * It's essentially a matter of appearance but having a not-so-short list is quite distracting. Also, the "See also" section is generally meant to list items that are not mentioned in the body of the article; in other words, the "See also" section is not meant to be comprehensive while lists are meant to be comprehensive. By the way, List of things named after Georg Cantor is still underdeveloped; it shouldn't just list items but list them with some short descriptions. --- Taku (talk) 12:54, 12 March 2022 (UTC)
 * I did not suggest to put this in the "See also" section, but rather in a separate section. PatrickR2 (talk) 03:54, 14 March 2022 (UTC)
 * The fact that there are generally no "list named after" sections in bio articles seems to indicate that people find a list distasteful (so we put it in a separate article). I should have said it’s a matter of aesthetic. Encyclopedic articles with long lists or tables are less preferred than texts, it seems to me. —- Taku (talk) 07:38, 14 March 2022 (UTC)
 * It's a good use case for Summary style. The biography can have a section on major accomplishments, short enough so as not to overwhelm the article and also including the major accomplishments that happen not to be named after the subject, while a more comprehensive list can be linked at the start of the section. ——David Eppstein (talk) 07:59, 14 March 2022 (UTC)
 * Makes sense. Thanks. PatrickR2 (talk) 22:06, 15 March 2022 (UTC)

Draft:Linear form for special categories of Pythagorean triples
Will someone please take a look at this draft? Robert McClenon (talk) 05:11, 13 March 2022 (UTC)
 * Never mind. I realized that this is not higher math, and so I can review it myself, and I have declined it as reading like it was copied from a textbook.  Robert McClenon (talk) 05:16, 13 March 2022 (UTC)
 * It would certainly be much better if it were copied from a textbook. It is WP:OR, and I have explained why in a comment on the draft. D.Lazard (talk) 17:46, 16 March 2022 (UTC)

Draft:Polynomials calculating sums of powers of arithmetic progressions
Will someone please look at this draft and at the one listed above? They both look as if they were copied from a mathematics textbook. Should the submitters be asked whether this is a class exercise? Robert McClenon (talk) 16:09, 16 March 2022 (UTC)
 * IMO, there is nothing to keep in this draft. I have left a comment on the draft for explaining this. D.Lazard (talk) 17:31, 16 March 2022 (UTC)
 * User:D.Lazard - Thank you. I thought so, but I'm a computer scientist, not a mathematician.  Robert McClenon (talk) 16:19, 17 March 2022 (UTC)

Elaborate code for notation
In the article titled π I found the following and thought maybe they've finally fixed a but in the way TeX code gets rendered:

Here's the code:

That someone took the trouble to create this suggests that the bug that prevented it from being done properly in TeX code is still there. Is this a bug that it is hopeless to fix between now and the end of Eternity? 15:30, 19 March 2022 (UTC)
 * This workaround is discussed in Help:MATH. D.Lazard (talk) 15:56, 19 March 2022 (UTC)

Latin Letters used in Mathematics
Dear WikiProject Mathematics,

Hello, I am a new editor on Wikipedia! When I first started editing, the Wikipedia algorithm suggested that I started referencing the Latin letters used in mathematics article. However, I was surprised to see that there were absolutely no citations. I started to add some, however, I am still in high school and I have only just finished learning about trigonometry. Therefore my knowledge is limited and I could use some help from more experienced editors, like you, to fully reference this incredibly important article. Thanks for your time Kabiryani (talk) 18:27, 23 March 2022 (UTC)
 * I have changed the name of the article into List of mathematical uses of Latin letters, because this reflects more accurately the content of the article. D.Lazard (talk) 20:26, 23 March 2022 (UTC)
 * That seems reasonable. --Trovatore (talk) 20:30, 23 March 2022 (UTC)
 * This change presents a problem however because scientific uses of these letters are also present in the list. Kabiryani (talk) 14:49, 24 March 2022 (UTC)
 * What about letters that have a special meaning when used in conjunction with an integer, e.g., $$\mathrm{H}_n(T,G)$$, $$\mathbf{T}2$$, $$\mathbb{R}^n$$? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:33, 23 March 2022 (UTC)
 * Earliest Uses of Various Mathematical Symbols may be helpful for some of this. XOR&#39;easter (talk) 01:16, 24 March 2022 (UTC)
 * Thank you for this source! Kabiryani (talk) 14:49, 24 March 2022 (UTC)
 * Thank you for this source! Kabiryani (talk) 14:49, 24 March 2022 (UTC)

"a combinatorial theory"
Our article titled Structural rigidity begins thus: "In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges." I have qualms about the phrase "a combinatorial theory". What phrase ought to be there, if any? Michael Hardy (talk) 19:36, 23 March 2022 (UTC)
 * Postscript in response to comments below: When I posted the above, it had never occurred to me that anyone might think I was expressing any qualms about the word "combinatorial."  Michael Hardy (talk) 17:40, 25 March 2022 (UTC)


 * Perhaps: "In discrete geometry and mechanics, structural rigidity is a theory describing the combinatorial aspects of rigidity for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges." -- 20:05, 23 March 2022 (UTC)

Why do you think "combinatorial theory" is incorrect? This theory largely concerns itself with combinatorial structures (often graphs or matroids) describing which subsystems of a system of interlinked objects are rigid, and which aren't. (MV's answer above addresses the details of wording, but not really the issue of whether this theory is combinatorial, which is what I interpreted your question as pointing to.) —David Eppstein (talk) 20:11, 23 March 2022 (UTC)
 * I guess it comes down to what you consider combinatorics, which is one of these categorization discussions that tend to be unsatisfying. It doesn't seem to be about counting things, and most "classic" combinatorics is in one way or another about counting things.  I don't really consider graph theory to be a subfield of combinatorics &mdash; it's a separate are of discrete math that overlaps with combinatorics.  That said, rigid boundaries between fields tend to be unhelpful, and I can see that this is at least combinatorics-adjacent. --Trovatore (talk) 22:37, 23 March 2022 (UTC)
 * Our article combinatorics says that it concerns both counting and "properties of finite structures." The Mathematics Subject Classification lists counting (05Axx) as only one of five major subdivisions of combinatorics, with graph theory (05Cxx) as another. Matroids are either under a third (05Bxx, Designs and configurations) or under 52-XX (convex and discrete geometry). —David Eppstein (talk) 22:46, 23 March 2022 (UTC)
 * I'd need convincing with good citations to mention combinatorics in the lead. It is not mentioned elsewhere in the article nor for instance in Flexible polyhedron. Any combinatorics is a small part of it rather than anything major. The lead shouldn't say things that are completely absent in the body of the article. NadVolum (talk) 10:56, 24 March 2022 (UTC)
 * Agree with : the theory is partly or even mainly about the combinatorics of the system. Although the word combinatorial does not appear below in the article, it does appear in that for most or all of the objects described in the Mathematics of Rigidity section.  I do like 's alternative wording a little better than what is in the article currently. Russ Woodroofe (talk) 12:02, 24 March 2022 (UTC)

I don't think it is a major issue one way or another; as far as I can see, the topic is combinatorial exactly in as much as it is at the intersection of discrete geometry and mechanics, so that it is justifiable but unnecessary to say. I am more dubious of the word "predicting" which seems overly specific. Maybe it could just say something like "... structural rigidity is a topic dealing with the flexibility of ensembles  ..."? Gumshoe2 (talk) 12:05, 24 March 2022 (UTC)

You wrote "Why do you think "combinatorial theory" is incorrect? This theory largely concerns itself..." This WHAT largely concerns itself....?? Maybe the theory of structural rigidity concerns itself with something. I expected to read that structural rigidity is a property of something, and that those things possessing that property are called structurally rigid things. Michael Hardy (talk) 17:32, 25 March 2022 (UTC)

"I guess it comes down to what you consider combinatorics" No, it doesn't. I never had an issue with that. You are the one introducing that issue. Seem my comment addressed to David Eppstein above. Michael Hardy (talk) 17:36, 25 March 2022 (UTC)
 * Ah. I completely missed that.  I suppose "structural rigidity" does indeed sound like a property, though tacitly reading an unwritten "the study of" does not cause me much distress. --Trovatore (talk) 18:23, 25 March 2022 (UTC)
 * You can call something a geometry or you can talk about geometry, the theory of geometric objects. You can call something an algebra or you can talk about algebra, the theory of algebraic structures. In the same way, you can say that something is structurally rigid, and call the property that it has structural rigidity (although usually in this area more specific terms are used), while also talking about structural rigidity, the theory of structures that have this property. We don't need to tack on extra "theory" filler-words: "the theory of geometric theory". —David Eppstein (talk) 18:32, 25 March 2022 (UTC)

Requested move at Talk:List of linear algebra topics
There is a requested move discussion at Talk:List of linear algebra topics that may be of interest to members of this WikiProject. Favonian (talk) 18:36, 28 March 2022 (UTC)

Draft:Glossary of linear algebra
Just to let people know that I have amalgamated the glossary of linear algebra from Wiktionary with those terms from Vector_(mathematics_and_physics) that appear to genuinely belong to linear algebra to a bare-bones glossary of linear algebra draft here. Needless to say, much that is indispensable to such a glossary is still missing. Any contributions very welcome! Glossary of linear algebra currently redirects to List of linear algebra topics, which should really be at Outline of linear algebra and currently has a navigation box leading to the Wiktionary glossary. Felix QW (talk) 15:55, 25 March 2022 (UTC)
 * Good work. I support to move it in the main space. Some suggestions:
 * The links to dab pages that remain must be disambiguated (I did this, except for the entry "Vector space")
 * Curently, some definitions contain terms of the glossary that are linked to the corresponding article. I seems better to link them to the entry in the glossary. For example, in the entry "Dual space", the phrase "linear form" is linked to Linear form instead of to the entry "Linear form" of the glossary. I did this change for two occurrences of "basis", and this required to modify the entry Basis.
 * D.Lazard (talk) 17:57, 25 March 2022 (UTC)
 * Very good suggestions! I must confess that I don't really understand the issue with the anchors though - for instance, the internal link to Draft:Glossary of linear algebra seems to have worked before and after the corresponding change by User:D.Lazard? Felix QW (talk) 21:36, 25 March 2022 (UTC)
 * The glossary has been moved to mainspace! Thank you everyone for your contributions! Felix QW (talk) 20:31, 28 March 2022 (UTC)

l-adic sheaf
I added a paragraph on why lisse sheaves are necessary in place of local systems here: ℓ-adic_sheaf. I read this from an article, which is cited in the entry. In the article it uses a specific scheme (a nodal curve) for demonstrating the counterexample but I found it works for general schemes (I might be wrong . Please tell me if so.) Please review this edit. Sorry in advance for this is my first edit on Wikipedia so there might be guidelines or requirements that I'm not properly following. Thanks. --Fourier-Deligne Transgirl (talk) 02:49, 26 March 2022 (UTC)
 * Welcome! Wikipedia is full of guidelines and requirements, most of which make sense if you think about them from the right perspective. (I wrote a brief introduction to the most common Wikipedia jargon here.) For example, Wikipedia isn't a platform for new ideas. Instead, we summarize what has already been written elsewhere. That's all we can do, given the nature of the project and the tools we have to work with. We don't have the infrastructure for formal peer review, it's hard to tell who contributed what to any article, and plenty of us are pseudonymous anyway. XOR&#39;easter (talk) 03:36, 26 March 2022 (UTC)
 * Many math articles in Wikipedia lack a discussion of motivation. This is NOT because such mentions of motivations are superfluous but because no one has bothered to add such discussions. So, adding motivations is unequivocally welcome (assuming the correctness of course). As for editing Wikipedia, the way things work here  is that the edits undergo the natural selection: the good edits will survive while the bad edits get slaughtered. This applies to the editors as well; if someone keeps making unconstructive edits, he or she will be banned from editing Wikipedia. In other words, as long as you are being constructive to the project, you shouldn't get into trouble or if you do, other editors will get behind you. -- Taku (talk) 11:24, 26 March 2022 (UTC)
 * I'll echo this -- many math articles are sorely lacking in this area and help is definitely appreciated. - CRGreathouse (t | c) 02:37, 27 March 2022 (UTC)
 * As an aspiring mathematician, I'm sure my intention is to add correct explanations of the topic. Yet there are times where I might be wrong and thus requires review and correction. I hope my contributions are constructive enough so that I don't get banned. That being said I'm only an undergraduate majoring in mathematics so my understanding of a lot of things will definitely be insufficient. BTW I noticed the page about pro-etale site is not created so maybe I will spend some time on creating it next few days. Thank you all for the support! --Fourier-Deligne Transgirl (talk) 08:38, 29 March 2022 (UTC)