# Wikipedia talk:WikiProject Mathematics

https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics
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## Squarefree

Is it Square-free integer or Square-free number? The page is being renamed and moved. Bubba73 You talkin' to me? 02:17, 25 September 2021 (UTC)

Square-free number sounds better to my ears, and most articles on special classes of integers are named "Something number" (example: Fibonacci number not Fibonacci integer), but square-free integer has about a 5-to-1 advantage in Google Scholar hits, so it seems to be winning WP:COMMONNAME. — David Eppstein ( talk) 07:41, 25 September 2021 (UTC)
I did this move mainly for reverting a previous move that was done without any discussion.
Here are the hits that I have found in Google scholar and Google: In Google scholar, 1,100 hits for "square-free number", 542 for "squarefree number", 2,060 for "squarefree integer", and 5,240 for "square-free integer". In Google, 26,700 hits for "square-free number", 10,500 for "squarefree number", 8,780 for "squarefree integer", and 29,200 for "square-free integer". This shows that "square-free integer" is clearly winning in advanced mathematics, and slightly winning in elementary mathematics.
Here is a possible explanation for these results. In the numerous article called "Something number", the word "number" is in fact an abbreviation of "natural number", that is, the concept does not include negative integers. On the other hand, when negative integers are included and/or when confusion with non-integer numbers is possible, "integer" is generally preferred, such as in coprime integers and integers modulo n. Here, "square-free" applies to negative integers, but not to general real numbers (the concept can be extended to rational numbers). So the title "square-free number" may confuse some readers.
However, these are a posteriori explanations. The main reason of my move is to revert a move done without discussion. D.Lazard ( talk) 09:10, 25 September 2021 (UTC)
I agree that reverting a move done without discussion is appropriate. Perhaps in elementary number theory, where "number" is sometimes used as a synonym of integer (or positive integer), it is natural to call them "square-free numbers", but my feeling is that for a broader readership, the more precise term "square-free integer" is better. Ebony Jackson ( talk) 00:59, 2 October 2021 (UTC)
If it is square-free then it is obviously not a general real number. Bubba73 You talkin' to me? 23:47, 3 October 2021 (UTC)
I would support Square-free number as less technical: the concept is understandable by people young enough to be uncomfortable with the technical language "integer", and there is no realistic possibility of confusion with some other concept (any more than there is with "number theory"). (Also obviously the reversion was appropriate!) -- JBL ( talk) 11:08, 5 October 2021 (UTC)

## I would like advice on the title of the article

See Talk:Ohsawa–Takegoshi theorem. thanks!-- SilverMatsu ( talk) 03:56, 2 October 2021 (UTC)

done!-- SilverMatsu ( talk) 06:11, 2 October 2021 (UTC)

I would like to store Coxeter–Dynkin diagram into wikidata, but now Coxeter–Dynkin diagram is display by multiple images e.g. . wikidata doesn't support. (see d:Wikidata:Project_chat#datatype_for_en:Coxeter–Dynkin_diagram?)-- Nanachi 🐰 Fruit Tea（宇帆· ☎️· ☘️） 08:57, 2 October 2021 (UTC)

I don't know about how wikidata works. Tom Ruen ( talk) 17:10, 10 October 2021 (UTC)
@ Tomruen: Is there any standard way of representing Coxeter–Dynkin diagrams as strings? -- Nanachi 🐰 Fruit Tea（宇帆· ☎️· ☘️） 06:54, 11 October 2021 (UTC)
I don't know what the question means. Ascii strings? Like x4o3o for ?
Yes, Ascii strings. Does x4o3o a standard way of representing Coxeter–Dynkin diagrams?-- Nanachi 🐰 Fruit Tea（宇帆· ☎️· ☘️） 09:04, 11 October 2021 (UTC)
There are a bunch of not particularly compelling attempts in Coxeter–Dynkin_diagram#Affine_Coxeter_groups to extend the natural notation for linear diagrams to more complicated graphs. (If one restricts to the finite case, life is not so bad because there is only ever a single branch-point.) Also of course there is the Cartan matrix. -- JBL ( talk) 11:04, 11 October 2021 (UTC)
Richard Klitzing lists all the uniform polytopes with a linearized CD, like polyhedra [1], including loops (common on star forms, w/rational branch orders), like *a at the end for a cyclic diagram returning to first node. Its a bit hard to read, but I'd recommend copying it, if you needed say an input format to generate solutions in a program. Richard also lists incidence matrices which count how many elements in each position of a Kaleidoscopic construction, grouped by element size, Tom Ruen ( talk) 11:01, 18 October 2021 (UTC)
Example , truncated cuboctahedron, [2], 1 type of vertex, 3 types of edges, and 3 types of faces: (Note: is an edge, and = = square)
x3x4x

. . . | 48 |  1  1  1 | 1  1 1
------+----+----------+-------
x . . |  2 | 24  *  * | 1  1 0
. x . |  2 |  * 24  * | 1  0 1
. . x |  2 |  *  * 24 | 0  1 1
------+----+----------+-------
x3x . |  6 |  3  3  0 | 8  * *
x . x |  4 |  2  0  2 | * 12 *
. x4x |  8 |  0  4  4 | *  * 6

• Thanks for your answer. But I still have a question. Can Coxeter diagram be rotation, deformation or reflection? I have observed that the wikipedia article Order-4 dodecahedral honeycomb writes but the diagram given by Richard Klitzing's website is o3o3o *b5x [3]. Does the description structures of (x5o3o *b3o) and (o3o3o *b5x) equal? I have the same question in {{ Octahedral truncations}}: for example, Coxeter diagram of Cuboctahedron are , does it same with ? If it can be rotation, deformation or reflection, does it mean that and represent the same structure?-- Nanachi 🐰 Fruit Tea（宇帆· ☎️· ☘️） 15:20, 19 October 2021 (UTC)
YES, A Coxeter-Dynkin diagram is just a graph, and node position is only aesthetic. Each node is a hyperplane of reflection, each branch order p represents a 180°/p dihedral angle between hyperplanes. A rank n diagram has n nodes and n(n-1)/2 branches, but usually right angles are suppressed (branch order 2) since orthogonal mirrors don't interact. For example, this graph shows diagrams and fundamental simplex domains for 3D space groups File:Coxeter-Dynkin_3-space_groups.png, red edges are orthogonal, so not in the diagram. Those three diagrams are related by doublings. [4,3,4] becomes [4,3^(1,1)]] with one mirror removed, and becomes [3^[4]] with another mirror removed. Tom Ruen ( talk) 16:13, 19 October 2021 (UTC)

## Messed up math display

A few formulae in De Moivre's formula are displayed wrong for me, for instance

{\displaystyle {\begin{aligned}\sin nx&=\sum _{k=0}^{n}{\binom {n}{k}}(\cos x)^{k}\,(\sin x)^{n-k}\,\sin {\frac {(n-k)\pi }{2}}\\\cos nx&=\sum _{k=0}^{n}{\binom {n}{k}}(\cos x)^{k}\,(\sin x)^{n-k}\,\cos {\frac {(n-k)\pi }{2}}.\end{aligned}}}

I'm using Chrome on Windows 10.

It looks like the SVG produced is fine - but when it is shrunk some of the lines disappear.

If I use Wikipedia to display that as a thumbnail the formula is fine even though it is much smaller! If however that SVG is downloaded and then displayed by itself in Chrome it is messed up.

I guess the problem is in Chrome since Wikipedia can shrink it nicely but should I pass this to someome here or any idea of where or how to report it?

NadVolum ( talk) 15:31, 4 October 2021 (UTC)

I think this is an upstream bug in chrome. The SVG is correct, but chrome does not always render it correctly. This was discusses a year or so back on WP:VPT and there may be a ticket about it. -- Salix alba ( talk): 19:15, 4 October 2021 (UTC)
I'd have never known ho to report it! Thanks. The Google Chrome version I'm using is Version 94.0.4606.71 (Official Build) (64-bit). NadVolum ( talk) 16:24, 5 October 2021 (UTC)
I managed to log in there and I uploaded a screen capture of the formulae as I see them too. NadVolum ( talk) 16:49, 5 October 2021 (UTC)
I've found the Village pump discussion Wikipedia:Village pump (technical)/Archive 186#bug in chrome causes "math" tag to display incorrectly. This is T269222 and the chromium bug is 1159852.-- Salix alba ( talk): 12:33, 9 October 2021 (UTC)

## Edits by User:Darcourse

User:Darcourse is a long-time editor of mathematics articles. Recently I had the bad experience of checking a chunk of their edits at Derangement. As you can see in the article history, in my view their changes made the article worse in a wide variety of ways, and I essentially undid all of them. I have serious qualms about the quality of their edits to other articles, but limited time and patience to check them. While I wouldn't recommend blanket reversion, I would encourage other editors to keep an eye on any edits from Darcourse that touch articles of interest or importance. -- JBL ( talk) 11:06, 5 October 2021 (UTC)

## Shuffle symbol ш

The symbol of the shuffle product is the Cyrillic letter ш (sha), and should be implemented in latex as \sha. This is lacking in our implementation. This leads, in our articles, to have awful formulas in raw html, and, in formulas that must be in latex, to use a non standard synbol such as ${\displaystyle \omega }$ (see Tensor product § Coproduct).

Please, can somebody (who knows how to proceed) ask for fixing this issue. D.Lazard ( talk) 13:10, 6 October 2021 (UTC)

I think that might be the Phabricator lot referenced in the box on the top right of my bug about #Messed up math display above NadVolum ( talk) 23:00, 8 October 2021 (UTC)

## List of perfect numbers and Mersenne prime#List of known Mersenne primes

Hi,

I was wondering if these two tables should be merged into one list article in some way -- after all, all known perfect numbers correspond to Mersenne primes and vice versa, and several columns are exactly the same between the two articles outside of the first few rows (rank, p, discovered, discoverer). My only concern is that the table could become too wide, but that could be rectified by shortening the number of digits shown on the big ones (don't think we necessarily need both the first and last 12 digits of every one..) Thoughts? (If there's consensus, I can start writing it myself.) Thanks, eviolite (talk) 15:26, 6 October 2021 (UTC)

I can see your point okay, and wouldn't lose too much sleep if someone did as you say. But I think it probably is better off as it is at the moment. It isn't as though those tables are going to grow at a fast rate and they're not too big and they work fine as they are. No point fixing it if it ain't broke. NadVolum ( talk) 22:57, 8 October 2021 (UTC)
M(57885161) has just been verified! I wonder if I say something similar about some other table the same thing will happen ;-) NadVolum ( talk) 20:47, 10 October 2021 (UTC)
I was actually checking that the other day since I was expanding List of perfect numbers -- it was supposed to have been done in September, but I had to settle for a "close to".. (Also, re the original question, it was honestly out of a bit of selfishness(?) as I wanted to try and get the article to featured list status, and it would probably be easier to include more context if it had both, especially with the discovered column (which de facto is just the Mersenne prime discoverers since Euclid). I do understand if it would make it actively worse/more complicated though.) eviolite (talk) 21:21, 10 October 2021 (UTC)
Welp @ NadVolum: I've gone and boldly started working on one in my sandbox (possibly out of sleep deprivation): see User:Eviolite/sandbox2 - I still need to find and place all the refs/notes in the table properly, but what do you think of it so far? Like I said I'm hoping to reach WP:FL status (it'll be my first piece of good/featured content, see the criteria here). eviolite (talk) 04:38, 13 October 2021 (UTC)
Boldly is actually doing it! It looks to me like someone else has already done it two days ago. It's better to actually do a few edits to the article rather than a big one elsewhere. You can always revert if an edit made things worse. The only reason for much discussion elsewhere and a proposed change is if there is a lot of controversy. Using Show Preview before publishing if editing source is always a good idea though! NadVolum ( talk) 10:06, 13 October 2021 (UTC)
@ NadVolum: the reason I use a sandbox is that the way I edit often results in incomplete section/articles/the etc. I'm not sure what you're referring to that happened 2 days ago but you might be looking at my own edits to List of perfect numbers? Thanks, eviolite (talk) 10:34, 13 October 2021 (UTC)
I had a look again and I am rather puzzled. What bits f the aricle are you hoping to change? Is it the introduction and table or the whole article? I'm a bit new to all this but I'd be very much more incremetal about changes. NadVolum ( talk) 10:43, 13 October 2021 (UTC)
I am changing the entire article of List of perfect numbers, incorporating info from the list on Mersenne prime. The entirety of that prose up there is just a lede for the table - there is no other part of the article. See the FL criteria that requires this. eviolite (talk) 10:48, 13 October 2021 (UTC)

## Volume of an N-ball new edits

Would someone from the Mathematics project please have a look at the last few days of edits to Volume of an n-ball? Guswen has made a number of changes, including a negative-dimension recurrence relation, that I am quite skeptical of the utility of. - Parejkoj ( talk) 17:21, 6 October 2021 (UTC)

I have tagged the whole section Volume of an n-ball#Recursions as possible WP:OR and not sourced. I suggest to remove the whole section as I do not see any encyclopedic value of giving complicated recursion formulas when one has rather simple closed form formulas. D.Lazard ( talk) 18:02, 6 October 2021 (UTC)
Agree the artcle is a mess and needs a bit of control. And the proofs are of little interest, perhaps just keep one short one. NadVolum ( talk) 22:51, 8 October 2021 (UTC)

## Calculus education, etc.

Currently, calculus education, geometry education, and algebra education are all redlinks. I'm not sure what article (if any) those should redirect to. User:力 (power~enwiki, π, ν) 21:51, 12 October 2021 (UTC)

None. Why do you think they should point anywhere? There not even used in any article. NadVolum ( talk) 22:40, 12 October 2021 (UTC)
I think calculus reform is a notable topic, to which calculus education could point, but we don't appear to have an article on it. I'm not convinced that the other two make notable subtopics of geometry and algebra more generally. — David Eppstein ( talk) 23:16, 12 October 2021 (UTC)
I imagine there's a robust literature about all of these things, but if so it's generated & consumed by people who study education, not people who study mathematics. I mean, people have been arguing about geometry education for 2000+ years. -- JBL ( talk) 23:44, 12 October 2021 (UTC)
I think there is (real) analytic education as a article similar to calculus education.-- SilverMatsu ( talk) 00:41, 13 October 2021 (UTC)
@ : Looking around a bit more, Mathematics education would be a suitable redirect target for all of these. -- JBL ( talk) 01:03, 13 October 2021 (UTC)
There is no benefit in turning any of these unused and un-asked-for red links into redirects. But if someone wanted to do the research about the history and/or practice of the education of any of these subjects, a worthwhile article could plausibly be written about any of them. Mathematics education would not be a suitable redirect target in its current form: it doesn’t specifically discuss any of these. – jacobolus  (t) 16:24, 13 October 2021 (UTC)
it doesn’t specifically discuss any of these That's ... not true. For example, a person looking for information about geometry education would find at Mathematics education some historical information, and would learn that geometry is taught both as an example of practical mathematics and as an example of an axiomatic system and a model for deductive reasoning, that it is conventionally introduced after arithmetic and alongside elementary algebra, and that in the US there is typically a year-long course focusing on geometry. (Is this enough material for a stand-alone article, or even a complete section? No, of course not. But is it enough to support a redirect? Sure.) -- JBL ( talk) 17:40, 13 October 2021 (UTC)

I saw Mathematics education, but agree with jacobolus that it isn't currently a good redirect target. That said, it is used as one. While Precalculus has an article, Algebra I does not - that link currently goes to mathematics education but should probably retarget to Elementary algebra. There is certainly enough material published to have a section somewhere on each; I may just add those sections to Mathematics education. Is the quadratic equation taught before ring theory, and why? Should elementary algebra classes be taught to 11 year olds or 14 year olds? When did "algebra" first become part of the curriculum at schools like Eton College? These questions and more are surely discussed and of interest to encyclopedia readers. User:力 (power~enwiki, π, ν) 17:48, 13 October 2021 (UTC)

Jacobolus's point seems correct, but I tend to agree with JayBeeEll's suggestion. see Wikipedia:Redirects are cheap. However, instead of redirecting the talk page, we recommend using "Template:WikiProject Mathematics" to create a place for discussion in case they want to create the stand-alone articles.-- SilverMatsu ( talk) 00:27, 14 October 2021 (UTC)

That's ... not true. – Two or three scattered throw-away sentences is not a meaningful amount of content for someone curious about “geometry education” or “algebra education”. The math education article currently does not cover these in a meaningful way, and creating redirects for these would not provide value to Wikipedia. If you want to add a separate section with a few paragraphs summarizing one of these subjects, go right ahead; at that point, you could make a redirect. Alternately, go write a whole article at one of those pages. Even a few-paragraph stub would be much more useful than a redirect. Otherwise, discussing more here is a waste of time. – jacobolus  (t) 01:29, 14 October 2021 (UTC)

I have no quibble with the claim that the coverage of these more specific topics in that more general article is very light (as you can tell by reading my comment, viz. Is this enough material for a stand-alone article, or even a complete section? No, of course not.). I only have a quibble with the particular (false) claim it doesn’t specifically discuss any of these. The reason that I object to that false claim is that it implies, incorrectly, that I didn't check whether geometry education etc. is mentioned in Mathematics education; whereas I did check to confirm that each of these topics is specifically mentioned there. I agree that further discussion of this point would be a waste of time, and I suggest that in the future you adopt a less aggressive tone (and particularly avoid saying false things aggressively) in order to avoid such pointless wastes of time. -- JBL ( talk) 20:18, 15 October 2021 (UTC)
@ : I suggest not changing the redirect target for Algebra I. Algebra I is used in some mathematics lectures (course) and textbook titles. (e.g. Michael Artin. 18.701 Algebra I. Fall 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, N. Bourbaki Algebra I: Chapters 1-3 at Google Books.) But I agree that "Algebra I" can mean Elementary algebra.-- SilverMatsu ( talk) 00:54, 17 October 2021 (UTC)

## Cognitively Guided Instruction

So while I was looking at mathematics education articles, I stumbled across the article Cognitively Guided Instruction, which was written in 2007 and has hardly been touched since. All its references are written by a single group of authors. I would welcome input on the question of whether this is a notable thing (studied by multiple groups, subject of sources not written by its inventors) whose article is poor but could be improved, or alternatively whether the current article reflects the best possible sourcing (in which case the article should probably be deleted). (I also left a note at Wikipedia talk:WikiProject Education.) -- JBL ( talk) 11:10, 13 October 2021 (UTC)

## Constructive set theory

Can someone knowledgeable enough take a look at this article, parts of it are written in an unencyclopedic way using phrasing such as "we use" etc. Lavalizard101 ( talk) 12:13, 16 October 2021 (UTC)

The word "etc." is doing a lot of work in this comment. Huge numbers of mathematics articles use the first person plural (because that's the norm in mathematics papers), and it doesn't require a mathematics specialist to fix this grammatical issue (though doing so is tedious and would take a while on an article of this length). Personally, it is also really low on my list of things to worry about because it does not impede reader understanding at all. -- JBL ( talk) 12:21, 16 October 2021 (UTC)
There is nothing "unencyclopedic" about standard mathematical style. MOS:WE explicitly says “some such forms [of first-person writing] are acceptable in certain figurative uses. For example: [...] The author's we found in scientific writing, though rephrasing to use passive voice may be preferable.”jacobolus  (t) 12:34, 16 October 2021 (UTC)
However, "we" is often confusing, as the reader cannot know whether "we" refers to the editor of the article, to the author of the source, to Wikipedia, or to the mathematical community. This is specially confusing in sentences such that "we define (or we denote) this as that". Does the reader should understand that it is a definition/notation that is specific to the article, or a standard definition/notation, or a common but nonstandard definition/notation? This important encyclopedic information is often lacking in articles that use "we". D.Lazard ( talk) 13:11, 16 October 2021 (UTC)