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Semi-protected edit request on 10 November 2023

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Add to categorizations that a square is a rectangular rhombus. 75.117.226.44 (talk) 23:35, 10 November 2023 (UTC)[reply]

 Not done: Not quite sure how you want this done... there currently isn't a rhombus category. Liu1126 (talk) 00:04, 11 November 2023 (UTC)[reply]

if and only if

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A quadrilateral is a square if and only if it is any one of the following:

The layman might not catch the implication of if and only if that if one definition is true then all are; I would prefer language like The following definitions of a square are equivalent. —Tamfang (talk) 07:18, 28 June 2024 (UTC)[reply]

Admins' noticeboard thread about semi-protection of this article

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Please see the admins' noticeboard thread "Indefinite protection of Square about the protection status of this article. Anyone can comment there, regardless of their admin status. Graham87 (talk) 09:52, 31 January 2025 (UTC)[reply]

Lead section as summary seems a bit too niche for intended audience

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@David Eppstein, thanks for working on this article, including the lead section. I'm a bit concerned that the detailed list of random topics in the lead section seems a bit arbitrary and may be confusing or overwhelming for readers. Topics such as the inscribed square problem, the square of squares, etc. don't really seem essential to the concept of a "square", and I don't think we really need to mention all of them in the lead, even if they are discussed later on. I'd recommend we try to pare the lead down to the most fundamental topics and not necessarily try to make the lead a complete summary of everything mentioned in the article. –jacobolus (t) 06:33, 17 February 2025 (UTC)[reply]

It was intended as a rough summary of the rest of the article. See MOS:INTRO: "The lead section should briefly summarize the most important points covered in an article, in such a way that it can stand on its own as a concise version of the article." Note that this is part of WP:GACR#1, so if we hope to reach GA status we need a proper lead, not just a brief paragraph. I tried to include material from most sections of the article, but some calculation-heavy parts were difficult to summarize briefly and readably. —David Eppstein (talk) 07:07, 17 February 2025 (UTC)[reply]
It is not required that every topic discussed in the article must be mentioned in the lead. I think mentioning these somewhat niche/obscure topics seems like a non sequitur and is not really helpful for many expected groups of readers who might skim the lead section without bothering to read further into the article (and frankly it seems like a bit of an NPOV problem; these topics are definitely not given such prominent place in the full range of published literature involving squares). –jacobolus (t) 07:30, 17 February 2025 (UTC)[reply]
"The published literature involving squares" mostly involves kindergarten mathematics textbooks, at least if one focuses on works directly about squares rather than covering them in passing. Is that what you think we should emulate? As for the topics you think are niche: they are topics that are directly about squares (and not about orthogonal repetition, a different topic) for which we have articles. I think we should discuss those topics in the main article on squares. Almost everything in the packing and quadrature sections is merely a brief summary of material covered in more detail at the linked articles; I think the only exception is the very recent proof of NP-hardness for square packing problems. We have a separate article on square tiling, where I think what you want to cover better belongs. It should be mentioned here, but not be the main focus of this article. And it is mentioned here, in a paragraph-length summary, like the other topics in these sections. But the current state of the square tiling article is pretty dire leaving little that can be summarized here. Your proposal to add an entire section on it here is premature until summarizing what is there would take an entire section. Also, re your opinion that square packing in a square or the square peg problem are niche: both have been the subject of publications by Fields medalists, suggesting that maybe there is more depth to them than you might have suspected. —David Eppstein (talk) 08:23, 17 February 2025 (UTC)[reply]
You don't need to get testy. The published literature involving squares is millions of items in a tremendous range, of which only a trivially tiny proportion is kindergarten books. But sure, the material from the kindergarten books is essential and must be covered, whereas topics such as inscribing squares in arbitrary curves, making squares from arrangements of smaller squares, and packing circles into a square are more or less mathematical curios, not essential to the concept of "square" and not important enough to be the first things we tell someone trying to learn the basics about squares. –jacobolus (t) 15:37, 17 February 2025 (UTC)[reply]
Says you. The Fields medalists disagree. —David Eppstein (talk) 17:48, 17 February 2025 (UTC)[reply]
Whether a problem was of interest to Fields medalists is not equivalent to whether a problem is of fundamental importance (either to mathematics or in particular to the concept of squares). [However, if you had a Fields medalist saying something like "one of the most important things about squares is that there are some packing problems ...", that opinion would be worth weighting.] –jacobolus (t) 17:58, 17 February 2025 (UTC)[reply]
I reorganized paragraph 3 so that it starts with square tiling (ubiquitous, easy to visualize) and then goes to squaring the circle (pretty famous) before getting into unsolved and comparatively obscure topics. I like having the latter in the lede, actually. It spices up mathematics, in a way, by showing that a simple idea like "square" is one step away from a question that nobody can answer yet. XOR'easter (talk) 17:59, 17 February 2025 (UTC)[reply]
Thanks, I think that was an improvement. –jacobolus (t) 18:27, 17 February 2025 (UTC)[reply]
I'm mostly OK with the introduction. I think the formula for the area is paragraph-1 material, so I added a sentence about that, thereby introducing it before we get to an unsolved problem. The sentence about ubiquitous squares could perhaps be split into a two-sentence paragraph. XOR'easter (talk) 17:26, 17 February 2025 (UTC)[reply]
Thanks. I agree that some of the formulas are lead-worthy; I just wasn't sure about how to work them into the lead without overwhelming it with technicality. —David Eppstein (talk) 17:49, 17 February 2025 (UTC)[reply]

Would be great to have a top level section about square grids

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It seems to me that Wikipedia overall doesn't have particularly good discussion about square and rectangular grids. We currently have articles about Square lattice, Lattice graph, Square tiling, Checkerboard, Graph paper, Regular grid, Analytic geometry, Coordinate system, Cartesian coordinate system, Projected coordinate system, Grid (graphic design), Grid plan, UV mapping, Bitmap, Grid (a disambiguation page), etc., but most of these are relatively short and incomplete, and there's not really any place with a solid overview of basic concepts and tools, the range of applications, a clear comparison or list of trade-offs with other types of coordinates or structures for various types of data, etc. It's probably worth having a new article called Square grid (currently redirects to Square tiling which doesn't seem quite right) or maybe more generally Rectangular grid with square grids as a prominent section, but in any event to have a complete article about Square, it seems to me a significant early section should discuss square grids, since many (most?) of the applications and points of interest of squares have more specifically to do with square grids, and square grids have become really fundamental to the way modern society organizes all kinds of information and even thinks about mathematical concepts

I haven't done any kind of literature survey, but I bet there are some nice sources discussing square grids at a high level, maybe including some kind of philosophical considerations etc.

Edit: here are a few sources that pop up in a very brief search:

  • https://books.google.com/books?id=bpOUDwAAQBAJ&pg=PT109
  • https://books.google.com/books?id=ms--K3jipt4C
  • https://dspace.mit.edu/handle/1721.1/74743
  • doi:10.1207/S1532690XCI2103_03
  • doi:10.1007/978-3-319-72523-9_7

jacobolus (t) 06:55, 17 February 2025 (UTC)[reply]

I disagree that most applications and points of interest about grids. They are important, but really a separate related topic. Most of the applications are about things with the shape of a (single) square. We should have an article (or two) about square and rectangular finite arrangements of points, though. Square grid is a natural title, but it points to something else. —David Eppstein (talk) 07:10, 17 February 2025 (UTC)[reply]
The applications mentioned here include tiles, square coordinates, graph paper, city grids, bitmap images, square-grid game boards, QR codes, etc. All of these are really applications of square grids in particular, more than the square shape for its own sake. I agree this is a separate related topic which should have its own article; I just think it's worth summarizing the topic here as well, since it is ubiquitous in (especially modern) human culture, including the basic structure of many areas of modern mathematics. –jacobolus (t) 07:25, 17 February 2025 (UTC)[reply]
Almost everything you mention is part of a single paragraph of a multi-paragraph section. That paragraph focuses on grids. The only exceptions in your examples, not from that paragraph, are "city grids", which are not mentioned at all in the article (they are mostly rectangular rather than square in my experience), game boards, which are primarily mentioned because the boards themselves are square and only secondarily because of the square grids some of them contain, and QR codes, where we do not even mention the grid layout of the pixels (it would be redundant to the first paragraph) and instead focus on the square overall shape and nested-square pattern of the alignment marks.
Taking a wider view, the intent of this section is to convey "squares are all around you in many familiar things", not "when you use square shaped things you are only allowed to place them in a grid". —David Eppstein (talk) 08:15, 17 February 2025 (UTC)[reply]
I feel like you are deliberately missing my point, and I'm not quite sure why. I am not talking about changing the "applications" section, which seems fine, though it could certainly keep accumulating examples if anyone wanted. I'm suggesting that this article is substantially incomplete (and Wikipedia's coverage of the topic more broadly is incomplete) insofar as it does a very poor and limited job discussing square grids.
"Squares are all around you" in large part because they fit into a grid, whether that's square kitchen tiles, square sidewalk sections, squares on a Go board or computer game grid, pixels in a bitmap image, square city blocks, squares as a unit of area, squares on a military map, etc. Other shapes (say, regular heptagons or non-rectangular trapezoids) are much less common as an organizing principle, because they are significantly less convenient for making a regular pattern with cleanly separated but equivalent directions, easily addressed by coordinates, etc. Just as triangles are culturally important to a significant extent because they are stable in a truss, squares are important because they are the basis for one of the most common types of human organizing structure. –jacobolus (t) 15:52, 17 February 2025 (UTC)[reply]
Your point in a nutshell, as it comes across to me, is, we should stop talking about these square things and instead talk about things that are periodic in square lattice patterns. Which is a fine topic for an article but to me is not really the topic of this article. —David Eppstein (talk) 17:50, 17 February 2025 (UTC)[reply]
Okay, well I'm doing a terrible job expressing myself, because no that's not it at all. What I am saying, in a nutshell, is that we should (a) have a separate article called something like Square grid, and (b) have a top-level section of this article called something like "Square grids", since that subtopic is extremely relevant and important here, but is not currently described very clearly or completely. Reframing the article titled "Square" to be entirely centered on a separate topic would be nonsensical. –jacobolus (t) 18:00, 17 February 2025 (UTC)[reply]
I agree that square grid is a reasonable topic for a separate article. (Having it redirect to square tiling as it does now doesn't quite fit.) I'm not sure that a top-level section with the heading "Square grids" would be the right way to organize the text in this article.
I'll admit that the discussion in this thread has left me a little confused. It looks like a dispute over whether a chessboard should be seen as a square grid or as a grid of squares. XOR'easter (talk) 18:17, 17 February 2025 (UTC)[reply]

Things that are in the infobox but not the article

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I think it goes against MOS:LEDE (in spirit if not explicitly) to state things in the infobox that the article does not elaborate upon. Currently, the infobox is generated by {{Regular polygon db}}, which dumps in a pair of Coxeter–Dynkin diagrams, two properties that the article does not define (isogonal and isotoxal), and the statement that the square is self-dual. This seems less than optimal. Defining all these terms in the article might bloat it unacceptably, but dumping unsourced and unexplained terminology into the intro for a basic shape isn't great either. XOR'easter (talk) 19:38, 18 February 2025 (UTC)[reply]

I think it would be preferable to remove the Coxeter diagrams from the infobox than to try to explain them in the article. It's just not a very significant topic for a shape of such low dimension and it's too technical for the most front-facing parts of this article. We can mention squares being isogonal and isotoxal in the symmetry section but I'm still not convinced they belong in the infobox either. —David Eppstein (talk) 21:10, 18 February 2025 (UTC)[reply]
{{Regular polygon db}} doesn't seem to offer any flexibility, so I guess we should switch to {{Infobox polygon}}. XOR'easter (talk) 21:24, 18 February 2025 (UTC)[reply]