Talk:Square (algebra)

message: The section Square number#Uses is about squaring numbers, so the definition of squares do not belongs here.  12:34, 19 March 2006 (UTC)
replies: text: Well, I've done the merge, as well as a bit in the other direction. If you'd like to expand on squares of integers, that material is accumulating at Square number, not here.  11:32, 24 March 2006 (UTC)
thread_title: Merging

message: Square (algebra) but Cube (arithmetic). I'd prefer cube (algebra). googl t 21:31, 14 June 2006 (UTC)
thread_title: Arithmetic/algebra

message: Should we perhaps note that the "square" of a vector as commonly denoted by \vec{x}^2 is usually understood to be |\vec{x}|^2? Shinobu 09:42, 13 November 2007 (UTC)
thread_title:  Square of a vector 

message: All I've done is clean up what was here, but the article needs to get organized.  Maybe I'll be back. Michael Hardy (talk) 18:49, 16 March 2010 (UTC)
replies: text: The phrase after the sigma/recursive formula (which I have just added) is redundant. It explains in words what the preceding symbolic representation should already convey. 2N+1 from N=0 to 2N+1 == sum of the first N odd numbers. (R-1)^2 = last square (= sum of odd numbers) + 2N-1 (= next odd number). The verbal explanation should precede the sum, if anything. If somebody more patient and artful with prose has time, could you please reword it to integrate them, so it doesn't look premature? Thanks. -- Qt-Q!U (talk) 13:22, 15 August 2010 (UTC)
thread_title:  state of this article 

message: This page has become a mess. The lead is too long, there aren't nearly enough sections, the "facts" section is trivia. Here are my proposals to clean this page up:
# the lead consists of just the bare definition. No formula for the sum, no properties, etc.
# the "facts" would either be converted to a list format on another list page
# most of what is in the lead would go in a section entitled "Properties", as that's what they are
Any opposition, or feedback? -- 124.150.75.37 (talk) 06:38, 24 September 2010 (UTC)
thread_title:  Page structure 

message: what about e.g. -2², does it mean (-2)² = +4 or -(2²) = -4 ?46.115.23.171 (talk) 10:51, 8 June 2011 (UTC)
replies: text: See Order of operations#Gaps in the standard. PrimeHunter (talk) 11:11, 8 June 2011 (UTC)

text: The above link is now Order of operations#Exceptions and says -2² can be interpreted in both ways. Microsoft Excel 2013 evaluates -2^2 as 4. PrimeHunter (talk) 01:01, 4 September 2017 (UTC)
thread_title:  -2² 

message: I believe that there is a mistake right there in the intro. Currently, the article says that square (perfect) can be obtained using the identity: 1 + 3 + 5 + ... + 2N + 1. This is incorrect. It should be 2N - 1. I am going to correct this but feel free to correct me if I am wrong. 
-M.N.  — Preceding unsigned comment added by Murtazanisar (talk • contribs) 23:11, 12 July 2011 (UTC)
thread_title:  Mistake in identity 

message: There has been occasional discussion on Talk:Square number of merging these two articles; this is obviously appropriate (and most people who have commented there agree).  I think further edits should mostly focus on this task.  The other article (square number) is among the top 500 most-viewed articles; I suggest this article be converted to a redirect once merging takes place.  -Joel B. Lewis (talk) 21:14, 31 July 2011 (UTC)
replies: text: The merger (BTW announced improperly) was repelled, and these arguments were refuted. Nevertheless, 2012 article is markedly different from 2011 one. Thanks to all users who helped to make a correct, good article, at last. Incnis Mrsi (talk) 18:43, 3 September 2012 (UTC)

text: See here. This is getting unnecessarily heated when it was announced. We have been though all this. Again - where the hell are the links saying that they (Robo37, Froogle1099, Physics is all gnomes) "disagreed": not you writing the "refutes" for them (and therefore lying about the situation, if they didn't actually refute themselves), but their comments typed from their own hands and minds? Maschen (talk) 20:57, 3 September 2012 (UTC)
replies: text:  The argument of Physics is all gnomes was obsoleted by a new article (also, he probably overlooked a section about uses). Froogle1099’s "the same grade" itself does not, actually, imply the direction Square_(algebra)→Square_number; but in the context of this direction such a merger argument definitely was refuted. Joel B. Lewis did not introduce his own argument, he only referred to other 3 guys. It is only Robo37’s argument what was not refuted, but it constitutes mostly of WP: I don't like it. Incnis Mrsi (talk) 21:53, 3 September 2012 (UTC)
thread_title:  Merge 

message: Sure, I understood what D.Lazard intended to say. But this is confusing: either the article must at least mention function composition, or this topic should be bypassed at all. BTW:
* Only endomorphisms (linear maps) usually considered for vector spaces.
:: Not true: For example, the diffeomorphisms of Rn are widely considered. More specific: the affine transformations of a vector space are not linear and are implicitly considered, when talking of reflections. D.Lazard (talk) 17:01, 5 September 2012 (UTC)
replies: text:  True, but too much generality would make the article too difficult for most readers. D.Lazard (talk) 17:01, 5 September 2012 (UTC)
replies: text:  By the way, I'll make exxplicit the fact that, in this paragraph, one considers the square of the composition. D.Lazard (talk) 17:01, 5 September 2012 (UTC)
thread_title:  The functions from a vector space to itself whose squares are the identity function… 

message: Within the article, this concept is discussed in two places. First, in the Square (algebra) #In rings in general section. Second (under composition), in the Square (algebra) #In geometry and linear algebra section. Meanwhile, it is only tangentially related to the square function:  is only one form of its definition. The same expresses also as  (which relates it both to quadratic polynomial and zero divisor), and other definition is  (which relates it to exponentiation, hence the name). How many people think that extensive considerations about idempotents in this article constitute an WP: undue weight? They have their own articles Idempotent element and Idempotence, at last. Incnis Mrsi (talk) 15:41, 16 January 2013 (UTC)
thread_title:  [[Idempotent]]s 

message: The following text was removed as being off-topic for this article
:Another, more well known, function is the square of the absolute value , which is real-valued. It is very important for quantum mechanics: see probability amplitude and Born rule. Complex numbers form one of four possible Euclidean Hurwitz algebras that are defined with a real quadratic form ; here . In a Euclidean Hurwitz algebra this  equals to the square of the distance to 0 discussed above, and the absolute value  can be defined as the (arithmetical) square root of . Multiplicativity of  in these algebras explains (or relies upon) certain algebraic identities (see below).
The squaring function is a primordial quadratic form used to generate composition algebras, as indicated now in the edited text. — Rgdboer (talk) 23:39, 19 May 2016 (UTC)
thread_title: Digression

message: The article uses "squaring function" without defining it clearly (only "squaring operation" is defined), but there is no redirect to this term. On the other hand, there is a redirect , that links here, where the term does not appear. Google Scholar provides 24,100 hits for "square function", and only 2,710 for "squaring function". So, it seems that "square function" is much more commonly used.
So, I'll add a definition of the function, with the mention of its two names. My opinion is that the systematic use of "squaring function" must be changed into "square function", but this needs further opinions. D.Lazard (talk) 08:43, 6 June 2019 (UTC)
thread_title:  Square function or squaring function? 

message: The following Wikimedia Commons file used on this page has been nominated for deletion:
* 
Participate in the deletion discussion at the . —Community Tech bot (talk) 09:06, 6 December 2019 (UTC)
thread_title:  A Commons file used on this page has been nominated for deletion 

message: I think the article needs a section about Differentiation and about Integral. Barecode (talk) 07:54, 25 June 2020 (UTC)
replies: text: These would be better placed in an article about calculus. 2601:182:C80:3E10:BD7A:135:CE5E:1C5B (talk) 20:27, 27 July 2022 (UTC)
thread_title: Differentiation

message: It would be useful to provide some link to how this symbol is encoded / represented in computer systems. e.g. 
https://en.wikipedia.org/wiki/Unicode_subscripts_and_superscripts#Superscripts_and_subscripts_block
ACED.wiki (talk) 22:33, 6 August 2020 (UTC)
replies: text: This is not an article about a symbol, it is an article about a mathematical operation. That information more naturally belongs in Subscript and superscript. —David Eppstein (talk) 22:40, 6 August 2020 (UTC)
thread_title: Unicode and character encoding

message: There used to be an interesting section relating to geometry about how square numbers are the sum : 1+1+2+2+...+n-1+n-1+n = n^2
This should come back as it gives a revealing insight, at least for integers. In addition, it allows for calculation of squared numbers not readily known. An example would be 1,000,002. It is 1,000,004,000,004 or 1,000,000^2 (easy) +1,000,000 + 1,000,001 + 1,000,001 + 1,000,002 2601:182:C80:3E10:BD7A:135:CE5E:1C5B (talk) 18:46, 27 July 2022 (UTC)
replies: text: This is an article about the operation of squaring.  You want the article Square number. 66.44.49.56 (talk) 11:50, 28 July 2022 (UTC)
thread_title:  Where is the interesting section? 

message: The squaring function is of course used frequently and extensively in algebra, but it's not unique to this branch of mathematics.  Squaring is also used in regular arithmetic and most other types of math.  This article seems to be about squaring in general, so would square (math) or square (mathematics) not make more sense as the title? -2003:CA:8717:D2C6:A8FD:4AFF:E0AB:636F (talk) 20:55, 18 March 2024 (UTC)
replies: text: Because that would be ambiguous with the other meaning of square, the geometric shape, you know the one, with four equal sides and four right angles. It's also math or mathematics. —David Eppstein (talk) 21:12, 18 March 2024 (UTC)
thread_title:  Why "(algebra)" in the title??