This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Text and/or other creative content from Square (algebra) was copied or moved into Square number with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.
where it is possible to choose either + or - in any of the cases.
My guess is that this relation will not hold for any natural n, and I would guess its proved by contradiction, but formulating this proof seems quite difficult. Any suggestions welcome, or even related material to look at.
Both these articles represent the same function, so I see no reason why they shouldn't be merged. I also wish for Cube (algebra) to moved to Cube number so we have something that can fit in Category:Figurate numbers that can coincide with other polyhedral numbers such as Tetrahedral numbers and Centered cube numbers. The idea of having two articles for square numbers and yet one for cubes seems odd to me. Robo37 (talk) 10:05, 23 November 2009 (UTC)[reply]
I agree with this because it is in the same "grade" —Preceding unsigned comment added by Froogle1099 (talk • contribs) 00:44, 4 February 2010 (UTC)[reply]
I disagree because perfect squares and squares in general have incredibly different properties from a set theory point of view. Proving things with perfect squares is completely different because they have a much more restricted set of properties. —Preceding unsigned comment added by 128.252.78.87 (talk) 02:16, 27 September 2010 (UTC)[reply]
Shouldn't it be mentioned that the sum of the digits of a square number must be 1, 4, 7 or 9? I don't know the exact term in English, but this is the same as saying that the rest if one divides by nine must be 0, 1, 4, 7. I don't have any proof of this property though.
Vittorio Mariani (talk) 13:20, 11 December 2009 (UTC)[reply]
It's mentioned at Digital root#Some properties of digital roots. I'm not sure it is worth mentioning in Square number. It follows from modular arithmetic that the property only has to be checked for 0^2 to 8^2. Suppose you write an arbitrary integer as (9n+k) where 0≤k<9. (9n+k)^2 = (9n)^2+18nk+k^2. Divided by 9 it must give the same remainder as k^2 divided by 9, because 9 divides (9n)^2+18nk. Similar rules for possible values of the remainder when a square is divided by any other integer d can be given. Just list the remainder when dividing 0^2 to (d-1)^2 by d (actually you can limit it to 0^2 to floor(d/2)^2 for symmetry reasons). PrimeHunter (talk) 13:58, 11 December 2009 (UTC)[reply]
Maybe just mentioning wouldn't do bad, I won't insist anyway :) --Vittorio Mariani (talk) 12:48, 22 February 2010 (UTC)[reply]
when you are using squares here is an easy patters.
1x1=1
(+3)
2x2=4
(+5)
3x3=9
(+7)
4x4=16
As you should see by now each time the factor goes up the solution goes up by an odd number. —Preceding unsigned comment added by Froogle1099 (talk • contribs) 00:51, 4 February 2010 (UTC)[reply]
An easy way to find square numbers is to find two numbers which have a mean of it, 212:20 and 22, and then multiply the two numbers together and add the square of the distance from the mean: 22 × 20 = 440 and 440 + 12 = 441.
That could bear translation into English. Michael Hardy (talk) 18:56, 16 March 2010 (UTC)[reply]
I think what it means is that to manually calculate , it is sometimes easier to calculate for some b. For example, if one would like to square 39, it is easier to calculate 38·40+1 = 1521 than to multiply 39·39 directly. —Dominus (talk) 19:07, 16 March 2010 (UTC)[reply]
I deleted it from the article, but I will not be offended if you think it is worth putting back. —Dominus (talk) 19:11, 16 March 2010 (UTC)[reply]
Added the Hexadecimal section to Properties chapter. Contains factorization without any division! May be interesting for young math geeks. Please correct me if some place is unclear. Neeme Vaino (talk) 09:15, 26 March 2010 (UTC)[reply]
[1] 24 hours to demonstrate the relevance of integer square numbers to "the real number system" and statistics. Otherwise, I will henceforth reduce such edits of Anita5192 (talk·contribs), possibly with my [rollback] link. Incnis Mrsi (talk) 19:14, 3 September 2012 (UTC)[reply]
Do you actually have rollback? Your link seems to be a fake, though even if you did, you have no right to use it so your edits dominate others.
There is no need for such a confrontational approach as you have done so here ("<span style="font-size:300%">integer</span>").
This is appalling. You are simply fighting and complaining for your own way against the rules - given your burning desire to overwhelm Anita5192. Maschen (talk) 20:45, 3 September 2012 (UTC)[reply]
Of course, it's a fake link here. I'm not a moron to put my own privilege to a publicly readable page ☺ The accusation that I "fight against the rules" requires evidences. There was no deception, only a part of statement was missing before the semicolon character. Note that I would not have such a grievance about user:Joel B. Lewis were the merger procedurally accurate. Probably, I fight against opinions of 4 users (although Joel B. Lewis virtually renounced his position, and Physics is all gnomes commented only what [contemporarily] "stands Square (algebra) is mostly about"), but opinions of 4 users are not the rules of Wikipedia, anyway. Incnis Mrsi (talk) 21:36, 3 September 2012 (UTC)[reply]
The content of the present "Uses" section is off-topical, because explicitly mentions "the system of real numbers". It belongs to the topic "square (algebra)", not to the topic "square number", which is defined as an integer or, in a very general sense, rational number. Incnis Mrsi (talk) 07:55, 4 September 2012 (UTC)[reply]
How exactly are aforementioned Anita5192's codes better than mine? Incnis Mrsi (talk) 20:27, 3 September 2012 (UTC)[reply]
As said, the ordinary markup is cleaner than ((mvar)). It is not possible to copy and paste the text into another edit window (if needed) using the templates, using the ordinary markup makes that easy. Maschen (talk) 20:45, 3 September 2012 (UTC)[reply]
As said by whom? I do not understand completely what do you speaking about. If you want to copy and paste between edit forms, then there is no difference between "the ordinary markup" and template formatting, and you certainly have to realize this. Assuming you speak about copying from a rendered page (i.e., a web page in the browser) to an edit form, which is another possibility, please, demonstrate how is it possible to easily copy and paste the ordinary markup such as m = 12 = 1 or (n − 1)-th to an edit form. Do you assert that by copying from this zoomed text on a web page will you obtain a workable wiki code, with superscripts and italics? Maybe, you could even demonstrate this? In which browser? In any way, this consideration have little to do with concrete, pronounced shortcomings which I listed. Incnis Mrsi (talk) 21:36, 3 September 2012 (UTC)[reply]
I do not insist on ((math)) and ((mvar)) and do not have a strong preference towards ((sqrt)) at the expense of <math>. Just fix not less formatting errors than I fixed, and I'll give up my version. If nobody will do it – sorry, but my version is the best in the article's history as of now. Do improve the article, if you do. But if you do not – please, do not hinder me with this job. Incnis Mrsi (talk) 07:55, 4 September 2012 (UTC)[reply]
Note: White gaps between squares serve only to improve visual perception.
There must be no gaps between actual squares._who is the idiot that needed to be told this?121.127.198.87 (talk) 04:00, 20 July 2014 (UTC)[reply]
This article is not for your own original research. Each addition must be supported by published sources that establish the notability of the result. D.Lazard (talk) 10:40, 19 March 2023 (UTC)[reply]
It's quite a trivial result, as splitting the sum gives (in this case) four columns each totalling 41 + 2 + 3 + 4 +3 + 2 + 1so it doesn't seem worth including, even if any reliable source has bothered to provide such a simple and obvious proof. Certes (talk) 13:25, 19 March 2023 (UTC)[reply]