Talk:Area of a circle/Archive 3

Assessment comment
Substituted at 01:46, 5 May 2016 (UTC)

Changes to article body
I was surprised that the closer moved the page to area of a circle already; while I support that outcome, and their assessment of the situation was pretty balanced, it was not what I expected, and as Sławomir pointed out, the article title should match the content, and so we should clarify some parts of the article. I think that regardless how anyone feels about the two names, it is worth considering that allowing the name to be a circle at least for a while will permit some data about page views and Google results to be gathered.

To start this, I changed the lead, mostly rearranging it. I was striving to be both accurate and clear about the terminology, and think overall it is a success. However if anyone disagrees they can revert or modify it, but please post why here. There are probably a few other changes that should be made throughout the text. I will work on them, too. Nat2 (talk) 19:16, 13 June 2016 (UTC)
 * I disagree with your changes to the lead, and have reverted them. (1) You added a new first sentence, "the area of a circle is the area of a circle". This is totally useless, and fails to inform readers of anything. Its only purpose is to work the title phrase "area of a circle" into a sentence. If we can't do that in a more natural and informative way, we shouldn't be doing it at all. (2) In doing so you merged the next two sentences into one more-complicated sentence, to the detriment of readability. (3) You exchanged the order of the remaining two paragraphs, one summarizing Archimedes derivation of the formula and one summarizing the dispute here about what to call it, to put the naming dispute in a more prominent position than the actual mathematics. That seems WP:UNDUE to me. —David Eppstein (talk) 19:52, 13 June 2016 (UTC)
 * Okay, I see where you're coming from. How about something like 'The area of a circle of radius r is pi r^2. Here the Greek letter...' for the first sentence. That seems pretty natural to me. Thinking about it I agree with what you said about paragraph order. However, I also changed the substance of the circle v. disk paragraph to something I thought was clearer. What do you think about that text? Also, I don't have strong feelings about the readability difference in the sentences I joined and altered in the first paragraph, but I think it could be significant that in explaining pi it essentially says pi ≅ 3.14159 = circumference/diameter, sort of implying that the ratio is exactly 3.14159 but pi isn't. Of course, if you know anything at all about circles or pi it is completely clear, but then you don't even need the sentence in that case anyway. Nat2 (talk) 21:02, 13 June 2016 (UTC)
 * What is wrong with the current first sentence that you are trying to fix? Because now, it is both mathematically accurate (talking about the area enclosed by the circle rather than the area of the circle itself) and unsurprising (based on the word circle instead of the more technical word disk). Your new proposed version loses mathematical accuracy, for no benefit that I can see. It is not necessary for the first sentence of an article to contain an exact copy of the title, and in this case I think it is better not to do so. —David Eppstein (talk) 21:19, 13 June 2016 (UTC)
 * It looks like by the time at least that you posted this comment, another user had edited the first sentence from where it was, dropping 'disk' out of it completely but keeping the enclosed by. I am completely fine with the first sentence as it now stands. Nat2 (talk) 21:26, 13 June 2016 (UTC)
 * Thanks, ! I agree with Nat2 that your compromise change (removing disk from the first sentence) is an improvement. —David Eppstein (talk) 21:30, 13 June 2016 (UTC)
 * Glad I could be of assistance. Tazerdadog (talk) 21:34, 13 June 2016 (UTC)

The first sentence of the article was recently changed from "In mathematics, the area enclosed in..." to "The area enclosed in..." here:. I think this should be discussed. I'm on the fence, leaning for the old wording. This is a mathematics article, and the subject should be noted. Tazerdadog (talk) 22:51, 15 June 2016 (UTC)
 * I don't feel strongly about this, but I slightly prefer having some context to having none. "In geometry" would also be ok. —David Eppstein (talk) 23:09, 15 June 2016 (UTC)
 * Yes, geometry. More specific topic area. wbm1058 (talk) 00:08, 16 June 2016 (UTC)


 * I am totally opposed to any effort to make the content of the article match the title. There is strong consensus against this in the preceding discussion.  Furthermore, it would result in an incomprehensible article, where by "integral over a circle", one means two different things.  I will reiterate: the article itself must use the proper mathematical terminology, regardless of the title.  I do not think WP:RANDY is in a particularly strong position to be making edits to mathematical articles.   S ławomir  Biały  13:51, 16 June 2016 (UTC)
 * Are there any specific places in the article that you feel should be discussed or changed? Tazerdadog (talk) 19:14, 16 June 2016 (UTC)
 * The proposal at the top of this section was to make the terminology used in the article match the title, in effect to redefine the term "circle" to mean both the curve on the boundary and the disk it encloses. I am opposed to that proposal, and I will definitely revert any further attempts to corrupt the mathematical content of the article with such nonsense.  S ławomir  Biały  20:01, 16 June 2016 (UTC)

Disputed adjustment to lede
I don't want to start an edit war, so let's first get some clarity here. You reverted my edit of the lede. OK. You claimed that it "...is not a clear improvement", which is a matter of judgement at worst, and not as such grounds for reversion unless you have a better improvement. (Feel welcome to present your improvements if you do). You claim that "...it introduces several errors" but mention none, and you ignore the errors that it corrects. Please at least clarify your points, which I think we could have expected of you before you reverted without stating any justification. Unqualified reversion is not the same thing as editing, and requires more definite justification. JonRichfield (talk) 17:04, 27 August 2016 (UTC)
 * I can't speak for Slawek, but one objection I have is that it prioritizes the wrong thing. Archimedes' derivation is more important than terminological pedantry. —David Eppstein (talk) 17:50, 27 August 2016 (UTC)
 * Errors: that a disc necessarily includes the boundary, and that a curve that is not space-filling necessarily encloses zero area. (Not that either of these small points is appropriate focus for the lead.) No idea what errors it supposedly corrects. Sławomir Biały  (talk) 18:14, 27 August 2016 (UTC)
 * I liked some things about JonRichfield's version, but overall I agree that it was lacking enough in other things to deserve at least serious editing. I kind of like the structure of the first sentence - 'Any circle in the Euclidean plane encloses area ...' is kind of appealing to my ear. But I am not sure I see the 'errors' it corrects, while I do agree with Sławomir and David Eppstein's objections, and also don't see the value of going into pi's unending digits in the first paragraph. Nat2 (talk) 02:45, 17 September 2016 (UTC)

Nice
What a brilliant article. Thank you EdEveridge (talk) 15:22, 10 January 2019 (UTC)

Sources???
Quoting: "Although often referred to as the area of a circle in informal contexts, strictly speaking the term disk refers to the interior of the circle, while circle is reserved for the boundary only, which is a curve and covers no area itself. Therefore, the area of a disk is the more precise phrase for the area enclosed by a circle."

This is clearly just opinion and violates WP:OR (there is no source in the article to backup this)... Nowadays, both "area of a circle" and "area of a disk" work equally fine and are equally right.

When one needs to do the distinction is when one makes the distinction... Otherwise it's often just pendantism for pedantism's sake... You doubt it? Let's see:

For example, we speak naturally about the "area of a square", "area of an ellipse" (what is the word for the interior of an ellipse?) Maybe people should start creating new words for each shape (or making other "safeguards" to make clear they refer to the interior)? Of course not. Why? Because it's not necessary. Simple. Some guys want to use different phrases then let they... Okay. But when it's perfectly clear what "area of a circle" means (or "area of a square", and so on), it looks just unnecessary.

Having said all that, my prediction: someday this article will inform: the two-dimensional Jordan measure of a disk is the most precise or something like that (because area of a circle is so obviously too primitive and cannot be accepted). Not even Bourbaki reached that far. But it seems it will happen someday. 189.6.241.79 (talk) 14:59, 22 February 2019 (UTC)


 * This issue has been discussed massively on this talk page in past. See Talk:Area of a circle/Archive 2. What you see in the article is a compromise. Many Wikipedia articles are imperfect compromises.


 * Regarding your specific objections: I understand why you find it pedantic, but I don't think readers are harmed by the text you mention. I don't think it's a violation of OR, though it might be a violation of RS (which is common in math articles). I don't know the answers to your "square" and "ellipse" questions. Circles and disks/balls are disproportionately important, and every topology book distinguishes between them carefully. Mgnbar (talk) 17:47, 22 February 2019 (UTC)


 * I agree that it does no harm. Maybe I was just making a tempest in a teapot because of intense emotions (yeah, it's funny how much I care about terminology discussions), sorry. Yes, this article lack of inline citations is maybe its biggest problem... It makes very hard to check its historical claims, for example. Thanks. 189.6.241.79 (talk) 20:54, 22 February 2019 (UTC)

"Proof of area of a circle(a=pi*r*r)" listed at Redirects for discussion
A discussion is taking place to address the redirect Proof of area of a circle(a&. The discussion will occur at Redirects for discussion/Log/2021 March 9 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Lithopsian (talk) 17:13, 9 March 2021 (UTC)

addition proposal
I'd like to add the following to this page:

Comparing a circle to a square

Defining the area of a circle means comparing the area of the circle to the area of a square. A possible way to compare the area of a circle to the area of a square is to draw the square first, and place four equal size quarter circles on it, with their origo on the corners of the square.

When the arcs of the four quarter circles cross each other on half way between the center and the side of the square, their combined area equals the area of the square. The distance between the midpoint and the closest corner of the square equals the radius of the circle, and its ratio with the side of the square can be calculated using Pythagoras' theorem. A=area of the square / circle

a=side of the square

r=radius of the circle

$$ r^2=(a/4)^2+(a/2)^2 $$ $$ r=\sqrt{(a/4)^2+(a/2)^2}=\sqrt{(a/4)^2+(2a/4)^2}=\sqrt{1+4}*(a/4) $$ $$ a/4=\tfrac{r}\sqrt{5} $$ $$ a=1.789r $$ $$ A=8*\tfrac{r}\sqrt{5}*2*\tfrac{r} \sqrt{5}=16/5r^2=3.2r^2 $$ or $$ A=\tfrac{16}5*r*r=3.2r^2 $$

Gmac4247 (talk) 15:34, 20 April 2021 (UTC)


 * As I posted to Teahouse ([//en.wikipedia.org/w/index.php?title=Wikipedia:Teahouse&oldid=998040517#area_of_a_circle permanent link]), your work is original research and would not belong in Wikipedia even if it was correct. PrimeHunter (talk) 14:31, 3 January 2021 (UTC)

Thank you for your feedback. I'm waiting for a publication in a reliable source. Gmac4247 (talk) 14:48, 3 January 2021 (UTC)


 * If you're waiting for publication, you should not be trying to add this to Wikipedia. - MrOllie (talk) 15:05, 3 January 2021 (UTC)

Thank you for your contribution. I'm extremely patient.Gmac4247 (talk) 15:27, 3 January 2021 (UTC)
 * You are essentially claiming that the existing formula for the area of a circle or the value of $\pi$ is wrong. That is a WP:EXCEPTIONAL claim that will not be allowed in Wikipedia just because you convince some "reliable" sources to publish it. It would have to be published by multiple highly reputable math journals and that is not going to happen. PrimeHunter (talk) 15:59, 3 January 2021 (UTC)

I put an obstruction here. I'm not claiming, that it's wrong, as you mentioned above. That would be against the 'neutral point of view' guideline. 37.76.12.117 (talk) 16:55, 3 January 2021 (UTC)


 * I agree with the other skeptical editors here. Your proposed contribution is prohibited by No original research. Best wishes. Mgnbar (talk) 16:19, 3 January 2021 (UTC)

Thank you, for your contribution. I guess now it's up to those publishers out there.37.76.12.117 (talk) 16:55, 3 January 2021 (UTC) It wasn't logged in.Gmac4247 (talk) 17:00, 3 January 2021 (UTC)


 * Nope. Waiting will not help. Below I'm copying my answer given to you on 9 January at my User_talk page, just for completeness:
 * [...] Your wanted addition is your original research, so publishing it here, at Wikipedia, would be contrary to WP:OR policy. Apart from that it is based on an unjustified claim, so it is actually not a proof, and it ends contrary to mathematical result, well-known for about thirty eight centuries. As such its chance to be accepted equals precisely zero.
 * In other words, you negate the correctness of computations made by hundreds generations of mathematicians. See Chronology of computation of π.
 * Archimedes knew $310/71 ≤ π ≤ 31/7$ which makes an error margin about 0.002, and it was about 22 centuries ago. Egyptians and Babylonians knew the value more accurate than yours about 4 thousands years ago! Al Khwarizmi knew the coefficient precise to 0.0001 about AD 800.
 * By forcing your result you imply all of them were wrong (even though you deny it in a reply to PrimeHunter).
 * Simply speaking, no reliable source of any scientific credibility will publish your reasoning as a mathematical result. CiaPan (talk) 11:46, 19 January 2021 (UTC)

History Section
The single paragraph in the history section doesn't flow logically. First it is stated that Eudoxus of Cnidus proved the area is proportional to the square of the radius. However, it is later claimed that "Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter". But, this raises the question why Eudoxus of Cnidus was mentioned first. Indeed, Hippocrates of Chios lived a century before Eudoxus of Cnidus, so what motivates the sequencing of the paragraph?

Another, more minor issue, is that proportional to the square of the radius, versus diameter, is trivially equivalent. But it wastes the reader's mental energy when these different ways of referring to the same thing are used, since it momentarily raises the question whether there is a difference. Ajrmmm (talk) 05:08, 5 July 2022 (UTC)