Talk:Isoperimetric inequality

message: The 'in R^n' section in the contents appears as
https://en.wikipedia.org/wiki/Isoperimetric_inequality#In_%7F'%22%60UNIQ--postMath-00000019-QINU%60%22'%7F
which probably isn't desired. I don't know how to embed math in contents so can't fix sadly.  — Preceding unsigned comment added by Hu5k3rDu (talk • contribs) 10:39, 9 February 2022 (UTC)
thread_title: Contents formatting error

message: It seems to me that the "proof using standard calculus" is flawed. The second term cannot be varied indepently of the first.
Asides, it is necessary to fix the perimeter of the curve; otherwise we can make the area infinite by blowing up the figure.
This boundary condition is not included at all in the "proof".
Yes, quite so. In fact it would be better to replace this so-called proof by (for instance) the proof from Hardy, Littlewood and Polya's book "Inequalities": they show that this isoperimetric inequality can be derived from Wirtinger's inequality (already proved in Wikipedia on its own page). Fathead99 08:44, 11 June 2007 (UTC)
replies: text: I was coming to the talk page to make the same point. I will move the flawed proof to the talk page so it can be scruitinized, and perhaps someone might fix it, of write i one of the proofs aboveBilllion 21:42, 4 July 2007 (UTC)
thread_title: Untitled

message: The article uses the term Dido's problem. And the lead-in mentions that varieties of this problem have roots in antiquity. Should these two matters and their connection (if any) be briefly explicated further? -- Cimon Avaro; on a pogostick. (talk) 15:47, 14 December 2007 (UTC)
thread_title:  Dido's problem 

message: If I recall, Pappus made important early contributions to isoperimetry, and should probably be mentioned here.  Does anyone have a good reference?  I should be able to dig one up in the next few days.  Silly rabbit (talk) 22:18, 11 February 2008 (UTC)
replies: text: There are some references in the website linked at the bottom. I am still searching for a good single source giving an overview of the history of classical isoperimetric problem through early 20th century. Blaschke's "Kreis und Kügel", Bonnessen–Fenchel, Hadwiger, Burago–Zalgaller and other standard mathematical sources tell only a small part of the story, making tantalizing hints (because it was, presumably, too well known to give the full account?) Arcfrk (talk) 22:49, 11 February 2008 (UTC)
replies: text: Chavel's book on differential geometry is probably the best source.  He may have spent more time than anyone else thinking about different proofs of the isoperimetric inequality. Katzmik (talk) 14:21, 1 June 2008 (UTC)
thread_title:  Pappus 

message: Presumably the statement currently on the page, that L^2 <= A(4pi-A) is the wrong way round, and it should say A(4pi-A) <= L^2 ? Fathead99 (talk) 09:27, 5 March 2010 (UTC)
replies: text: Good catch! Fixed. Arcfrk (talk) 00:03, 6 March 2010 (UTC)
thread_title:  Spherical isoperimetric inequality 

message: Substituted at 18:23, 17 July 2016 (UTC)
thread_title: Assessment comment

message: Hello fellow Wikipedians,
I have just modified one external link on Isoperimetric inequality. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20070713083148/http://mathdl.maa.org/convergence/1/ to http://mathdl.maa.org/convergence/1/
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 13:52, 15 April 2017 (UTC)
thread_title:  External links modified 

message: Hello fellow Wikipedians,
I have just modified one external link on Isoperimetric inequality. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20070715043457/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1186&bodyId=1314 to http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1186&bodyId=1314
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 14:24, 17 November 2017 (UTC)
thread_title:  External links modified 

message: "Although the circle appears to be an obvious solution to the problem, proving this fact is rather difficult."
But... Really? Stating about something true AND obvious that it was hard to prove rigorously kind of gives intuition a win over serious mathematics (even if other obvious intuitions are sometimes wrong). It is the kind of idea that flat-earthers and mystics would like to astound people with. "Look, how hard it was for the main-stream so-called scientists to understand this simple fact!"
I don't advocate for fabricating a more "flattering" and less abusable story, but I do hope that experts:
1. Make sure that claims that something has been hard to prove are also well founded, i.e. not contaminated by popular science misconceptions ("urban legends"), fringe sources etc., or – better – that the difficulties are explained: "The obvious intuitive approach X does not work because of counterexamples / inappropriate problem splitting / difficulty formalizing it / missing consensus over necessary underlying theories / something else."
2. Also make sure that claims about harder-to-grasp generalizations are not transferred unchecked to the simplest versions of the problem.
The intuitive idea of "flipping" dents to increase area will not always work, as a flipped dent may intersect another part of the non-convex shape. It is, however, quite obvious to me that the convex hull of any non-convex shape will have a larger area and a smaller or equal squared perimeter. Uniform scaling of the resulting shape allows, without altering L^2/A, preservation of the optimization constraint (area for perimeter minimization or perimeter for area maximization). I am not a mathematician, and what seems obvious to me may not be easy to prove, or even necessarily true. But these are the kind of intuitive approaches I would like to see being proposed and challenged. Elias (talk) 12:31, 9 November 2021 (UTC)
thread_title:  Was the basic problem really hard to prove? 

message: Is this possibly contradictory?
Compare [lead section]
In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname{per}(S) of a set S\subset\R^n by its volume \operatorname{vol}(S),
:\operatorname{per}(S)\geq n \operatorname{vol}(S)^{\frac{n-1}{n}} \, \operatorname{vol}(B_1)^{\frac{1}{n}},
where B_1\subset\R^n is a unit sphere. The equality holds only when S is a sphere in \R^n.
to [In \R^n section]
Given a bounded set S\subset\R ^n with surface area \operatorname{per}(S) and volume \operatorname{vol}(S), the isoperimetric inequality states
:\operatorname{per}(S)\geq n \operatorname{vol}(S)^{\frac{n-1}{n}} \, \operatorname{vol}(B_1)^{\frac{1}{n}},
where B_1\subset\R ^n is a unit ball. The equality holds when S is a ball in \R ^n. Under additional restrictions on the set (such as convexity, regularity, smooth boundary), the equality holds for a ball only.
Additional conditions seem to be required (convexity, regularity, smooth boundary etc.) for making the sphere/ball special. Yet, these requirements are not in the lead section. And the requirements aren't even properly listed, they're represented in a such-as style. A1E6 (talk) 22:04, 10 November 2021 (UTC)
thread_title:  Contradictory sections? 

message: In:
"Since the amount of water in a drop is fixed, surface tension forces the drop into a shape which minimizes the surface area of the drop, namely a round sphere.",
"...round sphere" is redundant, isn't it? Shouldn't it be changed to  just "sphere"?
174.194.148.3 (talk) 15:54, 12 August 2022 (UTC)
thread_title:  Round Sphere