Talk:Generalized Stokes theorem/Archive 1

Proof Process is too complexed
For one of Stokes theorem

$$ \int_{\Sigma} \nabla \times \mathbf{v} \cdot d\mathbf{\Sigma} = \int_{\partial\Sigma} \mathbf{v} \cdot d \mathbf{r}, $$ or         $$\int_{\mathrm{Vol}} \nabla \cdot \mathbf{v} \; d\mathrm{Vol} = \int_{\partial \mathrm{Vol}} \mathbf{v} \cdot d\Sigma$$

I think we could image its physical chart to early-learn.

--HydrogenSu 05:02, 22 December 2005 (UTC)

Examples
We really need an example here. (NB. I need an example, so I can't offer one!) - Drrngrvy 02:13, 12 January 2006 (UTC)


 * The following discussion is an archived debate of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the debate was move. &mdash; Nightstallion (?) 00:44, 29 January 2006 (UTC)

Requested move
Stokes theorem → Stokes' theorem – The theorem is named after Stokes, and thus his name should be used in the possessive (as in Euler's theorem or Lagrange's theorem). It was moved to Stokes theorem after disagreement over whether the proper title should be Stokes' theorem or Stokes's theorem, but clearly Stokes theorem is incorrect. The most common usage is Stokes' theorem. —Bkell 13:10, 24 January 2006 (UTC)


 * Note that this was only moved by copy+paste a few days ago - should probably be speedy moved back. — sjorford (talk)  20:40, 25 January 2006 (UTC)

Okay, help me out if I'm wrong here. I've been trying to glean what's happened to this page by browsing through the history.


 * The content of this page existed at Stokes theorem from 2001-Dec-2 to 2002-May-8.
 * Maveric149 then copy+pasted the contents to Stokes' theorem.
 * Content was at Stokes' theorem from 2002-May-8 to 2005-Feb-20.
 * Anon user 141.211.120.73 copy+pasted the contents back to Stokes theorem.
 * Current content has been at Stokes theorem since then (barring a brief move and revert to Stokes Theorem on 2005-Dec-10).

The talk pages have also been copy+pasted. We currently have this page as well as Talk:Stokes' theorem. I'm not sure what the correct name is, but it looks like we need to merge the histories. -- Fropuff 08:19, 26 January 2006 (UTC)


 * Support move because of common names principle. If this theorem was being discovered today I would try to get it named Stokes's theorem but I am more than a century late to advocate that. But, there needs to be a history merger before we can do anything. Stefán Ingi 10:48, 26 January 2006 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Piecewise
If M is only piecewise smooth, is it still possible to unambiguously define C1 functions on M? AxelBoldt
 * You definitely raise an interesting issue. I think a proper treatment of the piecewise case requires at least some indication of what sort of integration and differentiation we are performing in the statement of Stokes' theorem.
 * If differentiation is defined weakly (in the sense of distributions), then the theorem almost certainly requires the use of currents.
 * On the other hand, it is possible to relax the C1 condition slightly, and stay more or less in the realm of calculus on manifolds. Specifically, decompose M into its smooth components Mi, which are manifolds with boundary.  A differential form is (for lack of imagination) almost continuous if &alpha; is continuous on each Mi, and the pullback of &alpha; to every intersection $$M_i\cap M_j$$ is almost continuous.  A differential form &alpha; is almost C1 if it is C1 on each Mi and d&alpha; is almost continuous.  Stokes' theorem should then hold for almost C1 forms, at least when the boundaries of the Mi are sufficiently nice.
 * Anyway, it is probably best to restrict the statement of the theorem to manifolds with boundary to avoid technical issues like this. Silly rabbit 16:57, 15 June 2006 (UTC)

Give an example
To quote the beginning of the article:

'Let M be an oriented piecewise smooth manifold of dimension n and let $$\omega$$ be an n&minus;1 form that is a compactly supported differential form on M'' of class C1. If &part;M denotes the boundary of M with its induced orientation, then''' yaddayaddayadda.

It's great to have a precise definition in this article, but (and to relive already asked questions) it'll be great if there was an easier introduction first, maybe stemming from an everyday physical problem. Thank you, --Abdull 17:45, 31 May 2006 (UTC)

Does anyone have a picture of this theorem in action? I've heard it having to do with gradients (maybe I misheard or misunderstood), and I came to this article to see how it worked. A picture would work wonders here, if possible.RSido 03:56, 28 February 2007 (UTC)

Reorganize the article?
I think this article should be reorganized to reflect that it's in a general-reference encyclopedia and not a specialized one intended for mathematicians. The introductory section should explain what the theorem is to someone who doesn't know it, and anyone who knows what an oriented piecewise smooth manifold is, is certainly already familiar with the classic formulation of the theorem, so the current intro doesn't really do much good. So the presentation should start with the classical version, including the physics-textbook "proof" (e.g. Kleppner and Kolenkow, An Introduction to Mechanics) showing the usual diagram with little circulating arrows inside grid squares showing how the contributions from opposite sides of the squares almost cancel. This shows the physical significance of the curl. It could then explain that the modern treatment is a generalization of this old theorem from vector calculus. For the "modern" version, vol. 1 of Spivak's Comprehensive Introduction to Differential Geometry has a somewhat more abstract, but less terse, treatment than Calculus on Manifolds. Phr (talk) 00:54, 10 August 2006 (UTC)

Yes, I agree with Phr and Abdull, the article is much too technical. You dont need to know about mainfolds, compactly supported differential forms and homology groups to understand Stokes theorem. What is needed is a clear physical explanation with pictures. (And I'm a mathematician!) Paul Matthews 15:12, 17 August 2006 (UTC)

I third the suggestion. The people most likely to look up this topic are students taking Vector Calculus or E-M. It should be introduced at their level, and the theorem's significance from the viewpoint of differential geometry moved out of the intro and into its own section. - Arsian120 05:59, 17 September 2006 (UTC)

Here is another opinion regarding the level of sophistication and complexity of the articles in this encyclopedia.

This encyclopedia is a “Hyper-link” document. Any article should start with a very basic description of the article in a language, simple enough to be understood by the average reading public. However, each article should branch deeper and deeper into the subject. With this, it is obvious that the terminology and the mathematical apparatus will go more and more complicated. If developed correctly, at some level, even mathematicians should experience difficulties reading the text beyond certain level, if the subject is not in the area of their own expertise. This would be an excellent illustration for the usefulness of the encyclopedia for the reading public with vastly different areas of interest and level of expertise. After all, I would never look in any encyclopedia for something that I already know very well.

Regards, Boris Spasov

Would the article be more approachable if it were split into two articles? One article could describe the 2-dimensional case common in a vector calculus-level class (after all, we already have an article about Green's Theorem). The other would concentrate on the general form. Thanks for the fish! (talk) 21:59, 17 April 2008 (UTC)


 * For once, I agree with the technical tag. But the solution is fairly simple.  Just move the freshman/sophomore level vector calculus stuff to the top, redo the lede to reflect the change, and bingo, accessibility.  --C S (talk) 06:20, 14 August 2008 (UTC)

Flux cutting and flux linkage
In the main sectionon Stokes' theorem, I reached the equations described by

Maxwell-Faraday equation Faraday's law of induction:	 	   C and S stationary

I was able to derive that myself.

The restriction to a stationary contour C leaves out some interesting electrical phenomena. These involve how to calculate induced emf when the contour and the magnetic field both vary with time. Such situations can occur in electrical machinery. I think that time differentiation with respect to the contour corresponds to flux cutting emf while the time derivative of the surface integral corresponds to flux linkage emf. Unfortunately, typical electrical engineering programs do not treat this subject well.

I think that a derivative of the contour integral that includes both the derivatives arising arising from the time variation of the contour and the magnetic field will give the correct answer.

Since posting this, I have carried out a few simple integrations for varying contours. One case is that for a constant field through a rectangle with dimensions x=vt and y. Another case was a circular contour with r=vt. In both cases, I found that the emf from law of induction gave the expected result. Moreover, this result agrees with the flux cutting law.

This leads me to believe that the law of induction will remain correct even with moving contours. This leaves open the question of nonuniform magnetic field. I will try a multinomial field in x and y. The real question will be: What happens if B is a function of time as well. '' —Preceding unsigned comment added by 99.165.14.155 (talk) 05:57, 27 September 2008 (UTC) PEBill (talk) 21:32, 27 July 2008 (UTC)

Exam
I have a question, does anybody know exactly what form of Stokes' theorem was asked on Stokes' exams at Cambridge? Also what level was the course: undergraduate or graduate?

—Preceding unsigned comment added by 136.152.180.29 (talk) 19:02, 28 April 2008 (UTC)


 * I added a hyperlink to the text of the exam. --Yecril (talk) 14:38, 18 September 2008 (UTC)

this is gash —Preceding unsigned comment added by 78.105.240.153 (talk) 15:59, 10 November 2008 (UTC)

The linked exam, in the first question misspells "show" as "shew"bruno615 (talk) 23:33, 14 December 2008 (UTC)


 * Here is a dictionary entry. "Shew" is an archaic spelling of "show" which was often used prior to the 20th century as a synonym for "prove".  It is rarely used these days.   siℓℓy rabbit  (  talk  ) 03:15, 15 December 2008 (UTC)

Integration on manifolds?
Why does integration on manifolds redirect here? Is there a more appropriate redirect target? I'm curious what articles if any there are on topics related to integration on manifolds, such as integration on chains which is discussed ever so briefly at chain (algebraic topology). It seems to me that this is a topic which is most definitely article-worthy, or that at least we should make some effort to draw together related articles into a list or a category or somesuch. siℓℓy rabbit (  talk  ) 12:36, 15 October 2008 (UTC)
 * In fact, integration on manifolds should better redirect to the integration section in the article differential forms. The generalized Stokes theorem as described here is only the most prominent application, but there are other ones. Thus the redirection should be changed, in fact! If someone reading this is from the staff: please do so. - Thanks in advance, 87.160.93.125 (talk) 16:12, 17 September 2009 (UTC)

Physical approach
This article assumes quite a lot of mathematical background -- is it possible to do a simpler more "physical" treatment first, then do a more formal definition afterwards? The Anome
 * I agree, although I really think people looking up 'Stokes Theorem' will, by and large, have a mathematical background. One section of the page which seems redundant to me is the section expressing the formula in terms of dxdydz, which is just as, if not more, confusing than the curl notation.
 * My guess is that most of those looking up Stokes' Theorem are physics students taking an intermediate electromagnetism class. These students, of whom I was once one, have a mathematical background, but it very rarely goes beyond a semester of real analysis.  I doubt if the discussion currently in the article would be of much help to them. Tpudlik (talk) 06:32, 7 February 2010 (UTC)

Notation for curl
my textbook has this:


 * $$\int_\mathcal{S} \hat \mathbf{n} \cdot \operatorname{curl} \mathbf{v} dA =

\oint_{\mathcal{C}} \mathbf{v} \cdot d\mathbf{R}$$

which doesn't seem quite the same as what is in the article:


 * &int;&Sigma; rot v &middot; d&Sigma; = &int;&part; &Sigma; v &middot; dr

any thoughts? -- Tarquin


 * It is equivalent. - Patrick 19:00 Jan 9, 2003 (UTC)


 * Hardly anyone uses the notation 'rot' anymore. The curl notation is much more standard and I think it's more appropriate. JMO. - Revolver


 * I would agree, the textbooks, lectures, and other material I've read or worked on generally shy away from the 'rot' notation. I think using curl notation would be more widely recognizable and more easily understood by most readers of this article. Memeca16 (talk) —Preceding undated comment added 03:05, 13 September 2010 (UTC).

Fixing this article
It strikes me that great deal could be done to improve this article. As others have pointed out, the very technical lead section obscures the intuitive, more "down to earth" interpretation of this theorem (or at least some of its special cases).

Speaking of special cases or consequences of the theorem, there are many that aren't mentioned here, such as: and also some more easily accessible, "physical" consequences:
 * Cauchy's integral formula and the residue theorem
 * Brouwer's fixed-point theorem
 * The shoelace formula
 * The mechanism of a planimeter
 * Archimedes' principle

I would like to work myself on this article, but since I don't know for sure when I will have time to, I thought I'd bring up these points and solicit feedback!

4dhayman (talk) 01:34, 24 June 2012 (UTC)

History
Hello. Stokes' theorem is a great topic & I'm glad to see there is a nice article here. It seems the theorem has had a long & distinguished history. I wonder if someone wants to add a section on its history -- going from special cases through more general formulations and finally ending up with the version stated for differential forms. I don't know enough to write that stuff myself, although maybe I'll read up just for the fun of it! Happy editing, Wile E. Heresiarch 20:00, 1 Mar 2004 (UTC)

The Soviet Encyclopedia states that the general form is down to Poincare (c.1899) - with differential forms in general probably only defined in the following few years by Cartan. I think it's probably somewhat naive to look for a complete proof then, though. There were subsequent improvements, allowing a 'small' bad set on the boundary, for example.

Charles Matthews 21:59, 1 Mar 2004 (UTC)
 * I have a book by Arnold that calls it the 'Newton-Leibnitz-Gauss-Green-Ostrogradski-Stokes-Poincare formula' Billlion 14:19, 13 Sep 2004 (UTC)


 * What book, exactly? —Preceding unsigned comment added by 136.152.180.29 (talk) 19:00, 28 April 2008 (UTC)


 * Who first proved the Generalized form of the Theorem? Sugarfoot1001 02:47, 8 October 2012 (UTC)

Example?
So I can get a better sense of this theorem:

Suppose I had some paiper-mache machine that I could use to cover an object with a single layer of paiper-mache. What information would the machine need to record to calculate the volume of the object with stokes' theorem?

68.111.85.224 (talk) 04:51, 22 June 2013 (UTC)

Or am I reading it wrong? Could someone calculate the surface area of an object with a planimeter-like device and a pencil?

68.111.85.224 (talk) 21:21, 22 June 2013 (UTC)

Actually, now I get it. The net rotation of stuff going through a surface is equal to the rotation of stuff at the edge of the surface.

68.111.85.224 (talk) 07:30, 26 June 2013 (UTC)

The Name
The theorem is named after Stokes because of his habit of using it on the prize examinations. It aquired its name about 1845 after his students began publishing papers refering to it under this title. This is documented in some of the older mathematics books but does not seem presently to be locatable with Google or other search engines.

It is documented in my Multivariable Calculus book, Multivariable Calculus, Fourth Edition by James Stewart. It also recommends G.E. Hutchinson's The Enchanted Voyage as a source for information about Stokes. --APW 03:35, 20 January 2006 (UTC)

Should it not be "Stokes's theorem" according to modern English grammar? See http://www2.unb.ca/gge/Personnel/Vanicek/StokesPossessive.pdf. — Preceding unsigned comment added by 24.250.21.59 (talk) 22:57, 28 May 2015 (UTC)

More generality than manifolds with boundary
The statement in the article requires that we be interested in manifolds with boundary. But then it gives an example which is not on a manifold with boundary. Instead it's a manifold with corners.



I feel confident that Stokes's theorem extends to manifolds with corners: The corners have measure zero so should not affect any integrals. Nevertheless the article lacks a precise statement along these lines. Moreover, the right statement should be more general than just manifolds with corners. All kinds of bizarre things should be allowable as long as they occur on measure zero sets.

I looked around a little but didn't find anything satisfying. Can anyone supply a reference? Ozob (talk) 02:40, 25 October 2016 (UTC)


 * I figured out where to look; it's the literature on geometric measure theory that considers this question because they're interested in the behavior of rough subsets. Federer's book has a case of Stokes' theorem.  So does Whitney's Geometric Integration Theory; moreover, the latter version is simple enough that it's reasonable to put into the article (I feel like it would be too technical if the article were to start discussing flat chains).  I've edited the article accordingly.  Ozob (talk) 02:43, 26 October 2016 (UTC)

Is there an article on this topic designed to be accessible for the scientists and engineers who use these equations?
In physics, the term Stokes' theorem is used for what this article calls the classical or the Kelvin-Stokes theorem. But neither of these articles seem to be even remotely accessible to the majority of (quite technically capable) people in disciplines like engineering or physics or other technical fields that use vector fields. I realize that mathematicians have a completely different goal from physicists and engineers in the same sense that a tool maker has a different perspective than a tool user. But the curl theorem is a very useful tool to use. If article on the curl theorem exists that is accessible to engineers and I am missing it then I apologize. If not then can an article be dedicated to that purpose preferably either this article or the Kelvin-Stokes one. Thanks. TStein (talk) 22:22, 18 April 2018 (UTC)

Major equation problem
This equation makes no sense to me and is not used in Kelvin–Stokes theorem article. I'm removing it for now.

$$ \iint_\Sigma \nabla \times \mathbf{F} \cdot d\boldsymbol{\Sigma} = \oint_{\partial\Sigma} \mathbf{F} \cdot d\mathbf{r}\,, $$

Brian Everlasting (talk) 22:29, 3 February 2018 (UTC)

Here are some more incomprehensible integrals that I removed from the article

These variants are rarely used:
 * $$\begin{align}

&\int_\Sigma \Big( g \left(\nabla \times \mathbf{F} \right) + \left( \nabla g \right) \times \mathbf{F} \Big) \cdot d\boldsymbol{\Sigma} = \oint_{\partial\Sigma} g \mathbf{F} \cdot d\mathbf{r}\,, \\[8px] &\int_\Sigma \Big( \mathbf{F} \left(\nabla \cdot \mathbf{G} \right) - \mathbf{G}\left(\nabla \cdot \mathbf{F} \right) + \left( \mathbf{G} \cdot \nabla \right) \mathbf{F} - \left(\mathbf{F} \cdot \nabla \right) \mathbf{G} \Big) \cdot d\boldsymbol{\Sigma} = \oint_{\partial\Sigma} \left( \mathbf{F} \times \mathbf{G}\right) \cdot d\mathbf{r}\,, \\[8px] &\int_\Sigma (\nabla \mathbf{F}) \cdot d\boldsymbol{\Sigma} - (\nabla \cdot \mathbf{F}) \,d\boldsymbol{\Sigma} = \oint_{\partial\Sigma} d\mathbf{r} \times \mathbf{F} \end{align}$$

Brian Everlasting (talk) 22:33, 3 February 2018 (UTC)

The first equation the you removed is used (with different variable names) in the, and seems to be a nice compact way to represent the theorem. I'm not sure how it didn't make sense to you, but perhaps having it alongside the more verbose expression would be worthwhile. Azaghal of Belegost (talk) 22:04, 10 October 2018 (UTC)

Green's theorem
The text under the Green's theorem heading is cryptic and/or incorrect. Equating the third terms in the sums of each integral does not give Green's theorem, and why should anyone expect such a matching game will give you a correct answer? Is there a correct way to illustrate Green's theorem as a special case of the Kelvin–Stokes theorem? Azaghal of Belegost (talk) 22:15, 10 October 2018 (UTC)

Spelling
This seems to have been argued over for many years, but at least our spelling in the article should match the title. Few people think that Archimedes' principle needs another s, but most people write Charles's law. The problem is that different people use different pronunciations, and so disagree on the correct spelling. I prefer the s' version for Stokes' theorem and law because this seems to be used in the majority of papers, and Wikipedia follows common usage. All the cites in the OED use this spelling. What does anyone else think?  D b f i r s   23:23, 21 December 2017 (UTC)


 * Disagree, as this is not just a matter of personal preferences, but should be guided by the Wikipedia MOS (manual of style). And MOS:POSS is fairly clear on the choice of  's for singular possessives. cherkash (talk) 18:12, 6 November 2018 (UTC)


 * The policies you quote allow exceptions in line with COMMONNAME. See the references provided for what scientists actually use.   Dbfirs  18:37, 6 November 2018 (UTC)
 * "Common name" is not the same as "common spelling". In this case specifically, no one argues that it should be called anything else but Stokes's theorem (i.e. a "theorem by Stokes"). The only contention is how to spell a singular possessive. Using either Stokes' or Stokes's in this case is not a violation of "common name" policy – and therefore the choice is guided by MOS:POSS instead. cherkash (talk) 22:21, 15 November 2018 (UTC)

Requested move 4 December 2018

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this section. 

The result of the move request was: consensus not to move. In part this was due to the view that this move would run afoul of WP:COMMONNAME. I suggest that the current consensus at MOS:POSS be revisited, but that is beyond the scope of this requested move. However, for this article the spirit of Steve's suggestion is made part of the close: I recommend that the lede begin with a variation of Stokes' s theorem, also spelled Stokes' s theorem, is a statement about..., and will leave the specific phrasing to those who are more involved with this article. This was a -any admin should feel free to revert me if they decide I made the wrong call. Otherwise please talk to me first. -- DannyS712 (talk) 09:03, 22 December 2018 (UTC)

Stokes' theorem → Stokes's theorem – The choice should be guided by the Wikipedia MOS (manual of style). MOS:POSS is fairly clear on the choice of  's for singular possessives. A possible appeal to WP:COMMONNAME is inappropriate here: "common name" is not the same as "common spelling". In this case specifically, no one argues that it should be called anything else but Stokes's theorem (i.e. a "theorem by Stokes", where Stokes is used in its singular-noun possessive form) as opposed to "Stokes theorem" (where Stokes is in attributive use). The only contention is how to spell a singular possessive. Using either Stokes' or Stokes's in this case is not a violation of "common name" policy – and therefore the choice is guided by MOS:POSS instead. It's been discussed twice on the Talk page: see two "Spelling" sections. The first discussion resulted in a move – which was later reverted without a further discussion. And the second discussion has ended without any strong arguments against renaming (i.e. the arguments that weren't refuted by referencing appropriate Wikipedia policies on spelling and style). cherkash (talk) 23:10, 4 December 2018 (UTC) --Relisting. Favonian (talk) 17:34, 17 December 2018 (UTC)


 * Support – Almost all modern guides including our own MOS recommend the final s in singular possessive names ending in s like this one. Dicklyon (talk) 04:58, 5 December 2018 (UTC)
 * Oppose – Almost all sources, text books, and the OED use Stokes' theorem and Wikipedia follows common practice. See WP:Common name for policy.   D<i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  07:09, 5 December 2018 (UTC)


 * Comment: "Almost all" is a vague statement, and unfortunately made without any proof. Seems like an opinion rather than a fact. And I sure hope you didn't make it in the math sense (i.e. "except a set of measure zero") ;) Besides, it's an irrelevant point: I explicitly mentioned "common name vs. common spelling" distinction, seems you've conflated the two and haven't given much thought to it. Your statement could support a "common name" discussion if this was the discussion to be had – whereas this proposal is purely about spelling, as there's no disagreement on the "common name". cherkash (talk) 11:04, 10 December 2018 (UTC)
 * It's a bit like your "fairly clear" above, where you ignore the exceptions, and anyway, it's only a guide.  <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  15:20, 10 December 2018 (UTC)


 * Support – Wikipedia has a style guide, and should follow it, to provide some semblance of consistency and professionalism. On matters of styling, we should not just blow with the wind of random popularity in sources. The difference is such a minor matter that it should not confuse anyone, and maybe spotting the small difference would help educate readers. —BarrelProof (talk) 15:16, 5 December 2018 (UTC)
 * Oppose per usage in reliable sources. The addition of an extra letter isn’t a style issue like capitalization, so WP:AT takes precedence here. Further, nothing in our policy on article titles states we defer to the guideline that is our MOS, despite what some MOS fundamentalists claimhere.   Calidum   02:02, 6 December 2018 (UTC)


 * Reply: WP:AT is not contradicted by this proposal. If you were specifically referring to the WP:COMMONNAME part of WP:AT, then this is addressed above in the nomination already. cherkash (talk) 11:04, 10 December 2018 (UTC)
 * Please quote me the part of COMMONNAME that states spelling is not covered. I won’t hold my breath.  Calidum   22:26, 16 December 2018 (UTC)


 * Oppose per common use in mathematics. Mathematics doesn't have "official names" but Official names (of companies, organizations, or places) should not be altered. still feels relevant. power~enwiki ( π,  ν ) 05:13, 6 December 2018 (UTC)


 * Comment: indeed, the mathematics doesn't have "official names", so I wouldn't find it relevant. You could make an argument about "common name", but its irrelevance to this discussion has been addressed in the nomination already. cherkash (talk) 11:04, 10 December 2018 (UTC)


 * Oppose per common use in mathematics. Naming conventions should not override common use. We also won't call water Dihydrogen monoxide. Same logic.-- 1233 Talk 10:50, 9 December 2018 (UTC)


 * Reply: "Common name" is what you are probably trying to reference here. It's already been explicitly addressed in the nomination. cherkash (talk) 11:04, 10 December 2018 (UTC)


 * Support per nomination: "common name" is not contradicted, therefore MOS:POSS rules the style/spelling as a relevant policy. cherkash (talk) 11:04, 10 December 2018 (UTC) Nominator has already implied their support by nominating the article for moving Dreamy <i style="color:#d01e1e">Jazz</i> 🎷 talk to me &#124; my contributions 10:13, 12 December 2018 (UTC)
 * Oppose. This would just make ourselves look ignorant to every student of mathematics in the world... or worse still, to be suffering from purism. Perhaps people should call it Stokes's theorem, but they don't, and it's not our job here to correct that. If some of the the rules lead in another direction then they need to be tweaked. Andrewa (talk) 09:35, 12 December 2018 (UTC)
 * Oppose per the formulation of my personal opinion through User_talk:Dreamy_Jazz/Archive_2: If you compare the number of pages for both: Stokes's theorem gives you ~37,000 results, whereas "Stoke's theorem" gives ~319,000 results (through Google). So the majority (at least 88%) of sources use only the current article's name (otherwise they would show up in the other search too). Also, from looking down the list from "Stokes's law" a few of these sources have this as an alternative spelling. Dreamy <i style="color:#d01e1e">Jazz</i> 🎷 talk to me &#124; my contributions 21:46, 14 December 2018 (UTC)
 * It is not our usual plan to let sources vote on our styling. And contrary to some of the claims above, "Stokes's" was actually very common nearly a hundred years ago, and it has never been uncommon.  Styles changed, and they've changed back, as all modern English style and usage guides describe; that's why MOS:POSS evolved as it did, with a consensus of WP editors. Dicklyon (talk) 02:18, 15 December 2018 (UTC)
 * I agree that "s's" was once common, especially in British English, but you wouldn't let a style guide dictate that we use "Archimedes's theorem" would you?  <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  07:57, 15 December 2018 (UTC)
 * Hundreds of books do use "Archimedes's theorem". Are you saying that makes them look bad somehow?  Explain... Dicklyon (talk) 04:30, 17 December 2018 (UTC)
 * I'll let Dbirs speak for themselves, but I certainly think it makes all of these books a little less credible to many readers, myself included. And when I followed your link, Google gave me 250 ghits and helpfully asked Did you mean: "Archimedes theorem"?, so I followed the link they gave and got 1,810 instead (including most of those from the former search). I know we no longer have consensus that readers come first, but I intend to do what I can for them anyway, and opposing this move is part of that. Andrewa (talk) 09:42, 17 December 2018 (UTC)
 * Well of the the "hundreds of books" that Google finds for me, a few do use "Archimedes's" but many are repeats, and some use just "Archimedes'" despite the Google supposed filter.  <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  12:36, 17 December 2018 (UTC)


 * Support per MOS:POSS. There is no magical exception for this page. "Oppose per the formulation of my personal opinion"? Seriously?  "Oppose per usage in reliable sources" is also nonsensical.  RS use both styles; it's a house style matter. Those that follow one style guide write "Jones'" in all such cases, and those following another style guide write 'Jones's" in all such cases.  We have our own style guide and it follows the latter rule.  See also WP:SSF; this is very clearly a specialized-style fallacy (i.e., "write the way the journals I read do, even though WP is not a journal".  It's not valid reasoning here (or anywhere a particular style manual is in play).  — SMcCandlish ☏ ¢ 😼  16:21, 15 December 2018 (UTC)
 * Reliable sources most commonly use this spelling, so we use this spelling. Please show me the part of COMMONNAME that gives any deference to the MOS.  Calidum   22:28, 16 December 2018 (UTC)
 * LOL. The entire thing is devoid of any indication it could apply to style questions, site-wide consensus is that it does not (thousands and thousands of RMs over 17+ years using MoS rationales), and we would not have MoS rules about this if they could not be applied. Let's not be silly.  Your perpetual "AT is at war with MoS and AT wins" nonsense is against all the instructions we are provided about how to interpret our policies and guidelines, at WP:P&G, WP:CONSENSUS, WP:GAMING, WP:TE, WP:WIKILAWYER, WP:COMMONSENSE, WP:NOT, etc.  — SMcCandlish ☏ ¢ 😼  10:33, 20 December 2018 (UTC)


 * Support per MOS:POSS and . If someone wishes to revisit MOS:POSS then by all means do, but we have a house style and we should use it, and not make exceptions for things that do not merit one. For all of the mathematics students we will be offending, there will be a handy redirect at their preferred spelling.  C Thomas<sup style="font-size: x-small; color: brown;">3   (talk) 07:03, 16 December 2018 (UTC)
 * Comment ... so you wouldn't even make an exception for Archimedes's theorem? Strict adherence to such a policy in the face of common usage would make Wikipedia look silly.  It's our house style that need clarifying to allow for exceptions.  <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  08:46, 16 December 2018 (UTC)
 * Very well said... but with the redirect it's no big deal. We are a general encyclopedia. If math undergrads lose marks for following our style, serves 'em right for not reading and preferring the sources, and hopefully they have learned something, which is supposed to be the goal of education after all. I'd prefer we followed the sources and think that's our normal policy and practice, but again no big deal. Andrewa (talk) 15:26, 16 December 2018 (UTC)
 * , probably not. Were I to write my own paper on the theorem, I am sure I would use the ‘s construction. I personally don’t think it looks silly, nor do I think it makes Wikipedia look silly, though I can appreciate the fact that you do. In my opinion it’s merely a choice we get to make as a content publisher which way we spell it, and we’ve already decided in the MOS what our preference is. If we want to revisit that choice, let’s do so.  C Thomas<sup style="font-size: x-small; color: brown;">3   (talk) 04:46, 17 December 2018 (UTC)
 * If this RM is rejected, then that recent edit to the MOS should indeed be revisited and probably reversed, see below. Andrewa (talk) 09:26, 17 December 2018 (UTC)


 * Oppose. Current is convention. Xxanthippe (talk) 04:20, 17 December 2018 (UTC).
 * Oppose. When MOS collides with WP:COMMONNAME, COMMONNAME should win. This is not the right site to be crusading for people to name and spell things the way you think is right, when they don't already. Or, next are we going to be applying the same reasoning to proper nouns, like Bojangles' Famous Chicken 'n Biscuits? —David Eppstein (talk) 05:06, 17 December 2018 (UTC)
 * It's not a COMMONNAME matter, it's a matter of some publishers following style guides (or writing their own) that like to drop the trailing s from singular possessives that end in s (or an /s/ or /z/ sound, or ss, or names from antiquity, or Biblical names more specifically, or insert a dozen other variations on this), and some, including WP and The Chicago Manual of Style have dispensed with this and just use  's across the board.  of the consensus discussion on MOS:POSS was to confirm whether WP is going to have that particular style, to stop randomly veering between styles as you are arguing to do here.  — SMcCandlish ☏ ¢ 😼  10:33, 20 December 2018 (UTC)
 * Oppose. I agree with David Eppstein. Up until 6 Jan 2018 our MOS:POSS permitted both forms (it just required consistency within the article). This was changed in an effort to streamline our guidelines by one of the contributors to this discussion. I think that that edit should be revisited as it does not take this issue into account. --Bill Cherowitzo (talk) 05:33, 17 December 2018 (UTC)
 * Agree. Well said. But see also User:Andrewa/Rules, rules, rules. Andrewa (talk) 09:26, 17 December 2018 (UTC)
 * Support. I usually feel strongly that wikipedia should follow common scientific conventions / terminology / etc., rather than "improve" on them. The reason I usually feel that way is (1) various wikipedia rules, and (2) people read other resources besides wikipedia and get confused if they're inconsistent (3) people trying to "improve" over common practice on wikipedia often actually make it worse because the common practice often has advantages that aren't immediately obvious. I don't think any of those are really applicable here. (1) is at least debatable. For (2), I don't think readers will have trouble connecting this article to their textbooks, especially if the alternate spelling is in the first sentence. For (3), the consistent "'s" singular possessive is just plain better in general and we should look for excuses to use it. --Steve (talk) 10:50, 17 December 2018 (UTC)
 * ... so do you really support the move to s's?  <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  12:36, 17 December 2018 (UTC)
 * Yes! --Steve (talk) 11:58, 18 December 2018 (UTC)


 * Oppose. COMMONNAME is part of a policy. MOS is a guideline. Where guidelines and policies clash typically policies take precedence. And in this case it seems perverse to me to prefer an internal guideline over what outside sources say. I'll quote WP:5P1
 * Wikipedia is an encyclopedia
 * Our encyclopedia combines many features of general and specialized encyclopedias, almanacs, and gazetteers. Wikipedia is not a soapbox, an advertising platform, a vanity press, an experiment in anarchy or democracy, an indiscriminate collection of information, or a web directory. It is not a dictionary, a newspaper, or a collection of source documents, although some of its fellow Wikimedia projects are.
 * I think the business about being a 'encyclopaedia' and not a 'vanity press' is relevant here.Dmcq (talk) 14:57, 17 December 2018 (UTC)


 * Oppose per David Eppstein, basically. XOR&#39;easter (talk) 16:27, 17 December 2018 (UTC)
 * Oppose per English grammar. In ictu oculi (talk) 18:19, 17 December 2018 (UTC)
 * Oppose It is the style manual that needs to be changed, not the title of this article. The proposed new name is certain more logical: English grammar is not logical. —- Taku (talk) 20:52, 17 December 2018 (UTC)
 * Oppose. Especially because "Stokes's theorem" is pronounced differently from "Stokes' theorem", I think it is a different (much less common) name, not just a different spelling of the same name. Danstronger (talk) 00:03, 20 December 2018 (UTC)
 * It certainly would not be in my or many other dialects. We've been over this before many times, in the all the discussion relating to MOS:POSS.  — SMcCandlish ☏ ¢ 😼  10:40, 20 December 2018 (UTC)
 * Interesting point... I would pronounce Stokes's as Stokesez. Is this just me, or do others feel that way too? Andrewa (talk) 11:54, 20 December 2018 (UTC)
 * I wonder if there is an ENGVAR difference. I would always pronounce Stokes' as one syllable.   <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  12:11, 20 December 2018 (UTC)
 * ENGVAR may well be applicable. I am uncomfortable with Stokes's and James's and I think I therefore unconsciously assume that there's some point being made by the extra s, and add the ez in spoken English to preserve the intended meaning that I'm assuming is there. Except in the case of St James's Palace, I'm used to it and just pronounce it James. Andrewa (talk) 19:20, 20 December 2018 (UTC)
 * I think I would pronounce both "Stokes's theorem" and "Stokes' theorem" the same way – as Stokesez theorem (unless I was talking really fast, in which case I might blur the end a little) – since I think that's the way to verbally express the possessive nature. I just think of those as two different ways of writing down the term using characters and punctuation marks. If I didn't want to include the –ez, I might say "the theorem of Stokes" or "the Stokes theorem". (For some reason, I would never say "Baysez theorem".) —BarrelProof (talk) 20:09, 20 December 2018 (UTC)
 * I think it's familiarity. My brain is programmed to expect "Stokes'" and "James'" but "St James's Palace". That's how language works in practice (see Language Acquisition Made Practical... oops that's a redlink) and it seems so obvious but it's only fairly recently that this was acknowledged by linguists. But Wikipedia's naming conventions are right up to date (but not our content in this case). Andrewa (talk) 21:18, 20 December 2018 (UTC)
 * No, ENGVAR could not be applicable, because this varies regionally (sub-nationally), not nationally (in large parts of the southern US, for example, such possessive name constructions are compressed to avoid the double sibilant in spoken English, and this tends to affect resistance level to spellings like "Stokes's"). Nevertheless, major style guides like Chicago are moving to consistently applying  's instead of making up inconsistent exceptions. Even when exceptions were popular, style guides could never agree on when to make one or why.  Again: We've been over this before many times, in the all the discussion relating to MOS:POSS.  — SMcCandlish ☏ ¢ 😼  19:08, 21 December 2018 (UTC)
 * Oppose I'm usually a stickler for following the MoS, but in this case it would seem the MoS was recently changed in an effort to simplify things, but simpler isn't always better. I think that change to the MoS needs to be reverted back to its previous state. Rreagan007 (talk) 00:24, 22 December 2018 (UTC)

Discussion
I had a look at the MOS page history and this seems to be the edit referred to above. There seems no mention of it at Wikipedia talk:Manual of Style (or have I missed it?). , was it discussed elsewhere? Andrewa (talk) 04:05, 18 December 2018 (UTC)
 * The edit summary gives a pretty good hint about where to look for the relevant RFC discussion. Dicklyon (talk) 04:07, 18 December 2018 (UTC)
 * Here it is: Village_pump_(policy)/Archive_140. Dicklyon (talk) 04:10, 18 December 2018 (UTC)
 * Thank you! Should we simplify the advice of the WP:Manual of Style to choose between a pronunciation-based option and a uniform "add apostophe and s" option, in favor of just the uniform approach, since the pronunciation-based approach is complicated, seems to be misunderstood, and is hard to apply? closed as consensus in support of the proposal. And I like the simplification, but it seems that it might now be oversimplified. See how this RM ends up I guess. Andrewa (talk) 04:19, 18 December 2018 (UTC)
 * I recommend people go back and read that discussion, and the earlier one at Wikipedia talk:Manual of Style/Archive 198, to understand how thinking evolved on this. There has been a lot of misunderstanding, and probably still is.  Also consult any modern style guides about this to see how thinking has evolved in recent decades. Dicklyon (talk) 05:11, 18 December 2018 (UTC)
 * The goal is to write the best encyclopedia, not necessarily the best rule book. This particular rule seems not to work in this particular case. Yes, recommend that people read the past discussion, and also the RfC itself, to reduce the reinventing of the wheel. Maybe the RfC first as the previous discussion is a bit daunting, lacking focus IMO. But then so is Wikipedia generally. Andrewa (talk) 08:07, 18 December 2018 (UTC)

There is nothing in the text or examples of COMMONNAME, nor in sources, to suggest that Stokes' theorem and Stokes's theorem would be considered different names for the same topic. Rather, they simply use different ways to typographically style the possessive of the name Stokes. "Stokes's" is the more modern and preferred way according to all modern style and grammar guides and our own Manual of Style, while "Stokes'" is a common traditional way that is more ambiguous with respect to pronunciation and interpretation, and is often used just because so many people confuse the rules for singular and plural possessives (as becomes very clear when you read past discussions about this topic). The comments above about COMMONNAME and MOS being in conflict is simple nonsense, as is the notion that COMMONNAME gets extra power from being on a page called policy; it is simply a strategy for WP:RECOGNIZABILITY. Adding the final s makes these names no less recognizable, and less ambiguous of interpretation. Dicklyon (talk) 15:59, 18 December 2018 (UTC)
 * Comment on WP:COMMONNAME.
 * Case well made but flawed IMO. Yes, there is a sense in which Stokes' theorem and Stokes's theorem are names of the same thing. But the latter is confusing, owing to the former being used in sources. My reaction on seeing Stokes's theorem is "What? I know what Stokes' Theorem is, so what are they talking about here?" Remember we are dealing with people who are for some reason interested in the theorem, and we (I include myself) tend to be an infuriatingly but naturally pedantic lot in some ways, and less interested in style guides than in the underlying logic of language and meaning.
 * Two examples... for one, see my long-standing essay at User:Andrewa/Andrew's Principle and note the distinction from User:Andrewa/Andrew Point. More famously, Wolfgang Pauli hated to see the Pauli exclusion principle called the Pauli Principle, as he used the latter term to describe the principle that the competence of a theoretical physicist could be best assessed by noting their (in)competence in experimental physics. Pauli was noted for his exceptional performance in a physics lab (apparatus would smoulder and burn if he so much passed by the laboratory door in the corridor, and he once allegedly destroyed a complex vacuum rig at Gottingen Academy of Sciences just by travelling on a train that unfortunately stopped at a signal adjacent to the laboratory), and he maintained that this was the best proof of his high rank in theoretical physics.
 * So to some it is confusing, and that means, less recognisable.
 * So disagree that Stokes' theorem (however capitalised) is in any way ambiguous of interpretation. It is Stokes's theorem that is (however slightly) ambiguous of interpretation. Andrewa (talk) 20:53, 18 December 2018 (UTC)
 * , I get where you are going, but I can't say I agree with your line of reasoning. The examples you give are about two similarly-named principles. Pauli wasn't upset because he thought the "Pauli Principle" was somehow wrong or confusing: he wanted to save the term for a completely different principle. Similarly, if people are mixing up your two essays, then perhaps they need more descriptive names. There is no such confusion or need for differentiation here: Stokes's theorem is famous enough that it needs no qualifier, and there are no other theorems associated to George Stokes. Nor are there any other famous Stokeses with theorems of their own that we might somehow confuse them with. If there were another Stokes with a theorem, calling it "Stokes's Theorem" in an attempt to differentiate it from "Stokes' Theorem" would be utterly confusing.To your other points: I am also one of those 'pedantic people' you speak of. I find no such confusion between "Stokes'" and "Stokes's", and I studied the theorem in college as well. It is not as though all sources everywhere use only "Stokes'" and it is just Wikipedia that is proposing "Stokes's"; it is relatively common to see it either way. If it were truly that confusing, those sources would be issuing corrections in subsequent editions to "fix" the problem. Finally you say that we pedants are more concerned with underlying logic of language and meaning than we are with style. The whole point of style is to bring logic and consistency into writing so that it becomes more meaningful (or at least better retains its original meaning). Is this comment suggesting that you find the "Stokes's" construction illogical?  C Thomas<sup style="font-size: x-small; color: brown;">3   (talk) 22:31, 18 December 2018 (UTC)


 * The first sentence would presumably say "Stokes's theorem, also spelled Stokes' theorem, is a statement about...". I think between this sentence, and general knowledge of English, and the article content, that's enough to ensure that virtually all readers will realize that this is the article about the same topic that they saw in their textbook, even if it's spelled s's here. --Steve (talk) 11:37, 19 December 2018 (UTC)
 * Agree. The confusion is trivial and will be quickly resolved. It's no big deal, as the reasons for avoiding the extra s are almost as trivial as the reasons for adding it, when reader benefit is considered... but then we don't care about that any more, do we? (-> Andrewa (talk) 20:51, 19 December 2018 (UTC)
 * There is no need to change anything. The current title is the spelling commonly used in references and in my opinion should be retained according to policy.  If some editors don't see the application of WP:COMMONNAME and see this as purely a spelling issue, then I quote from Manual_of Style/Spelling: "In both British English and American English, many words have variant spellings, but most of the time one variant is preferred over the other. In dictionaries, the preferred spelling is listed first among the headwords of an entry." and I quote the entry in the Oxford English Dictionary: "Stokes' theorem  n. the theorem that the line integral of a vector function round a closed path is equal to the surface integral of the curl of the function over any surface bounded by the path." and in Oxford Online: "Stokes' theorem  (noun, Mathematics) A theorem proposing that the surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function around that path." and in Merriam-Webster: "Stokes' law".  In fact I can't find a single dictionary that spells it "Stokes's".  The supposed "rule" in our manual of style was changed, by an editor involved above, earlier this year, to exclude such exceptions to the practice of adding 's for all possessives, regardless of the length or ending.  This is by no means universal practice in the UK, and I don't think this opinion should be forced on Wikipedia even if there are some American style manuals that recommend the practice.  The discussion was not closed, but the editor decided that there was enough support to make the change.  Perhaps we should revisit the wording of our manual of style as suggested above.   <i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i>  17:29, 19 December 2018 (UTC)
 * Well said. Andrewa (talk) 20:55, 19 December 2018 (UTC)

Have we seen it all before
It's stated above (by a supporter of the extra s) that this has all been settled elsewhere. If so perhaps it's a case of wp:CCC.

To avoid reinventing the wheel, links to those previous discussions, with a comment as to what consensus was reached and when, would be good IMO... make them on my talk page if you'd prefer not to clutter here, or somewhere else and give me a link. For my part I think this off-wiki archive St James' or St James's (which cites an authoritative linguist), and the titles of St James's Palace and St James' Church, Sydney (which might even invoke ENGVAR as also suggested above), seem relevant. Hang in there. Andrewa (talk) 19:20, 20 December 2018 (UTC)


 * The above discussion is preserved as an archive of a requested move. <b style="color:red">Please do not modify it.</b> Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Mathematical Interpretation - Kelvin-Stokes theorem?
User:Binishjoshi recently gave a mathematical section in the introduction its own subheading and paragraph. The conceptual split seems appropriate but now it looks oddly placed, having a subsection in the introduction.

Is the description given under Mathematical Interpretation the Kelvin-Stokes theorem specifically? Meanwhile the subsection Kelvin-Stokes theorem is missing a statement of its main formula. Suggest moving this content if someone can confirm that the content can be identified with Kelvin-Stokes theorem. CyreJ (talk) 19:34, 10 March 2020 (UTC)