Talk:Curl (mathematics)

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Archive 1

uniform curl

The "uniform" in the "depiction of a two-dimensional vector field with a uniform curl" caption to this figure confuses me:

https://en.wikipedia.org/wiki/Curl_(mathematics)#/media/File:Uniform_curl.svg

I can see it as uniform around [0,0] at any radius but it doesn't seem like uniform at any point in the image. Is uniform the right word?

Drf5n (talk) 18:55, 15 May 2024 (UTC)[reply]

×

the sign × is not written using the math quotes, and it is not amongst special characters; someone more experienced from wikipedia should fix that.79.115.168.132 (talk) 20:18, 25 February 2014 (UTC)[reply]

Proposed mnemonical illustration

Here is something which may help, I hope it is self-evident enough to not require a source and not be original research [it isn't - if people can draw illustrations to represent concepts like the Levi-civita tensor: [[File:Epsilontensor.svg]] or integration by parts: [[File:Integration by parts v1.jpg]] which are of course excellent images! - then this should also be allowed]:

Opinions? Sorry about the notation but the basis notation (e_x, e_y, e_z) is clearer than (i, j, k) since these are also used for quaternions, and the e notation has clear extension to any other general curvilinear coordinates. F = q(E+v×B)⇄ ∑_ic_i 13:49, 28 June 2012 (UTC)[reply]

See also here, if interested in the cross product analogue of this picture. F = q(E+v×B)⇄ ∑_ic_i 13:59, 28 June 2012 (UTC)[reply]

if it is by me the second curl is counterclockwise,not to make the modification !! (and eq. 0)79.115.168.132 (talk) 20:18, 25 February 2014 (UTC)[reply]

Better examples?

The current examples are misleading, especially the firs: it starts out with a vector field that is rotating, and tries to implicate that the curl should be non-zero because the vector field is rotating: counter example: 1/(x^2+y^2) (-y,x) . This field rotates quite vigorously, yet it's curl is zero. Another example: (y,0). Nothing rotates, but the curl is quite non-zero!--345Kai (talk) 15:01, 24 October 2012 (UTC)[reply]

Gnarl

According to Wiktionary, gnarl is the "average value of the magnitude squared of the curl of a vector field over a continuous path that is tangent to the vector field at every point". I'm not even going to pretend I understand that. Would some knowledgeable person like to add a reference to 'gnarl' on this page? Cnilep (talk) 03:54, 28 March 2016 (UTC)[reply]

That sense at Wiktionary might be dubious; it is now being challenged. [1] Equinox ◑ 12:00, 5 December 2019 (UTC)[reply]

Dubious claims about geographical usage of terms

"The alternative terminology rotor or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del operator and the cross product, is more used in other countries) for curl and curl F."

Should have some citations or should maybe just be removed. It's pretty vague and pretty irrelevant. I just have anecdotal evidence against it (read: at least my calculus and physics professors at a renowned european university have different habits). — Preceding unsigned comment added by 83.78.181.178 (talk) 11:24, 4 May 2016 (UTC)[reply]

Explanation missing

the angular speed of the rotation is half the magnitude of the curl

94.191.138.186 (talk) 13:52, 27 November 2017 (UTC)[reply]

Comic book analogy?

First paragraph goes:

One analogy shows a man seeming to stand in a Euclidean space graph hologram with arrows coming from him showing how he is actually moving, just like in a comic book except the arrows show where he's going and not where he's been.

What kind of comic book has arrows showing where one has been? Readers will erroneously infer mathematicians don't read comics :) — Preceding unsigned comment added by 5.88.100.66 (talk) 12:58, 16 March 2018 (UTC)[reply]

Article's overall tone

I've noticed that the overall tone of this article is very conversational and seems too casual for a Wikipedia article. I started with rewriting Examples 1 & 2 (while still keeping the content the same), but noticed after reading over it that it had issues outside of the sections that I modified. Some cleanup is needed overall. --Loverthehater (talk) 23:49, 11 May 2018 (UTC)[reply]

Hello @Loverthehater:! With this edit, You introduced an error into the first example, by stating that a stationary object placed in the field would rotate. Now that I know what the sentence said previously, I can see what You probably tried to express. As it reads now, I would not understand a "stationary object" to be able to rotate. Indeed, my first interpretation was that the object in question were a mass point rotating around the center of the system, which is not what would happen. Do You think You could clarify that sentence? I liked the analogy to the paddle wheel very much, since it provides a very powerful intuition. --Lpd-Lbr (talk) 13:14, 11 November 2019 (UTC)[reply]

Definition of curl contains an undefined term p

Here is the definition as I find it today:

$(\nabla \times \mathbf {F} )(p)\ {\overset {\underset {\mathrm {def} }{}}{=}}\lim _{A\to 0}\left({\frac {1}{|A|}}\oint _{C}\mathbf {F} \cdot d\mathbf {r} \right)\mathbf {\hat {n}}$

where $\oint C F \cdot d r$ is a line integral along the boundary of the area in question, and $| A |$ is the magnitude of the area. If $n̂$ is the unit vector perpendicular to the plane, whereas $ν̂$ is an outward-pointing in-plane normal (see caption at right), then the orientation of $C$ is chosen so that a tangent vector $ω̂$ to $C$ is positively oriented if and only if ${n̂, ν̂, ω̂}$ forms a positively oriented basis for $ℝ 3$ (right-hand rule).

In the paragraph following the equation I find no mention of p.

I am guessing that p refers to the point at which the curl is being evaluated. Is that correct?

If that is the meaning of p -- or whatever the meaning -- does it not need to be called out as such in the explanatory paragraph?

Dratman (talk) 02:47, 17 June 2019 (UTC)[reply]

Curl definition should be more similar to divergence definition

I am referring to the divergence definition found on Wikipedia here.

The unused term p referring to a point could be substituted for a clear notation like the one found in the link above.
The "def" above the equal sign is unnecessary.
The right side of the equation as presented is a scalar value, whereas the right side is vector valued. I really think this should be expounded on further/corrected in the article because it won't make sense for beginners.
There exist derivations for both the curl and divergence which highlight their relationship to flow and flux which I feel could serve both articles well. Here's a link to some lecture notes which feature a pretty simple (albeit not mathematically rigorous) derivation of curl and divergence by relating them to infinitesimal flux/flow. (EDIT: A derivation is found already on Wikipedia here). — Preceding unsigned comment added by Sqrtpapi2001 (talk • contribs) 22:45, 20 April 2020 (UTC)[reply]

Replacement of the old-American-Centric notation "curl" by the international notation "rot", in agreement with the international norm ISO/IEC 80000-2

I have replaced the old American-centric notation "curl" by the modern and international notation "rot". See ISO/IEC 80000-2 (section 2-16.17 in the document published by the International_Organization_for_Standardization). I hope you agree with this change. Otherwise, please stop impose English as the international language of science. But I'm sure you will agreed with the use of the norm (after all, we are in the 21th century). — Preceding unsigned comment added by 2a01:cb10:72:1d00:1c26:baf8:7e44:d7ac (talk)

No, thanks. --JBL (talk) 23:47, 8 May 2021 (UTC)[reply]

Usable as a source for something?

I removed a recent IP addition sourced to [2]: basically, I think it's a pedagogical note that might deserve a place in a good textbook or course but not in an encyclopedia. However, the source (by Duane Nykamp) seems of solid quality; can it be used to source anything? For the moment I will stick it in the external links section. --JBL (talk) 22:06, 12 February 2022 (UTC)[reply]

Index notation representation

Wouldn't sqrt(g) be the sqrt of the determinant of the metric tensor, not the Jacobian? Babai08 5Foot2 (talk) 02:51, 7 November 2022 (UTC)[reply]

Regarding the explicit definition of curl

I have tried to find the explicit definition of curl in other sources without luck; and it makes sense to me even more than the implicit definition. However, given that this is the only place where I have seen it, I don't know if I trust it, even though I would like to. TheDogRoscoe (talk) 04:17, 11 February 2024 (UTC)[reply]