Talk:Torsion of a curve

Animation not animated

I cannot see the animation moving. Is there something wrong with it or it is just me? I'm using firefox in a Debian wheezy box. Juliusllb 09:56, 20 November 2013 (UTC) — Preceding unsigned comment added by Juliusllb (talk • contribs)

For me it only plays when viewed at full size. — NuclearDuckie (talk) 14:45, 9 April 2014 (UTC)

Same for me. —DIV (120.17.85.139 (talk) 04:39, 22 June 2017 (UTC))

"any space curve with constant non-zero curvature and constant torsion is a helix"

Doesn't a helix require non-zero torsion as well, given that constant curvature with zero torsion is a plane curve? — Preceding unsigned comment added by 130.209.117.36 (talk) 16:07, 11 October 2015 (UTC)

You are right. I have fixed this. (A curve with constant curvature and zero torsion is a circle.) Arcfrk (talk) 08:09, 13 October 2015 (UTC)

Examples / illustrations

Besides the animation, I think it would be instructive to have static images with very simple curves rendered in colour with respectively their curvature and torsion (i.e. images would have to be paired). A suggestion would be a plane ellipse that is then shown projected/bent onto increasingly curved 'planes'. —DIV (120.17.85.139 (talk) 04:42, 22 June 2017 (UTC))

Are the "Definition" and "Alternative description" intended to be equivalent?

Are this article's "Definition" and "Alternative description" of torsion equivalent?

The article doesn't explicitly say they are, but it might be implied ("Then the torsion can be computed from ..."). I'm led to wonder because the Encyclopedia of Mathematics article "Differential geometry" gives a formula for torsion—

$k_{2}={\frac {(\mathbf {r} ^{\prime },\mathbf {r} ^{\prime \prime },\mathbf {r} ^{\prime \prime \prime })}{|\mathbf {r} ^{\prime }\times \mathbf {r} ^{\prime \prime }|^{2}}}$

—that, apart from notation, seems the same as this article's "Alternative description"—

$\tau ={{\left({r'\times r''}\right)\cdot r'''} \over {\left\|{r'\times r''}\right\|^{2}}}{\text{,}}$

—yet EoM shortly afterward states a version of the Frenet–Serret formulas in which the torsion $k_{2}$ seems to be the negative of the torsion $\tau$ known to this article's "Definition" section and to the Wikipedia article on Frenet–Serret formulas.

— 2d37 (talk) 01:25, 15 June 2020 (UTC)

Notation for arclength derivatives

Hello, I was just using this page as quick-reference during a tutoring session, and at a glance it was easy to mistake the $B'$ in $B'=-\tau N$ as a derivative with respect to $t$ rather than $s,$ which led to some confusion and lost us some time as I was scrambling to check calculations in different formulas that were getting different answers. This is my fault, to be clear, and I should've realized that for torsion to be intrinsic to the curve that derivative would have to be a derivative with respect to arclength, but I do think it'd be easier to prevent that mistake if the derivative was written with Leibniz notation instead, as ${\frac {dB}{ds}}.$

Is there a particular reason why this wouldn't be the preferred notation? I don't find it too cumbersome in this sort of context, and I think it adds a good deal of clarity, but if it's just not the convention then I understand. AMathTutorUsername (talk) 09:21, 18 January 2025 (UTC)

In my textbook these derivatives are designated by dots instead of primes. I think this is done for conciseness and clarity, and I think it is the preferred notation in differential geometry. I think the traditional notation you suggest would probably be too cumbersome, but I think the primes should be changed to dots throughout the article to avoid confusion.—Anita5192 (talk) 16:17, 18 January 2025 (UTC)

Thank you for your reply. I would like to say that personally the overdot is highly associated with its use in mechanics as a derivative with respect to time, so this would also have been likely to confuse me at a glance. This is in part due to my personal background with these subjects, but I also think that difference in experience is a meaningful consideration in terms of how an article like this should be written, compared to a textbook which has a higher degree of context associated with it and a more uniformly experienced audience.

I would also like to clarify what I meant by "the preferred notation": I understand that in situations where there are more complicated expressions in terms of these derivatives, the prime and dot notation is often superior, and I have encountered that myself in mechanics. I just don't think anything in this article really takes advantage of that, so in this particular context I see little cost associated with using the Leibniz notation. Apologies if this feels like I'm moving the goalposts, I realize I was just less clear than I should've been previously.

Personally I think the Leibniz notation would be unmatched in terms of its clarity here, but I can also understand the idea that the article should be written with the notational convention which matches its field - I just also think it's worth noting that not all users will have that background. AMathTutorUsername (talk) 22:27, 26 January 2025 (UTC)