Talk:Torsion of a curve/Archive 1

Archive 1

"Torsion is analogous to curvature in two dimensions."

Dunno that I like that analogy. Curves in 2D have zero torsion (always). Maybe a better analogy might involve a corkscrew (on the physical side) or a helix (on the abstract side).

This page and the one on curvature might stand to see more discussion of the different formulas for torsion and curvature of parametric curves. There should also be a link to the Frenet-Serret formulas. (That page - on the Frenet formulas - looks nice.)

Lunch 02:06, 28 February 2006 (UTC)

Torsion and curvature are two separate quantities that together define a curve in three dimensions. It is even sometimes called "Second Curvature" because of this. The two quantities define different properties: curvature is the magnitude of the curvature vector, while torsion is the ratio of the normal vector and the derivitive of the binormal vector. They share the properties of defining how a curve is shaped, and that they are intrinsic properties of the curve, but the relationship between them is definitely not just an analogy. — Preceding unsigned comment added by 68.49.149.206 (talk) 21:50, 28 February 2006 (UTC)

Planar curve criteria

A curve is planar if and only if it's torsion is 0 and it is twice differentiable, I believe. I'm not sure who watches this page, but that ought to be changed. — Preceding unsigned comment added by Benjaminsanborn (talk • contribs) 06:25, 28 February 2007 (UTC)

Do we need this as a separate article?

I think this article may be a good beginning section of Torsion tensor, which deals with the general usage of torsion in differential geometry. (Torsion (differential geometry) redirects there.) There is too little to say only about 1-dimensional cases; that is why we don't have Curvature of curves article. How do you think? --Acepectif 06:35, 16 November 2007 (UTC)

No. Besides the somewhat relevant fact that the torsion of a curve is not an example of torsion in the sense of the torsion tensor, the other article is essentially impenetrable. What this article needs is examples and figures. If there is any article it can be merged with, that would be Frenet-Serret formulas.Arcfrk (talk) 04:49, 30 January 2008 (UTC)