Talk:Torsion of curves

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[edit] "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.