Torsion vs Curvature of a curve

Question

I was wondering if there is a simple explanation of the torsion and curvature in $\mathbb{R}^3$ of a curve.

The curvature measure somehow the acceleration perpendicular to the tangent vector, but what does the torsion tell me and how does this concept only become necessary in $\mathbb{R}^n$ with $n \ge 3$?

Answer 1

I am trying to answer your first question: "I was wondering if there is a simple explanation of the torsion and curvature in R3 of a curve".

Torsion of a curve measures the planarity of the curve. That is, the curve is planar (i.e. it lies on a plane) if and only if its torsion is identically equal to zero. You can see here.