### Curvature and Torsion

**Definition:**
Let \(f:\, I\rightarrow\mathbb{R}^{3}\) be a \(C^{2}\) regular curve
parameterized by arc length \(s\in I\). The *curvature* of \(f\)
is the function \(k\) given by \[k(s)=\left|f'(s)\right|\]

**Important observation about the curvature...**

**Definition:**
Let \(f:\, I\rightarrow\mathbb{R}^{3}\) be a \(C^{2}\) regular curve parameterized by arc length
\(s\in I\). The *torsion* of
\(f\) is the function \(\tau\) **defined on the points where
\(f''(s)\neq0\)** (that is, where the curvature is strictly positive),
such that
\[B'(s)=-\tau(s)N(s).\]