Now that we are familiar with numerous examples of plane curves and space curves and can also calculate the length of curves, we turn to further special properties of curves: curves can be parametrised in many ways. Among these many types, the parametrisation by arc length plays a prominent role. We introduce this parametrisation. Furthermore, curve points generally have an accompanying trihedron, a curvature and a torsion. These vectors or quantities are easy to determine. The Leibniz’s sector formula allows the calculation of surface areas enclosed by curves, or more generally the surface area swept by a ray.