The curvature and torsion: how to distinguish the shape of a curve 
Important remark about curvature
Unlike the planar case, in the three-dimensional case the curvature takes only non-negative values. At the points where the curvature is different from zero, the curve "turns" to the side to which the
normal vector (of the Frenet-Serret frame) points. In the planar case, the curvature with sign has the additional feature of providing information about the behavious of the normal over time.
Note that, in the planar case, it was possible to include the information about the normal in the curvature function because the normal vector can only take two positions relative to the tangent line - to the left (\(k>0)\) or to the right (\(k<0)\). In the three-dimensional case this is not possible because the normal vector can take an infinite number of positions with respect to the tangent line.
