The curvature and torsion: how to distinguish the shape of a curve 
Example 1
Let \[\begin{array}{rl} f:[0,2\pi] & \rightarrow\mathbb{R}^{2}\\ t & \rightarrow\left(\cos(t),\,\sin(t)\right) \end{array}\]
Then \(f'(t)=\left(-\sin(t),\,\cos(t)\right)\); \(v(t)=\left|f'(t)\right|=1\) and the trace of this curve is:
