Planar curves have zero torsion
= Planar curves have zero torsion
All derivatives of a planar curve lie in one fixed two-dimensional vector plane, so $\det(r',r'',r''')=0$ and its torsion vanishes wherever defined.
= Planar curves have zero torsion
All derivatives of a planar curve lie in one fixed two-dimensional vector plane, so $\det(r',r'',r''')=0$ and its torsion vanishes wherever defined.