Editing Differentiable curve (section)

=== Torsion ===
{{main|Torsion of a curve}}

The second generalized curvature {{math|''χ''<sub>2</sub>(''t'')}} is called {{em|torsion}} and measures the deviance of {{math|''γ''}} from being a [[plane curve]]. In other words, if the torsion is zero, the curve lies completely in the same osculating plane (there is only one osculating plane for every point {{math|''t''}}). It is defined as
<math display="block">\tau(t) = \chi_2(t) = \frac{\bigl\langle \mathbf{e}_2'(t), \mathbf{e}_3(t) \bigr\rangle}{\left\| \boldsymbol{\gamma}'(t) \right\|}</math>
and is called the [[torsion (differential geometry)|torsion]] of {{math|''γ''}} at point {{math|''t''}}.