Editing Differentiable curve (section)

===Curvature===
{{main|Curvature of space curves}}

The first generalized curvature {{math|''χ''<sub>1</sub>(''t'')}} is called curvature and measures the deviance of {{math|''γ''}} from being a straight line relative to the osculating plane. It is defined as
<math display="block">\kappa(t) = \chi_1(t) = \frac{\bigl\langle \mathbf{e}_1'(t), \mathbf{e}_2(t) \bigr\rangle}{\left\| \boldsymbol{\gamma}'(t) \right\|}</math>
and is called the [[curvature]] of {{math|''γ''}} at point {{math|''t''}}. It can be shown that
<math display="block">\kappa(t) = \frac{\left\| \mathbf{e}_1'(t) \right\|}{\left\| \boldsymbol{\gamma}'(t) \right\|}.</math>

The [[Multiplicative inverse|reciprocal]] of the curvature
<math display="block">\frac{1}{\kappa(t)}</math>
is called the [[radius of curvature (mathematics)|radius of curvature]].

A circle with radius {{math|''r''}} has a constant curvature of 
<math display="block">\kappa(t) = \frac{1}{r}</math>
whereas a line has a curvature of 0.