# Is a curve's curvature invariant under rotation and uniform scaling?

The title really say's it all, but once again is a curve's curvature invariant under rotation and uniform scaling?

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A curve's curvature is invariant under rotation. Intuitively, a curve turns just as much no matter how it is oriented. More formally, for a curve $\gamma(s)$ that is parametrized by arc length, the curvature is $\kappa(s) = ||\gamma''(s)||$. Rotation does not change the length of the $\gamma''(s)$ vector, only the direction; therefore, rotation does not affect curvature.