- #1

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[tex] \kappa = \left | \frac{d \hat{\textbf{t}}}{d s} \right | = \left | \frac{d^2 \hat{\textbf{r}}}{d s^2} \right | [/tex]

where t hat is the unit tangent to the curve and r hat is the unit vector describing the curve.

Is the second equality correct? Surely you have to normalize the tangents and not the vectors....