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Frenet vector moves about an "origin" which is the centre of the rigid object (pick some point within the object and call it its centre). The areal velocity of the tangent vector is:
:

::

Likewise,
:

:

Now apply the Frenet-Serret theorem to find the areal velocity components:
:

:

:so that

:as claimed.

The Darboux vector provides a concise way of interpreting curvature ? and torsion

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