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In differential geometry, the torsion of a curve, represented with τ, is a measure of how much a curve twists out of the plane containing its tangent and principle normal vectors. It is equal to

\tau = - \hat{ \bold{ n }} \cdot \frac{d \hat{ \bold{ b }}}{dt} =  - \frac{1}{\kappa} \ \frac{d \hat{ \bold{ t }}}{dt} \cdot \frac{d \hat{ \bold{ b }}}{dt}

where κ is the curvature and t, n, and b are the tangent, normal and binormal vectors respectively.

Similarly to how curvature is the reciprocal of the radius of the osculating circle, torsion is the reciprocal of the radius of torsion, represented with σ.

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