The torsion of a curve in $\mathbb{R}^3$ indicates how much it twists around. The curl of a vector field indicates how much the vector field twists around. Is there a relation between the curl of a vector field and the torsion of a curve through that vector field at a given point?
Relation between torsion of a curve and the curl of a vector field
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calculus
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1Does curve "through" a vector field mean a "flow curve" of that vector field? – 2010-09-22