In
differential geometry, the notion of
torsion is a manner of characterizing a twist or
screw of a
moving frame around a curve. The
torsion of a curve, as it appears in the
Frenet–Serret formulas, for instance, quantifies the twist of a curve about its tangent vector as the curve evolves (or rather the rotation of the Frenet–Serret frame about the tangent vector). In the geometry of surfaces, the
geodesic torsion describes how a surface twists about a curve on the surface. The companion notion of
curvature measures how moving frames "roll" along a curve "without twisting".