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The tools of calculus developed so far allow us to describe most of the important properties of a smooth curve: which are its direction at any point, and how much it deviates from straightness there. This is measured by its curvature. How its path differs from planarity is measured by its torsion, also easily calculated.
15.1 Parametric Representation of a Curve and its Intrinsic Properties
15.2 Intrinsic Properties of a Curve
15.3 Curvature and Radius of Curvature
15.5 Torsion