A smooth curve is a curve given locally by a parametrization whose derivatives of every order exist and are continuous. A curve having continuous derivatives only
through order 
is instead called a 
curve.
Smooth Curve
See also
Closed Curve, Simple Curve, Smooth StructurePortions of this entry contributed by Christopher Stover
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Cite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Smooth Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SmoothCurve.html