A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic
geometry context. In particular, a smooth curve is a continuous
map 
from a one-dimensional space
to an 
-dimensional
space which on its domain has continuous derivatives up to a desired order.
Smooth Curve
See also
Closed Curve, Simple Curve, Smooth StructureThis 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