The closed curve problem asks one to find necessary and sufficient conditions that determine when the
integral curve of two periodic functions 
and 
with the same period 
is a closed curve.
Closed Curve Problem
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Cite this as:
Weisstein, Eric W. "Closed Curve Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ClosedCurveProblem.html