Definition:Line/Curve
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Definition
A curve is a line which may or may not be straight.
Plane Curve
A plane curve is a curve which can be embedded in the plane.
Space Curve
A space curve is a curve which cannot be embedded in the plane, but can be embedded in $3$-space.
Arc
An arc is a specific part of a curve.
Also known as
The term curve can often be seen for curved line, but is then specifically understood to mean a line which is specifically not straight.