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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.


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.

Historical Note

Definition:Curve/Historical Note