Page "Curve" Paragraph 34

A plane curve is a curve for which X is the Euclidean plane — these are the examples first encountered — or in some cases the projective plane.

A space curve is a curve for which X is of three dimensions, usually Euclidean space ; a skew curve is a space curve which lies in no plane.

These definitions also apply to algebraic curves ( see below ).

However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.