Space curve

Topological curve

A plane curve is a curve for which ${\displaystyle X}$ 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 ${\displaystyle X}$ is at least three-dimensional; a skew curve is a space curve which lies in no plane (for example, a helix). These definitions of plane, space and skew curves apply also to real algebraic curves, although the above definition of a curve does not apply (a real algebraic curve may be disconnected). An older term for a space curve is a "curve of double curvature", since it is curved in two ways (with both curvature and torsion).