User:Boris Tsirelson/Sandbox1

In Euclidean geometry, a line (sometimes called, more explicitly, a straight line) is an abstract concept that models the common notion of a (uniform) curve that does not bend, has no thickness and extends infinitely in both directions.

It is closely related to other basic concepts of geometry, especially, distance: it provides the shortest path between any two of its points. Moreover, in space it can also be described as the intersection of two planes.

It is, however, difficult to give a self-contained definition of straight lines. Assuming an (intuitive or physical) idea of the geometry of a plane, "line" can be defined in terms of distances, orthogonality, coordinates etc. (as we shall do below).

In a more abstract approach (vector spaces) lines are defined as one-dimensional affine subspaces.

In an axiomatic approach, "line", together with "point", is a basic concept of elementary geometry. It is an undefined primitive.