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 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. In space it can also be described as the intersection of two planes.

Assuming a common (intuitive, physical) idea of the geometry of a plane, "line" can be defined in terms of distances, orthogonality, coordinates etc.

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

In an axiomatic approach, basic concepts of elementary geometry, such as "point" and "line", are undefined primitives.