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.

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In Euclidean geometry, a line (sometimes called a straight line) is a straight curve having no thickness and extending infinitely in both directions. Line, together with point, is a basic concept of elementary geometry. It is closely related to other basic concepts, especially, distance: it provides the shortest path between any two of its points. "Line" can be defined in terms of distances, orthogonality, coordinates etc. In the axiomatic approach it is an undefined primitive. In a more abstract approach a line is defined as a one-dimensional affine subspace.