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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. | 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 | 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 space]]s) lines are defined as one-dimensional affine subspaces. | In a more abstract approach ([[vector space]]s) 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. | In an axiomatic approach, basic concepts of elementary geometry, such as "point" and "line", are undefined primitives. |
Revision as of 14:05, 26 May 2010
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.