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In [[Euclidean geometry]], a '''line''' (sometimes called, more explicitly, a '''straight line''') is an abstract concept that models the common notion of a | 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. Moreover, 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. Moreover, in space it can also be described as the intersection of two planes. | ||
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 a more abstract approach (vector spaces) lines are defined as one-dimensional affine subspaces. | ||
In an axiomatic approach, " | In an axiomatic approach, basic concepts of elementary geometry, such as "point" and "line", are undefined primitives. | ||
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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. | 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. | ||
Revision as of 13:56, 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. Moreover, in space it can also be described as the intersection of two planes.
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, basic concepts of elementary geometry, such as "point" and "line", are undefined primitives.
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.