Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel. Colloquially, curves that do not touch each other or intersect and keep a fixed minimum distance are said to be parallel. A line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are also said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines. Parallel planes are planes in the same three-dimensional space that never meet.

Non-Euclidean geometry
5 months ago

Non-Euclidean geometry ... of metric geometry and affine geometry, non-Euclidean geometry arises by either relaxing the metric requirement, or replacing the parallel postulate with...

Euclidean geometry
5 months ago

Euclidean geometry ... other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that...

Hyperbolic geometry
5 months ago

Hyperbolic geometry ... mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean...

Parallel postulate
5 months ago

Parallel postulate ... In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom...

Geometry
5 months ago

Geometry ... and Riemannian geometry. Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries) can be developed...

Affine geometry
5 months ago

Affine geometry ... notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines...

Elliptic geometry
5 months ago

Elliptic geometry ... Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines...

Parallel transport
6 months ago

Parallel transport ... In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine...

Projective geometry
5 months ago

Projective geometry ... for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said...

Absolute geometry
5 months ago

Absolute geometry ... Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...

Spherical geometry
5 months ago
Line (geometry)
5 months ago
Transversal (geometry)
5 months ago
Taxicab geometry
6 months ago
Parallel
4 months ago
Cross section (geometry)
6 months ago
Translation (geometry)
6 months ago
Synthetic geometry
5 months ago
Plane (geometry)
5 months ago
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