Parallel (geometry) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-05

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Parallel_(geometry)


00:00:50 1 Symbol
00:01:35 2 Euclidean parallelism
00:01:45 2.1 Two lines in a plane
00:01:54 2.1.1 Conditions for parallelism
00:03:01 2.1.2 History
00:06:12 2.1.3 Construction
00:06:26 2.1.4 Distance between two parallel lines
00:12:17 2.2 Two lines in three-dimensional space
00:12:52 2.3 A line and a plane
00:13:19 2.4 Two planes
00:13:53 3 Extension to non-Euclidean geometry
00:14:46 3.1 Hyperbolic geometry
00:15:51 3.2 Spherical or elliptic geometry
00:16:29 4 Reflexive variant
00:17:50 5 See also



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SUMMARY
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In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are 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.
Parallel lines are the subject of Euclid's parallel postulate. Parallelism is primarily a property of affine geometries and Euclidean geometry is a special instance of this type of geometry.
In some other geometries, such as hyperbolic geometry, lines can have analogous properties that are referred to as parallelism.