Talk:Parallel (geometry)
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hello but info about the parallel lines operator?mijlr
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- Omegatron 04:24, August 9, 2005 (UTC)
I think parallel lines should never intersect. This should make proving easier when you use Euclid's axiom 5 or Hilbert's axioms. i.e. if line m parallels to line l, then m!=l (this contradicts to the article in wiki). You can refer to http://mathworld.wolfram.com/Parallel.html Cheerful coffin 21:11, 18 October 2006 (UTC)
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[edit] Just a suggestion
Shouldn't we give a precise definition for what a parallel line is in this article? For example, I propose the definition of: "a parallel line is any straight line that is relative to any other given straight line that has the same slope as the other and both of which do not poses the same exact line. In Euclidean geometry this means that the lines never intersect but this not necessarily the case in other non-flat geometries such as elliptic geometry or hyperbolic geometry. Also, by 'straight line' it should be concieved to mean the shortest distance between any two given points possible- in Euclidean this looks like the common straight line, but in other geometries this is a geodesic (exempli gratia: in spherical geometry, a sub-geometry of elliptic geometry, a straight line is really a geodesic following the curve of the sphere)."
Also, either on this article or that of elliptic (or both, I guess), I propose a more laymen's version of how to describe that parallel lines can intersect and how triangles can have more than a measurement of 180 degrees for their interior angles. I will do this now (in the elliptic geometry article) but if one wishes to, they can edit and remove it.
76.188.26.92 20:30, 31 May 2007 (UTC)
A line is not parallel with itself. "being parallel" is a textbook example of a relationship that is not reflexive. This page needs to be edited to have being parallel NOT include the degenerate case of l=m.
[edit] Your welcome
I hope this article was useful:D —Preceding unsigned comment added by 216.78.42.3 (talk) 21:04, 2 April 2008 (UTC)
[edit] What do Parallel Lines look like in real life?
Parallel Lines are like railroad tracks that never intersect. —Preceding unsigned comment added by 63.215.28.94 (talk) 16:26, 6 April 2008 (UTC)
[edit] Only straight lines?
Do parallel lines imply that they must be perfectly straight lines? I mean aren't two curves that have equations y = sin(x) and y = sin(x) + 10 parallel to each other by the euclidean definition? - Temporary1139 (talk) 02:39, 19 May 2008 (UTC)
- Parallel lines typically exhibit the following property: If you make a straight line from any point on line A to the nearest point on line B, then that straight line will intersect line A and line B perpendicularly. Your example does not meet that criterion. (OTOH, I just made that criterion up. I don't know if it is really a necessary property of parallel lines.) —Preceding unsigned comment added by 128.187.80.2 (talk) 23:37, 10 November 2008 (UTC)
[edit] Parallel planes and hyper-planes?
This article lacks discussion of parallel planes and hyper-planes. It should discuss dihedral angles, and give methods for determining the angle between two hyper-planes. —Preceding unsigned comment added by 128.187.80.2 (talk) 21:53, 10 November 2008 (UTC)
