Talk:Parallel (geometry)

message: Some info about the parallel lines operator?
:A \| B - Omegatron 04:24, August 9, 2005 (UTC)
::Just found it in ISO 31-11 as Unicode character "∥" as well. --Abdull 22:09, 28 May 2006 (UTC)
thread_title:  Parallel lines operator 

message: 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)
thread_title:  parallel lines should never intersect 

message: 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)
replies: text: This depends on the textbook & context used. For example, in high school I took geometry and "advanced math" (third-level algebra) in the same year. The former class said that two lines are parallel if they have no intersecting points. The latter class said that two lines are parallel if their slopes are identical. (Obviously these were limited to a coplaner space). The former definition mandates that a line cannot be parallel with itself; the latter does not. --Joe Sewell (talk) 19:07, 4 May 2011 (UTC)
thread_title:  Just a suggestion 

message: I hope this article was useful:D  —Preceding unsigned comment added by 216.78.42.3 (talk) 21:04, 2 April 2008 (UTC)
thread_title:  Your welcome 

message: 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)
thread_title:  What do Parallel Lines look like in real life? 

message: 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)
thread_title:  Parallel planes and hyper-planes? 

message: can parallel lines be curved  —Preceding unsigned comment added by 86.179.85.25 (talk) 10:01, 16 January 2010 (UTC)
thread_title:  home work  

message: Can you give the legend for the formula? for example what is b1 and b2? thank you  —Preceding unsigned comment added by 203.201.160.66 (talk) 04:16, 28 December 2010 (UTC)
thread_title:  Question About Formula (Legend) 

message: Hi all,
I think the italic l used in this section looks like a slash. Maybe it should be changed to the script ℓ to avoid confusion?
Thanks,
The Doctahedron, 03:02, 6 January 2012 (UTC)
replies: text: I think this would cause larger problems with consistency than it would solve in readability. The standard in Mathematical literature is to use italics rather than script. You might try changing your browser settings so that your default font is serif rather than sans serif; sans serif is harder to read in general and this issue is one example.--RDBury (talk) 15:37, 6 January 2012 (UTC)
thread_title:  Symbol confusion in [[Parallel (geometry)#Euclidean parallelism|section]] 

message: It says "In a non-Euclidean space, parallel lines are those that intersect only in the limit at infinity." This doesn't seem to make any sense. Can anyone confirm or clarify? Rschwieb (talk) 02:11, 22 November 2013 (UTC)
replies: text: That is quite wrong, many spaces have no "infinity" and some of these are non-Euclidean (e.g. the surface of the sphere as a finite elliptic 2-space). I have deleted it, and also tried to make the lead more understandable to the absolute beginner. — Cheers, Steelpillow (Talk) 10:12, 22 November 2013 (UTC)
replies: text:  I thought so too: thank you! Rschwieb (talk) 15:11, 22 November 2013 (UTC)
thread_title:  Comment at end of lead section 

message: I had added two lines about the property of "parallelism" in a curved surface (space). Those are removed and I was asked to get the source of them.
" We’ve known for a hundred years, since Albert Einstein, that space itself is fundamentally curved. We wrote a bit about this here. Lines and circles in real space simply do not do behave the way Euclid imagined, and so thinking in a non-Euclidean manner is fundamental to understanding the Universe. "
--from http://www.qedcat.com/archive/97.html
On basis of many such reads, I added, "if a space is 180° twisted, any pair of parallel straight lines will intersect each other."
I hope, Math Students will be able to understand this simple relativity.
Thanks. --Aaniya B (talk) 14:39, 16 January 2014 (UTC)
replies: text: Hi, thank you for coming here to discuss it. I have looked at the paper you reference and I cannot find the idea you mention. Nor am I familiar with it from elsewhere, in fact quite the opposite. In particular, a smooth manifold has (by definition) no topological "point of twist". As a counter-example, a hyperbolic manifold is non-Euclidean and may be visibly twisted so it will not lie flat, yet can have many lines parallel to each other and which never meet. So I am reverting your edit again. If you still feel that it is valuable, please post it here for further discussion and do not restore it directly to the article again, as that might be seen as edit warring. — Cheers, Steelpillow (Talk) 17:33, 16 January 2014 (UTC)
thread_title:  About parallel Lines in a Non-Euclidean Space 

message: This article is entirely mathematical definition based.  May I suggest that the colloquial use of the word parallel is valid and should also be covered in the same article ?
For example: http://www.oxforddictionaries.com/us/definition/english/parallel
I think that most ordinary people (non-mathematically trained) would regard curved lines that remain equidistant from one another to be parallel.   For example, railway lines are generally said to be parallel, but they are not necessarily straight.   Lines of latitude are circles of different sizes, and are said to be parallels.   
(Even the inner and outer handrails of a spiral staircase, which remain equidistant from one another in a horizontal (or spiral) plane, are parallel in my mind.)   Darkman101 (talk) 17:02, 6 March 2016 (UTC)
replies: text: The disambiguator (geometry) indicates that this is an article about the mathematical meaning of parallel. There is a disambiguation page for parallel that helps readers find other usages of the term, including several that you have mentioned and many that you haven't. Perhaps the hatnote should be expanded to point to that page (at present it only points to parallel line, a different disambiguation page). I would want to avoid the colloquial use of the term parallel in reference to equidistant curves on this page as it is more likely to confuse than clarify the concept for the natural set of readers for this article. Bill Cherowitzo  (talk) 18:29, 6 March 2016 (UTC)
replies: text: I did look at the disambiguation page for "parallel lines" but I saw nothing for "parallel".  I agree that some kind of note should be added, at least to state that this narrow mathematical definition differs from the colloquial use of the term.   As they are used to create parallel lines, do you think the parallel ruler and rolling ruler should also be on that page ? Darkman101 (talk) 02:02, 7 March 2016 (UTC)

text: I'll take care of the hatnote. The section on constructions is a little thin and an important statement is buried in a footnote, so I think I will work on this section and can incorporate links to those technical tools when I do so. Bill Cherowitzo  (talk) 05:24, 8 March 2016 (UTC)
thread_title:  Non-mathematical definition ? 

message: I honestly feel like the redirect of Parallel lines should be removed. Why? There is a page with this exact title, (Blondie's 1978 album), with no parenthesis in it. If there should be a redirect with those words, it should be for that page.  — Preceding unsigned comment added by The 10th Doctor (talk • contribs) 16:54, 12 July 2016 (UTC)
replies: text: Something needs to be done. For now I have redirected Parallel lines to Parallel lines (disambiguation). At least the Blondie album can now be found. I am not sure of the official way to disambiguate this, but I believe that making Parallel lines into the disambig page would be a good option. Sorry, must dash now. — Cheers, Steelpillow (Talk) 17:11, 12 July 2016 (UTC)
thread_title:  Parallel lines redirect