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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
1157:" 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
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It strikes me that to be consistent with the rest of the page the image of "parallel curves" should be removed. I actually looked at this page to figure out if it was acceptable to use the term parallel to describe curves that in 2d cartesian space for any x value, the y values of the two curves were
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In mathematics, a curve is not a line: a line has zero curvature within the space in which it is embedded, i.e. all lines are by definition perfectly straight*. If two curves such as sine waves do not meet this is trivial, for example many circles do not meet. If two curves remain a constant distance
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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,
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I don't think there's much danger, although bluelinking the terms in the caption to the diagram to the right articles might dispel that confusion before it arises. It's not as if anyone is claiming parallel curves are parallel lines. Illustrative pictures often contain things pertaining to related
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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
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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
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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
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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
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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
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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
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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
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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,
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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
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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.
455:, no, they don't. Consider the vector definition of a line in parametric form. I don't have time to write it up, class soon, but if someone wants to take this be my guest. Basically as long as the distance between any two points
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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
257:. 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
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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.
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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.
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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? -
743:, concentric circles are an example. Yes, a line between two nearest points on distinct parallel lines will be orthogonal. However, contrary to the previous reply, this applies especially in
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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?
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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 ?
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a constant arithmetic difference from eachother. Seems like this is not "parallel" and I will stick to a wordier more precise definition. Anwyays, perhaps remove the image?
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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.
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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. --
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1220:(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.)
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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.
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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.
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The disambiguator (geometry) indicates that this is an article about the mathematical meaning of parallel. There is a disambiguation page for
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line. In
Euclidean geometry this means that the lines never intersect but this not necessarily the case in other non-flat geometries such as
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727:{\displaystyle \Rightarrow {\mathit {\mathbf {d} }}((x_{1},y_{1}),(x_{2},y_{2}))=(c_{1},c_{2}),(c_{1},c_{2})\in \mathbb {R} ^{+}\cup \{0\}}
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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.
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This is so stupid stupid stupid it doesn't make any sense that i typed in parallel lines and i got a movie this is some real bull...
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I honestly feel like the redirect of
Parallel lines should be removed. Why? There is a page with this
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apart (as measured along any a line orthogonal to both curves) they are not parallels but
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Can you give the legend for the formula? for example what is b1 and b2? thank you
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https://en.wikipedia.org/Parallel_rulers)(https://en.wikipedia.org/Rolling_ruler)
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into the disambig page would be a good option. Sorry, must dash now. — Cheers,
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think the parallel ruler and rolling ruler should also be on that page ?
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don't know if it is really a necessary property of parallel lines.)
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http://www.oxforddictionaries.com/us/definition/english/parallel
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Parallel Lines are like railroad tracks that never intersect.
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However, as far as I understand, in the usual
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Under the Old-School
Euclidian Definition, Yes, they do. See:
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article) but if one wishes to, they can edit and remove it.
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Something needs to be done. For now I have redirected
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915:{\displaystyle \mathbb {E} ^{3}}
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1185:edit warring
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325:Your welcome
287:
281:76.188.26.92
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337:216.78.42.3
331:—Preceding
291:—Preceding
123:Mathematics
114:mathematics
70:Mathematics
1409:Categories
1269:Darkman101
1222:Darkman101
1167:Thanks. --
311:Joe Sewell
969:home work
741:isocurves
211:ISO 31-11
204:Omegatron
39:is rated
1395:Rschwieb
1333:contribs
1321:unsigned
1246:parallel
1237:parallel
1169:Aaniya B
1134:Rschwieb
1100:Rschwieb
1064:Thanks,
1050:Hi all,
1025:unsigned
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359:unsigned
333:unsigned
293:unsigned
259:geodesic
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297:Jfrosen
150:on the
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1080:RDBury
271:sphere
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