Talk:Line (mathematics)

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More prose in "definition" section; general tidy-up needed. Tompw 19:19, 5 October 2006 (UTC)

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WikiProject Echo has identified Line (mathematics) as a foreign language featured article. You may be able to improve this article with information from the Polish language Wikipedia.

1 Collinear vs Coplanar?
2 Too advanced?
3 Side of a line?
4 Multiple concepts in one article?
5 Two links to Bulgarian (Български)
6 Question
7 Notation
8 Discussion of more abstract definitions
9 POLYLINE
10 3D Lines
11 Title
12 y=mx+c to y=mx+b
13 Requested move
- 13.1 Discussion
14 Colinear or Collinear?
15 Line with two origins

[edit] Collinear vs Coplanar?

If 3 points are collinear, are the necessarily coplanar? 76.111.81.183 —Preceding signed but undated comment was added at 22:52, 22 September 2007 (UTC)

Yes. Any three points are coplanar. The fact that three collinear points doesn't define a unique plane containing them doesn't mean they aren't coplanar, it just means there is more than one plane containing them. Coplanar doesn't mean "exactly one" plane contains them, it just means at least one plane contains them. --Cheeser1 00:06, 23 September 2007 (UTC)

[edit] Too advanced?

This page is good, but delves right into the advanced stuff. What of all the middle school geometry students who stop by to learn about the line? We should introduce things a little more gently, in the context of ordinary Euclidean geometry in the plane, and then in 3D, before getting into the fancier abstract concepts. I'll make these changes if there's no objection and no one else does first. Deco 04:09, 2 Jun 2005 (UTC)

Please do. I've linked to the somewhat simpler Linear equation (which should be consulted by editors to prevent inordinate duplication), but I'm afraid it's not very prominent. - dcljr (talk) 7 July 2005 06:48 (UTC)

[edit] Side of a line?

Given a point and a line in a plane, how do you determine what side of the line the point is on?

The easiest way is with the cross product. If two points a,b are on the line, and p is your point, all with z coordinate zero, then the z component of (p-a) × (b-a) will be positive or negative, depending on which side of the line z falls. Deco 04:07, 5 November 2005 (UTC)

[edit] Multiple concepts in one article?

Here Line and Line segment are treated as part of the same article. In Polish Wikipedia - they are separated. How can it refer to both articles in Polish now?

I think all we can do is crosslink between Polish "Line" and English "Line", and leave Polish "Line segment" without an en: link. There's a similar situation on English with Addition and Summation; all but a few languages treat these in a single article (including Polish), so there are lots of interlanguage links for Addition but few for Summation. Melchoir 21:07, 31 January 2006 (UTC)

[edit] Two links to Bulgarian (Български)

This is because the content of this article is in two bg articles.

[edit] Question

No where in the article does it say that a line contains infinite number of points. Is this correct, or does Quantum Physics state that this is incorrect? —The preceding unsigned comment was added by 70.59.199.11 (talk • contribs) 14:43, 10 March 2006.

In Euclidean geometry, which seems to be the context of this article, it's correct: a line contains infinitely many points. I wouldn't worry about quantum physics in the real world, which doesn't affect mathematical models. Why don't you try adding this information in? Melchoir 22:48, 10 March 2006 (UTC)

Yes, but in theory, does a line actually have infinite number of points? This seems impossible according to Quantum. —The preceding unsigned comment was added by 70.59.199.11 (talk • contribs) 16:05, 10 March 2006.

I don't see the connection. A line is a mathematical abstraction, and quantum physics has little to say about it. In reality, there is no conceivable experiment that could determine whether an "actual line" has infinitely many "points", so the question is only a philosophical matter. If you're interested in the impact of quantum physics on indivisibility you can read up on Zeno's paradoxes here or an even longer reference at the Stanford Encyclopedia of Philosophy. Melchoir 01:09, 11 March 2006 (UTC)

Don't get math confused with physics. because physics is almost completely dependent on mathematics does not mean the reverse is true. as a matter of fact, the inverse of the reverse is true--math is completely independent of physics (the only part of math that is affected by physics is what mathematicians choose to explore, but thats not really math being affected, thats mathematicians being affected.) get it? This is the generally accepted view among mathematicians and physicists alike (who are often the same people of course.) Brentt 11:47, 16 August 2006 (UTC)

[edit] Notation

The article on Interval_(mathematics) includes various notations on number sets, including the French notation I grew up with. This article doesn't include the equivalent notation I learned, which was:

(A, B) -- line passing through A and B
[A, B) -- half-line starting at A, continuing through B
]A, B) -- half-line starting at, but not including, A, continuing through B
[A, B] -- segment between A and B
]A, B[ -- segment between A and B, excluding both ...

I don't know if that's also used for American notation, but an equivalent reference here would be handy. (I see something vaguely similar, but less complete, in the french version of Segment 67.171.149.4 20:07, 16 March 2006 (UTC)

[edit] Discussion of more abstract definitions

Perhaps this article could benefit from some discussion of more abstract definitions of a line? e.g. ("a straight line is a curve, any part of which is similar to the whole" from topology) Brentt 11:52, 16 August 2006 (UTC)

Do you have references for that? if yes, it could go at the bottom, in a section called "Generalizations". Oleg Alexandrov (talk) 16:15, 16 August 2006 (UTC)

[edit] POLYLINE

POLYLINE redirects to this page but is then not discussed. Can someone mention POLYLINE here, or make a distinct page?

Beau Wilkinson

colinear also redirects here, but is not mentioned on the page. What gives? Sim 14:15, 24 March 2007 (UTC)

[edit] 3D Lines

The article said "In three dimensions, a line must be described by parametric equations". This is wrong: a line in any dimension can be described by a linear equation. I changed "may" to "must" and added a couple of linear equations for a 3D line. This leaves the definitions section a bit rambly, in my opinion --- why describe a 2D line in slope-intercent, versus a 3D line in parametric and standard form? --- but I felt it was a step in the right direction since it is at least correct. It does have the advantage of getting the link to linear equation earlier in the page. Owsteele 14:39, 14 December 2006 (UTC)

[edit] Title

Should the title be renamed to "Line (geometry)"? This would match "Point (geometry)" and "Square (geometry)". Jason Quinn 17:51, 4 April 2007 (UTC)

The concept of line is used in branches of mathematics outside geometry (analysis, for example). --Cheeser1 00:02, 23 September 2007 (UTC)

[edit] y=mx+c to y=mx+b

I changed it because that is how the formula actually is written, according to the math courses I have taken. —The preceding unsigned comment was added by 75.4.13.98 (talk) 23:46, 14 May 2007 (UTC).

[edit] Requested move

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was No Move.--Hús ö nd 02:30, 31 July 2007 (UTC)

Line (mathematics) to Line - Most basic usage of line, and the basis for all other uses ~ JohnnyMrNinja 01:01, 26 July 2007 (UTC)

Oppose again "most basic" does not mean "most common". Also, you should probably wait to move and redirect all these pages (Plane, Square, etc.) until after you've requested the moves. Ewlyahoocom 02:11, 26 July 2007 (UTC)

~~Support~~. The main page should never be a redirect - this is not a standard style of disambiguation. The article explains the context without the need for a disambiguator. If you were claiming that Line ought to be a disambiguation page, that would be an alternative valid viewpoint, but no one seems to be claiming that. Dcoetzee 11:06, 26 July 2007 (UTC)

Changing my opinion - I'm don't think this article should be at Line, but having it redirect here is just as bad. Line (disambiguation) ought to be moved to Line instead. Dcoetzee 23:41, 26 July 2007 (UTC)

Oppose. Several other important uses of the word are only historically related to the geometric usage, and then indirectly. Line should either point to or be a disambiguation page. Andrewa 14:47, 26 July 2007 (UTC)
Oppose. The request is based on wrong assertions. “Line (mathematics)” matches a marginal meaning of the word “line”. --Juiced lemon 16:02, 26 July 2007 (UTC)
Oppose, and move Line (disambiguation) back to Line where it was before the requester moved it yesterday. The word simply has too many ordinary meanings besides the mathematical one. ●DanMS • Talk 00:59, 27 July 2007 (UTC)
Oppose - There is not one primary usage for "linee". Clarification with (mathematics) works fine. Raime 13:24, 27 July 2007 (UTC)
Oppose line is not necessarily in any way related to the mathematical term, how does your line of reasoning match your mathematical usage? 132.205.44.5 19:10, 27 July 2007 (UTC)
Oppose and suggest that the premise that the mathematical usage "is the basis for all other uses" is wrong. Children are able to recognize "lines" as a description for thin, long, and straight things, before they grasp the geometric concept of lines as "infinitely thin" and "infinitely long." It is likely that humans were already conceiving of "lines" before they formulated the concept of three dimensions and geometric lines. --Groggy Dice T | C 15:23, 28 July 2007 (UTC)

[edit] Discussion

These arguments (among others) also appear to apply to the requested move of Square (geometry) to Square, again displacing a disambiguation page which was recently moved to Square (disambiguation). Andrewa 04:02, 27 July 2007 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

[edit] Colinear or Collinear?

I was surprized to find that collinear (with two l's) seems to be more widely used than colinear. Are they both correct? Colinear makes more sense to me (as in co-linear), but I'm not a native speaker. --CyHawk (talk) 21:45, 3 February 2008 (UTC)

I'm fairly sure that it's two Ls. The Oxford English Dictionary contains only an entry for collinear. I believe colinear is an unambiguous (and probably common) misspelling, but two Ls is correct. --Cheeser1 (talk) 20:26, 6 April 2008 (UTC)

[edit] Line with two origins

This is a cool example of a line with two origins and I was thinking of making a wikipedia article on it, but I wasn't sure if it deserves its own article or if it should be put in some other related article? LkNsngth (talk) 20:09, 6 April 2008 (UTC)