Talk:Line (mathematics)

From Wikipedia, the free encyclopedia

	This article is within the scope of WikiProject Mathematics.
	Mathematics grading:	Start Class	High Importance
More prose in "definition" section; general tidy-up needed. Tompw 18:38, 5 October 2006 (UTC) A vital article.

Contents 1 Too advanced? 2 Side of a line? 3 Multiple concepts in one article? 4 Two links to Bulgarian (Български) 5 Question 6 Notation 7 Discussion of more abstract definitions 8 POLYLINE

[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