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Mathematics rating:	Start Class	High Priority	Field: Geometry
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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. All sections need expansion; needs less technical introduction to subject. Tompw 19:19, 5 October 2006 (UTC)

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Additional information: Start This article has been rated as Start-Class on the assessment scale. ??? This article has not yet received an importance rating on the assessment scale. This article is a vital article. The following comments have been left for this page: All sections need expansion; needs less technical introduction to subject. Tompw 19:19, 5 October 2006 (UTC) (edit)

[edit] Lines in intersecting planes

"Lines drawn on intersecting planes will either intersect or be skew, but will not be parallel. Intersecting planes may be perpendicular, or may form any number of other angles."

Imagine 2 intersecting planes α and β. Intersection of two planes forms line k. There is infinite amount of lines in α e.g. l such that l | | k. Same is true for plane β where e.g. m lies in β and m | | k. If l | | k and m | | k then l | | m.

Therefore 2 lines (m and l) drawn on intersecting planes can be parallel.

Can do a drawing if you need one. Could please check this conclusion and update article. --Cliff (talk) 13:32, 13 May 2008 (UTC)

[edit] Not yet done, but do chip in!

I'm not done with this page by a long shot; I see a few logical overhauls in its future. Still, if anyone wants to chip in, like 63.162.240.46 has recently, I promise not to completely undo your edits! Melchoir 21:02, 15 November 2005 (UTC)

[edit] = algebraic geometry

Someone should write something about the affine plane in algebraic geometry, Spec k[x,y].

[edit] Euclidean definition needs clarification or correction

The statement defining a plane "...a plane is a surface such that, given any two distinct points on the surface, the surface also contains the unique straight line that passes through those points." is also satisfied by a cylinder. I'd defer to the common page maintainers whether they'd rather mention this or change the defining statement. —Preceding unsigned comment added by Poppafuze (talk • contribs) 17:17, 17 April 2008 (UTC)

I'm not sure what is meant by this. The cylinder (x, y, z)(s, t) = (cos t, sin t, s) goes through (1, 0, 0) and (-1, 0, 0). A line through (1, 0, 0) and (-1, 0, 0) goes through (2, 0, 0). The point (2, 0, 0) does not lie on the cylinder, so the cylinder does not contain the line.

Many surfaces contain at least one line through two points on that surface, not limited to planes or cylinders. But that is not what the definition says. 96.26.243.241 (talk) 04:10, 17 May 2008 (UTC)

[edit] Is this article accessible to enough people?

I don't think it is. Terms like R³ and Euclidean Geometry, and objects like determinates and normal vectors need knowledge of degree level mathematics to understand.

I intend to restructure parts of the article to bring some concepts down to a simpler level where possible, e.g. using terms like 3 dimentional space instead of R³ where possible. And, I think, giving a warning and some guidance when the concepts do get compliacted, like links to web pages and books that will give a relevent introcuction to the theory.

I am for keeping all of the results - and am impressed by the expertise and effort shown by contributers - perhaps I may ask up to what level you have studied maths Melchoir?

So while I believe that the technical jargon is needed for some of the results, it is important to keep things simple. Fuzzyslob 12:16, 16 November 2005 (UTC)

Well, I carry a BA in pure math and a BA in physics, so I'm torn in several directions. I still remember, from years ago, slogging through Stewart's presentation of the material here and thinking that it was scatterbrained and inelegant. That's why I'm trying to emphasize vector notation, and why I want to write about the relationships between all the concrete descriptions of planes in the future.

As for accessibility, among other reasons, I wonder if this article should be split in two. Currently it's dominated by boring calculations in 3D; maybe we should split that material into a separate, more technical page, and try to expand on conceptual stuff here. What do you think?

Anyway, I'm interested in seeing what you have in mind, so fire away! Melchoir 14:37, 16 November 2005 (UTC)

[edit] non-infinite planes

Intuitively, [a plane] may be visualized as a flat infinite sheet of paper.

What about planes that are not infinite but rather limited, therefore creating a fraction of a infinite plane? --Abdull 17:39, 10 July 2006 (UTC)

In my experience, even if a plane is represented as a non-infinite area in space, it is still understood to extend to infinity. If you restrict the area of a plane, it becomes a shape, like a polygon, only a (small) portion of the given plane on which the shape occurs. -Kanogul ^(talk) 23:08, 5 May 2008 (UTC)

[edit] rendering graphics

I can't read the R-cubed symbol on my browser. It just comes out as a blob!

[edit] Requested move

[edit] Intersection

We talk alot about planes in R³, would it be worth pointing out that in higher dimensions stranger things can happen, such as two planes that intersect in exactly one point. Thenub314 (talk) 16:47, 16 May 2008 (UTC)