Talk:Plane (geometry)/Archive 1

Picture

Sorry, again. But this is even more a bad idea! This picture may -- perhaps! -- be used to illustrate the topological concept of a surface, certainly not that of a plane. --Peter Schmitt 00:42, 18 March 2010 (UTC)

Remarks

"A plane is a surface on which a line perpendicular to a line which lies on that surface also falls entirely on the surface" — where is it taken from?? Hopelessly bad "definition".

"A plane is made up of an infinite number of straight lines" — it surely contains infinitely many straight lines, as well as infinitely many triangles, circles etc. But is it "made up" of them??

"Surfaces can be parallel" — really? what is the definition of this notion?

"Thus the surface has on it point A, point B, and point C is called surface ABC" — a plane is determined by three points (if not on a straight line), but a surface is not.

"If this crumpled picture of the Earth was spread flat on a perfectly flat table, and the picture had absolutely no thickness, then it would be a plane" — no, it would be a finite domain on a plane.

Boris Tsirelson 15:29, 28 March 2010 (UTC)

Rewritten

I was bold enough to rewrite it completely. Hope you do not object. Could someone please add an appropriate lead, and probably introduction with a completely informal idea of plane? It would be also nice to have pictures to the three geometric definitions. Boris Tsirelson 09:57, 29 March 2010 (UTC)

Analytic geometry

I added some high-school-level analytic geometry plus two drawings. --Paul Wormer 10:46, 1 April 2010 (UTC)

Getting better

Excellent article! This ain't a plain-old article by any flat stretch.--Thomas Wright Sulcer 16:07, 1 April 2010 (UTC)

Thank you for the compliment to Paul and me. However, a good article must have a lead, and probably introduction, right? Maybe you can try? Boris Tsirelson 17:51, 1 April 2010 (UTC)

Maybe in a bit. I'm off doing errands now. Thanx for your vote of confidence in me but I'm not scientific by any flat stretch!--Thomas Wright Sulcer 17:55, 1 April 2010 (UTC)

I looked it over. I think you're making excellent progress on it! I'm impressed. It soon gets into technical areas that are above my pay grade that I'm not going to understand like the equations (I was an anthropology major in college! -- arrgh). A suggestion I might offer at this point is to have the first paragraph focus more on the conventional (ie simple, that is -- three points in space define a plane etc) sense of plane -- a flat surface -- because I think this is what will be sufficient for most people. So maybe add a few more sentences perhaps to the first paragraph which explains the basic sense, perhaps, if you feel it's warranted. Then, I think it would be good to make a case for why one should consider exploring the more difficult mathematical questions about a plane -- that is, why a reader will benefit fro getting more involved in this subject. And then keep your great stuff you've got thereafter. Overall, highly impressed!!! My son is into math and he may want a look at it.--Thomas Wright Sulcer 20:30, 1 April 2010 (UTC)

By the way, I've linked this article from the corresponding Wikipedia article. It does not increase our Google rank (because of "nofollow" tag...) but could attract some readers. Boris Tsirelson 05:39, 2 April 2010 (UTC)

About lead/intro I feel I am too much mathematical for doing it. I am hardly understanding what do non-mathematicians think about planes (and other mathematical objects). Maybe an antropologist or chemist would do it better? Boris Tsirelson 05:43, 2 April 2010 (UTC)

About lead/intro: isn't it sufficient what is there now?--Paul Wormer 07:17, 2 April 2010 (UTC)

Oops... I am sorry, I did not note that it has appeared! Yes, probably it is OK. Boris Tsirelson 08:40, 2 April 2010 (UTC)

About the "flat surface in which a straight line joining any of its two points lies entirely on that surface" I wonder: does "flat" already mean "in which a straight line joining any of its two points lies entirely on that surface", or does it mean something different? Boris Tsirelson 08:50, 2 April 2010 (UTC)

[unindent]

The first sentence is from the Oxford Dictionary and hence "flat" is as the non-mathematician perceives it. (Undefined, intuitively clear, and perhaps somewhat redundant). I added to the lede a paragraph about Hilbert's work on classical Euclidean geometry. I found it illuminating that Hilbert assumes the plane to be an undefined object. Further the mentioning of Hilbert's book is (IMHO) a piece of information of encyclopedic nature. Feel free to change/delete/add anything. --Paul Wormer 09:37, 2 April 2010 (UTC)

"(Undefined, intuitively clear, and perhaps somewhat redundant)" — Ah, yes, this is why I am reluctant to write introductions; I know that I am too much mathematical for this business.

"Hilbert assumes the plane to be an undefined object" — Oh yes; this is what I mean by "In the axiomatic approach points, lines and planes are undefined primitives" in "Axiomatic approach".

"mentioning of Hilbert's book is (IMHO) a piece of information of encyclopedic nature" — surely it is. Boris Tsirelson 12:24, 2 April 2010 (UTC)

Overall highly impressed with this excellent article. Not that I understand it. It's just that stuff with equations in it looks cool. Just one comment about the first sentence -- maybe it's because I'm not quite mathematical enough to grasp it -- but I have trouble wrapping my mind around the idea of a plane with only one line in it. I keep thinking multiple lines, or 2-D; but it's the handyman in me to think of a flat board, not warped, since warped boards cause problems, particularly when trying to build stuff.--Thomas Wright Sulcer 14:26, 16 April 2010 (UTC)