Talk:Real projective plane

Geometric vs. topological properties

Continuing the 2013 discussion Talk:Real projective plane/Archive 1 § "Topology is not concerned with flatness, and the real projective plane.."

Then the elliptic plane really should be mentioned, ie. the geometric projective plane as opposed to the topological projective plane. Maybe this distinction should even be written near the top of the article. --2607:FEA8:86DC:B0C0:561:D589:AD84:9BC7 (talk) 15:25, 19 April 2022 (UTC)

Cross cap disk

In Cross cap disk You realized six images, maybe drawn in TikZ. For the Figure 1 and 3 You wrote the surface equation, but for Figure 2 there is not a surface equation. Could You write it, please? Thank you so much. Best regards at all. 94.38.53.130 (talk) 14:44, 6 June 2022 (UTC)

More on homogeneous coordinates

Continuing the 2007 discussion Talk:Real projective plane/Archive 1 § Homogeneous coordinates

A line l in the plane corresponds to some P plane in R^3 (namely span of the union of l and the origin). Though there might be a formal difference (line in the real projective space is a set of points of the real projective space, i.e, a set of the lines through the origin --- whose union is P), this is their point 178.255.168.233 (talk) 19:31, 31 March 2024 (UTC)

@178.255.168.233, I am finding your changes today special:diff/1188534080/1216566057 to be pretty confusing; I can't tell what exactly you are trying to say there. Absent a rewrite for clarity, I think they should be reverted. –jacobolus (t) 20:27, 31 March 2024 (UTC)

@Jacobolus, today I improved the clarity. Originally, I came to learn about the real projective plane in context where it was understood as an extension of the plane. Need to say, the linear structure (of both) is involved. Reading about the Moebius strip right in the introduction did not help me (indeed, on that day, I could not be satisfied by the topological properties of the real projective plane). Actually, the introduction names some of the properties, mostly topological; it does say a word on what the real projective plane actually is (i.e., "space of lines ..."), but not enough for visitors like me. Therefore I added a few words on the relation of the real projective plane and the (ordinary) plane. Today I corrected some typos in improved readability, which I hope can satisfy you. 178.255.168.233 (talk) 20:02, 6 April 2024 (UTC)

What something "is" is a bit of a philosophical question. There are a number of isomorphic structures any of which can be called the "real projective plane".

Personally I think it is most natural to imagine the real projective plane as the space of orientations of lines in 3-dimensional space. But other interpretations are no more or less inherently valid.

I agree with you that "an example of a compact non-orientable two-dimensional manifold;" is not an adequate definition. –jacobolus (t) 20:51, 6 April 2024 (UTC)

why not explain this to a layperson?

I can't parse this (or any other higher level maths article) because I don't know what any of terms mean and clicking through to their articles just presents me with more terms I don't know. why are all maths articles written for a very advanced audience (I get that the editors are mathematicians, but you are not your audience!)? since when are actual mathematicians using wikipedia to learn maths concepts? 172.242.161.154 (talk) 20:06, 27 August 2024 (UTC)

You've got a good point. The issue boils down to "who is the audience" for the article? For example, when the Geometrization Conjecture became a big news item, considerable effort was made to transition the Wikipedia page from one solely written for 3-manifold topologists (a niche in professional mathematics) to one that was readable to a non-mathematician that had some enthusiasm for math.

I think that's basically the rule for Wikipedia pages. If it's a fairly specialist item, often the pages are written in the comfortable lingo of that speciality. As the page trends towards more public interest, they're given some more accessible components.

Regarding your last question, actually quite a lot of mathematicians read Wikipedia for definitions. While much mathematics appears in textbooks, strangely there is a lot of more "colloquial" mathematics that never makes it to textbooks, and people go to things like Wikipedia looking for answers.

We don't make all pages accessible to everyone because there's the risk that we make the page completely useless in the process, by "fogging out" the relevant information with vague language that isn't helpful to anyone. Crafting an accessible page to a broad audience is an enormous amount of work. The idea is to initially write something that's useful to a significant audience. You can broaden the appeal of the article later, when authors have sufficient insight into how you could potentially soften the technical prerequisites. Rybu (talk) 18:05, 8 September 2024 (UTC)

I'd also like to complain, that "In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface." is a poor initial description. Problems include (1) it is completely full of jargon that is not necessary for describing the real projective plane (2) it doesn't actually say what the real projective plane is, (3) this is a parochial take from topology which doesn't describe the origin or primary use of the projective plane (projective geometry). I think the article would be much improved by leading with a clear description relevant to projective geometry, something along the lines of "The real projective plane is a two-dimensional space whose basic objects are points and straight lines, in which every pair of points is joined by exactly one straight line and every pair of lines has exactly one intersection, and there are no concepts of distance, angle measure, parallelism, or circles. ..." In paragraph ~3 we could mention that topologists also use the name "real projective plane" for any manifold which is topologically equivalent, ignoring projective geometry concepts. –jacobolus (t) 18:26, 8 September 2024 (UTC)

It is a pervasive problem. I have enough mathematical edumacation to contribute usefully on polytopes for example, but whenever I look up something outside what I already know I hit a wall. —Tamfang (talk) 00:06, 10 September 2024 (UTC)

@172.242.161.154, I rewrote the lead section, does that help at all? –jacobolus (t) 07:12, 10 September 2024 (UTC)