Talk:Euclidean plane

Focus

What should the focus of this article be? I've been trying to improve it, but there's so many directions it could go in. Complex analysis? Linear algebra? Graphing transformations? Calculus of parametric equations in the plane? What's the big guiding principle? — Preceding unsigned comment added by Brirush (talk • contribs) 04:15, 2 November 2013 (UTC)[reply]

Complex analysis in general? Not a good idea, because from the geometric (not topological) perspective these objects are 1-dimensional. But write about the uniformization theorem: when it formulated (as usually) in complex language, it does not appear as a fact unique for

n = 2

, but it can be formulated in terms of conformal geometry, as a classification of oriented 2-dimensional (over real numbers) simply connected Riemannian manifolds. For

n = 1

the classification is trivial. For

n = 3

it just does not exist. For

n = 2

it exists, but it is a serious theorem, not a simple observation.

Also you can say something about 2 × 2 real matrices. Incnis Mrsi (talk) 15:35, 2 November 2013 (UTC)[reply]

Both directions lie in the same plane

What is the statement "Both directions lie in the same plane" supposed to express? Two directions always lie in the same plane. Maybe what was meant was that they provide an orthonormal basis, but that, too, is always the case for any orthogonal directions. — Sebastian 00:45, 19 December 2017 (UTC)[reply]

should name move to 'Euclidean plane'

The terms "two-dimensional space" and "plane" are synonyms, and the latter is used much more often in practice. –jacobolus (t) 23:28, 8 August 2022 (UTC)[reply]