Talk:Flat (geometry)

Assessment comment
Substituted at 18:18, 17 July 2016 (UTC)

The basic definition here should probably include also affine subspaces
It should be possible to discuss primarily affine geometry here, and then also discuss Euclidean features in some sections. –jacobolus (t) 11:46, 24 October 2023 (UTC)


 * Is that a suggestion for merging this article and Affine geometry? I am not sure that it would be a good idea. On the opposite, for making this article accessible to the widest possible audience, it seems better to start with flats in Euclidean spaces, and, then, say that everything but the content of the last section ( extends verbatim to affine spaces. D.Lazard (talk) 14:27, 24 October 2023 (UTC)
 * No, the article previously only discussed Euclidean subspaces. I just changed it, though it could use more expansion and sources. I don't think there's any benefit in leading with metrical features; the affine features also apply to Euclidean space. –jacobolus (t) 17:01, 24 October 2023 (UTC)
 * I mostly agree with your changes. My comment was motivated by my belief that Euclidean spaces and vector spaces are better known by most readers than affine spaces. So, it seems better to start the article by flats in vector spaces and in Euclidean spaces, and, then, to explain that Euclidean spaces and vector spaces are examples of affine spaces, and that the preceding examples are special cass of the general definiton of flats in affine spaces.
 * This change suggestion is only for the lead. For the body, I fully agree with your point of view. D.Lazard (talk) 20:15, 24 October 2023 (UTC)
 * This article could briefly introduce what an "affine space" is (in the lead, and maybe at slightly greater length in the first section or two). I also think our articles about affine space and affine geometry can be made a bit more accessible to less-technical readers by adding some more elementary and visual material near the top of each. –jacobolus (t) 20:22, 24 October 2023 (UTC)