Talk:Flat (geometry)
Latest comment: 3 months ago by Fgnievinski in topic The basic definition here should probably include also affine subspaces
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editThe comment(s) below were originally left at Talk:Flat (geometry)/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
| Split off from linear subspace. Might be B class. Probably needs more references. Jim 09:04, 2 September 2007 (UTC) |
Substituted at 18:18, 17 July 2016 (UTC)
The basic definition here should probably include also affine subspaces
editIt 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 (§ Euclidean geometry 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)
- 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)
- @D.Lazard, @Fgnievinski it might be good to hash out what folks think the scope / organization should be for this article here. I reverted D.Lazard's revert on the basis that "flat" is at least sometimes defined to mean "affine subspace" in general. But it would be good to figure out what set of things we want to say about subspaces, both in affine and in Euclidean geometry, and whether there are clear sources discussing those in an organized way. I agree with D.Lazard's comments from last year above that focusing on Euclidean geometry toward the top of this article could help readers unfamiliar with affine spaces and transformations. –jacobolus (t) 16:31, 4 September 2024 (UTC)
- I tried to emphasize the distinction between a flat and non-flat subspaces of an Euclidean space. I suspect illustrating such a distinction would be pedagogical for the average reader, like showing a space curve and a straight line in 3D. fgnievinski (talk) 16:41, 4 September 2024 (UTC)