Talk:Isometry

message: The example I just deleted does not belong either in this article or even in isometry group, it rather belongs in Euclidean group and there only. It is way too specific to provide any useful illustration anywhere else. A good example in the right article is invaluable, a good example in the wrong article is useless ranting distracting form the point of the article. Oleg Alexandrov (talk) 04:05, 9 October 2005 (UTC)
thread_title: Recent deletion

message: I see the term "rigid motion" used on this page repeatedly, but when I click the link for the definition it takes me to the page for "rigid body".  I glean that "rigid motion" as used here is just another word for translation and/or rotation.  I propose using those terms instead. One reason I propose this is that, although used by physicists, this is clearly a general mathematics concept. There needn't actually be any kind of literal movement involved, and referring to "motion" without reference to precise meaning suggests to me we are restricting the concept of isometry to contexts involving positions and times. Alternatively, a nice mathematically general definition for "rigid motion" could be provided, so as to make it clear we are not making such a restriction. Thanks. 24.233.151.201 (talk) 22:01, 22 November 2013 (UTC)
thread_title:  Rigid Motion or Translation + Rotation? 

message: I clicked through quotient set because I was not familiar with the term. I was expecting something similar to quotient group, but it redirects equivalence class. I have a hard time believing quotient set is the wikipedia standard. Surely equivalence class is more common?? (This may be a US-centric view). --Jpawloski 14:37, 16 February 2006 (UTC)
replies: text: Okay, well, never mind. Next time I'll read the page first. I will continue, however, to post without thinking. --Jpawloski 14:38, 16 February 2006 (UTC)
thread_title:  Equivalence Class or Quotient Set? 

message: *The map R\toR defined by  x\mapsto |x| is a path isometry but not a global isometry.
Am I missing something? The map x->abs(x) is not an isometry (under Euclidean metric); it doesn't preserve the distance between 1 and -1. (It isn't even injective.) - Mike Rosoft (talk) 11:12, 9 June 2010 (UTC)
replies: text: I have tried to clarify things with consistency between lead and definitions section, and restored the example in modified form.--Patrick (talk) 08:07, 10 June 2010 (UTC)
thread_title: Huh?

message: The addition of a paragraph in the lead to an unrelated topic (Allometry, aka isometric scaling) in response to an IP's insertion of a mention thereof seems strange and out-of-place to me. At most, a hatnote could be devoted to this. —Quondum 19:37, 2 February 2014 (UTC)
replies: text: You're right, it felt that way to me as well ... as I put it in. The hatnote was getting too crowded and I didn't want to just remove the statement, even though it was incorrect. I replaced it with a correct statement, but it really doesn't belong. Let's just put this down to too much late night editing. Bill Cherowitzo  (talk) 06:08, 3 February 2014 (UTC)
replies: text: That still leaves the question of what to do with it. My inclination is towards an even more crowded hatnote, if "isometry" is used sufficiently in that context that interested readers may end up here; otherwise to simply remove it. A further (and not unreasonable) alternative is to move all the hatnotes to a disambiguation page, leaving a hatnote pointing to that page. —Quondum 17:24, 3 February 2014 (UTC)

text: but it was a little more complicated (more than one disambiguation page) and may require some adjustment. Bill Cherowitzo  (talk) 18:24, 3 February 2014 (UTC)
replies: text: Wow, yes, I see that the disambiguation pages are a little confusing, but at least this page is essentially sorted now. —Quondum 03:57, 4 February 2014 (UTC)
thread_title:  Isometric scaling paragraph in lead 

message: I've seen a lot in physics about "angle and distance preserving" transformations (when talking about metric spaces). It would be nice to see something explaining the relationship between concepts such as isometry and that.216.96.76.37 (talk) 13:59, 28 May 2015 (UTC)
replies: text: An isometry is precisely a distance-preserving function. On the other hand, it is not immediately clear how to define angles in a general metric space. (Angles between what entities?) JoergenB (talk) 23:48, 23 August 2015 (UTC)
replies: text: The metric defines a dot-product between vectors in the tangent manifold. Whenever you got a dot product, you can write the angle as the arc-cosine of the dot product of two unit length vectors. And you know what unit length is, because the dot product tells you that. This article should be expanded to explain such things. 67.198.37.16 (talk) 02:34, 10 November 2020 (UTC)
thread_title:  What is the relationship between Isometric and "angle and distance preserving"? 

message: Does this article really need sources?  I think that most of it's pretty open source/common knowledge.  — Preceding unsigned comment added by Schuddeboomw (talk • contribs) 14:30, 10 February 2016 (UTC)
replies: text: Yes, absolutely, it does. As the comment above immediately shows, what is "common knowledge" to you is totally opaque to others. Anyway, this article is sorely deficient in even the most basic details as to what isometries are. It needs to be expanded. 67.198.37.16 (talk) 02:36, 10 November 2020 (UTC)
thread_title:  Citations 

message: In the last example (maps on C^n), shouldn't C^n be "C^n with the Euclidean norm"?  Or does Wikipedia say somewhere that C^n is always assumed to have that norm?  Vaughan Pratt (talk) 16:43, 2 December 2021 (UTC)
replies: text: C^n is not always assumed to have any norm, but, when metric properties are considered, the norm defined by the dot product is generally implicitly implied, if not otherwise specified. On the other hand, I am not sure that the term "Euclidean norm" is common for complex vector spaces. Nevertheless, I have clarified the example. D.Lazard (talk) 19:10, 2 December 2021 (UTC)
thread_title:  Is C^n always assumed to have the Euclidean norm? 

message: Should add more ? 1.47.12.38 (talk) 06:48, 19 December 2022 (UTC)
thread_title:  Isometry in Quantum Unitarity research.