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Is f:x->|x| an path isometry from R->R? f(1)-f(-1)=0 but 1-(-1)=2.
IMHO, the second paragraph should be moved to much later in the article. It's definitely way too involved to be part of the initial summary.-- Paul 17:07, September 11, 2005 (UTC)
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)
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) (PS: The first two words of the rigid body page are "In physics...")
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)
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)
Removed the example completely. (It's been there for quite a bit of time; see this revision.) As for "path isometry", note that length of a curve isn't defined in a general metric space. - Mike Rosoft ( talk) 11:23, 9 June 2010 (UTC)
Further question: is path isometry defined on a general metric space, or just on R (or R^n)? Or, more to the point: how (if at all) do you define the length of a curve on a general metric space? - Mike Rosoft ( talk) 15:53, 10 June 2010 (UTC)
Okay, but the fact remains that earlier in the article, "isometry" is said to be automatically injective. The example is a valid path isometry, however it needs to be stated that not all path isometries are injective. The sequencing of the article makes it seem as though both global and path isometries are subsets of isometries, but the latter clearly isn't true; instead, we have that every isometry (global or not) is a path isometry, but not the converse. Jtabbsvt ( talk) 11:47, 10 July 2013 (UTC)
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)
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)
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)
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)
Should add more ? 1.47.12.38 ( talk) 06:48, 19 December 2022 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
Is f:x->|x| an path isometry from R->R? f(1)-f(-1)=0 but 1-(-1)=2.
IMHO, the second paragraph should be moved to much later in the article. It's definitely way too involved to be part of the initial summary.-- Paul 17:07, September 11, 2005 (UTC)
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)
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) (PS: The first two words of the rigid body page are "In physics...")
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)
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)
Removed the example completely. (It's been there for quite a bit of time; see this revision.) As for "path isometry", note that length of a curve isn't defined in a general metric space. - Mike Rosoft ( talk) 11:23, 9 June 2010 (UTC)
Further question: is path isometry defined on a general metric space, or just on R (or R^n)? Or, more to the point: how (if at all) do you define the length of a curve on a general metric space? - Mike Rosoft ( talk) 15:53, 10 June 2010 (UTC)
Okay, but the fact remains that earlier in the article, "isometry" is said to be automatically injective. The example is a valid path isometry, however it needs to be stated that not all path isometries are injective. The sequencing of the article makes it seem as though both global and path isometries are subsets of isometries, but the latter clearly isn't true; instead, we have that every isometry (global or not) is a path isometry, but not the converse. Jtabbsvt ( talk) 11:47, 10 July 2013 (UTC)
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)
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)
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)
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)
Should add more ? 1.47.12.38 ( talk) 06:48, 19 December 2022 (UTC)