Talk:Isometry

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Mathematics rating: Start Class High Priority  Field: Geometry

Is f:x->|x| an path isometry from R->R? f(1)-f(-1)=0 but 1-(-1)=2.

Right, but that's not the length of the curve. I assume you're talking about defining \gamma:[-1,1]\to\mathbb{R} by γ(t) = t. Then
\mbox{Length}(\gamma)=\int_{-1}^1\left| \, {d\gamma \over dt} \, \right|dt=\int_{-1}^1|1|dt=2
But
\mbox{Length}(f\circ\gamma)=\int_{-1}^0\left| \, {d(f\circ\gamma) \over dt} \, \right|dt+\int_0^1\left| \, {d(f\circ\gamma) \over dt} \, \right|dt=\int_{-1}^0|-1|dt+\int_0^1|1|dt=2
So that's not a counterexample.

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)

[edit] Recent deletion

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)

[edit] Equivalence Class or Quotient Set?

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)

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)