Talk:Reflection (mathematics)

message: reflection (also spelt(also spelled 'spelled') reflexion)? :)
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This article does not contain information for the novice (me). Anyone want to translate into non-technical english?Hyacinth 23:37, 22 Dec 2003 (UTC)
replies: text: a reflection is a mirror image of something.  put a triangle on a graph.  then imagine moving the origin to the triangle or away from it.  that is translation.  now draw the same triangle upside down.  then, without flipping or redrwaing the triangle, try to move the origin to it so that they are the same triangle.  in fact, you cannot do this, since it requires flipping the triangle over, or imagining the mirror image to do so.  that is reflection.  it is the mathematical concept representing the everyday concept of a mirror.  Oemb1905 19:24, 6 March 2007 (UTC)
thread_title:  Untitled 

message: Reflection is everywhere in the universe but a simple logical discussion is necessary for me to work on P vs. NP.
Would anybody know of a book I can buy or look at in a library?
My theory:
Look at your hands.
They both have fingers.
They both have the ability to pick up objects.
They both have the ability to snap their fingers.
They DO NOT have the ability to interchange.  That would mean your left hand and your right hand could be exchanged but for all *practical* purposes they would be backwards.
Now you have the concept for my theorom:
That P != NP for all cases
But for NP Complete cases you coulds see true interchangeability.
Whew!  I have a theory so please be kind and email me if you have any thoughts or ideas..
:Wha??? Melchoir 03:30, 1 December 2005 (UTC)
thread_title:  Curious 

message: I always thought that I knew what reflection is about, but after reading this article I am more confused than before. I think it needs a rewrite. In particular, looking at this diff, it looks to me that the old version is better than what we have in here. It is not as rigurous, but does a better job of explaining the essense of the thing without going into too many specifics. Comments? Oleg Alexandrov (talk) 00:21, 20 October 2005 (UTC)
replies: text: What's wrong with going into specifics? Giving the formulas for reflections makes precise what is stated in the introduction. -- Fropuff 00:28, 20 October 2005 (UTC)
replies: text:  I don't refer to the formulas section, rather to the section right before. Sorry for not being specific. Oleg Alexandrov (talk) 00:35, 20 October 2005 (UTC)

text: Ah. In that case, I agree. That section could well do with a rewrite. -- Fropuff 00:52, 20 October 2005 (UTC)
replies: text: The old section seems confused. It claims that you can't reflect through a point; in fact, I reflect through points all the time in both math and physics, in different dimsensions, and I don't need a Euclidean structure to do it. Melchoir 20:53, 1 December 2005 (UTC)
replies: text:  I totally agree that this needs a re-write. And many Math Articles Do!!  Even though I understand this article, as I am a Math Teacher, I think this article reminds me of an issue of mine.  That is, in all the math articles, we should divide the articles into two parts:  a plain English and non-mathematical summary, and a Mathematical Model.  Thanks and good night.  Oemb1905 19:28, 6 March 2007 (UTC)
thread_title:  Fixing this article 

message: I noticed that the two articles Reflection (linear algebra) were on largely the same thing, with similar algebra for the general reflection and at a similar level, and also that this article needed some improvement, so I've done the two things at once. Merge that article into this (mostly the reflection in a line section, but also some matrix related points and the link to Householder transformation for the more algebraic approach, then tidy up this article: splitting it into sections with a better introduction, then copyediting the result so it was clearer.--JohnBlackburnewordsdeeds 12:44, 27 January 2010 (UTC)
thread_title:  Merged [[Reflection (linear algebra)]] into this article 

message: The phrase "reflection in a hyperplane" is thoroughly standard; "reflection about a hyperplane" and "reflection through a hyperplane" are not.  It is used, for instance, in Coxeter's "Introduction to geometry".  Coxeter is widely regarded as authoritative.  It is in Dan Pedoe's "Geometry: a comprehensive course".  It is also used in every textbook on linear algebra that I have consulted with.  For instance, Apostol's "Calculus and linear algebra".  Even if other usages were found, these references alone show that "reflection in" is quite standard and should be kept in the spirit of WP:RETAIN.  (Also I should add that, contrary to the IP's edit summary, "reflection in" is a standard English idiom, in addition to being a standard mathematical one—one says "reflection in a mirror", not "reflection about a mirror" or "reflection through a mirror".)  Sławomir Biały (talk) 11:45, 4 August 2013 (UTC)
replies: text: A search of Google books shows that "reflection about" and "reflection through" are commonly used in geometry books. --50.53.46.137 (talk) 08:09, 3 October 2014 (UTC)
replies: text:  Your point?  The same search for "reflection in" returns an order of magnitude more hits, not to mention the authoritative books on the subject to which I referred.  Sławomir Biały (talk) 14:51, 3 October 2014 (UTC)
thread_title:  Recent edits