Talk:Reflection (geometry)

About the definition

Do you really mean any involutive linear map? Should the map be also isometric? Is an identity map a reflection? Boris Tsirelson 17:29, 18 July 2009 (UTC)

Boris is right. There is also rotation about π. And it should not be restricted to linear spaces since it is a geometric term. I'll give it a try. Peter Schmitt 19:25, 18 July 2009 (UTC)

I hadn't finished yet (I know I should have used a sandbox, but until recently hardly anybody read my work). Now I have finished and I'm open to any criticism you gentlemen may have. Remember that as a mathematical amateur I'm using a nomenclature that comes mainly from physics sources. As far as I can see, mathematicians understand the physical language very well—although they often don't like it because they find it too verbose—but the converse is not true, many physicists and practically all chemists do not know advanced mathematical terminology.

Maybe you could also have a look at Affine space?

--Paul Wormer 13:34, 20 July 2009 (UTC)

Paul, physicists are not mathematical "amateurs" - some things they can even do (much) better. I noticed that this is work in progress (and why not?), but I thought that changing the definition would not do any harm. Mathematical language is not "better" than physical language (unless, of course, physicists forget about checking for convergence at all ;-). And as I have said in another discussion - the only "problem" will be how to satisfy -- in the end -- the needs of both sides. Peter Schmitt 14:52, 20 July 2009 (UTC)

As for me, the article is nice enough. Yes, a mathematician would do it differently, but what of it? I only wonder why this is an operation of analytic geometry. I'd say, it is an operation of Euclidean geometry (easily formulated in a purely geometric language). It may be described by means of analytic geometry. However, vectors probably are not quite analytic geometry. Coordinates are. Boris Tsirelson 15:34, 23 July 2009 (UTC)