----- Original Message ---- From: Fred lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, January 27, 2008 5:25:36 AM Subject: Re: [math-fun] Reflections on Orientation ... The Lie group corresponding to Euclidean isometries has 4 connected components rather than 2. ... ----------------------------- How can there be 4 connected component? I thought the general Euclidean isometry is (R,t) where R is a rotation, t is a translation, and the action is (R,t)x = Rx + t. Two connected components correspond to R being proper or improper. What are the other 2 components? Are you confusing this with the case of Lorentz transformations, where space reflections and time reflections are independent? Or, is it me that is confused? Gene ____________________________________________________________________________________ Never miss a thing. Make Yahoo your home page. http://www.yahoo.com/r/hs