On Jan 25, 2008 11:35 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Experiment 1: rotate M through one half turn about the origin. It is now in state DL. Both components indicate that the orientation has been reversed --- belt and braces cooperating magnificently.
But I would call this the same orientation. Maybe I'm thinking wrongly about what you mean by this word.
Experiment 2: reflect M in N. It is now in state DR. Huh?
Experiment 3: reflect M in M. It is now in state UL. Urgh!
I would say both of these states are signs that the orientation has been reversed.
Extending this argument, it becomes evident that under proper isometries the L/R and U/D components of the state always agree about the orientation; however, under improper isometries they always disagree!
I think I'm confused about whether we're talking about isometries of the line or of the plane or of the way the line is embedded in the plane? --Joshua Zucker