> > So are we able to define these: > > - Euclidean plane (compass and straight edge only)
There are points in the Euclidean plane that can't be constructed with straight edge and a pair of compasses alone.
> - Real affine plane (I'm guessing, adding machinery of vectors to above, but still no coordinates.. and the vectors do not have to start at origin ... equivalence classes of them exist like previously stated by someone) > - Euclidean space (same as above but with inner product, and thus a distance) > - Euclidean point set (2 dim.) (I'm guessing adding coordinates to above) > - Euclidean vector space R^2 (I'm guessing, same as above but the vectors have to start at origin ... so there is a 1-1 correspondence betweens points and vectors) >
-- Sorrow in all lands, and grievous omens. Great anger in the dragon of the hills, And silent now the earth's green oracles That will not speak again of innocence. David Sutton -- Geomancies