fom
Posts:
1,968
Registered:
12/4/12


Re: What does one call vector geometry without a coordinate system?
Posted:
Sep 1, 2013 12:49 PM


On 9/1/2013 9:41 AM, Shmuel (Seymour J.) Metz wrote: > In <WrudnVYbz_glnL_PnZ2dnUVZ_q6dnZ2d@giganews.com>, on 08/31/2013 > at 09:46 AM, fom <fomJUNK@nyms.net> said: > >> It would be called a Euclidean point space. > > I might believe affine. > >> The point difference (the additional algebraic structure) >> then becomes a ground for a distance function. > > No; you can only correlate distances on parallel lines. >
Thanks. The affine structure had been clarified elsewhere.
Could you explain your second statement a little more. Does it relate to the difference between a vector space and an inner product space?
That would make sense to me. In order to correlate magnitudes with respect to nonparallel directed line segments, one would need to have a notion of rigid rotations. That would suggest angle measure. In turn, that would suggest that an inner product would be required.

