Date: Sep 1, 2013 12:49 PM
Author: fom
Subject: Re: What does one call vector geometry without a coordinate system?
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 non-parallel

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.