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Kevin Wampler wrote:
> I suppose I normally view distance in Euclidean space from the same
> definition that applies to non-Euclidean spaces, rather than the
> sqrt(dx^2 + dy^2) form, so I didn't really consider this. You're right
> though, if you're starting from the pythorgean theorem view of distance
> it does bear some thinking about how it generalizes to the non-Euclidean
> space.
>
> That said, I'm not sure it's necessary to actually understand the proper
> definition of distance in order to talk about circles in other spaces --
> particularly if we limit ourselves to spherical and hyperbolic spaces
> which are more or less easy to visualize.
So how *do* you compute the distance between two points in a non-Euclid
space anyway?
For that matter, is there a way to unambiguously refer to a specific
point in such a space?
(Normally you would of course just use Cartesian coordinates, but it is
not clear to me that this works any more once you remove the parallel
postulate.)
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