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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