Stephen wrote:
> 
> What about xyz = the ratio of any circle's circumference to its diameter?
> 

The main problem here is that xyz is not a constant, but is rather a 
function.  In spherical and hyperbolic spaces it can be defined as a 
function of the radius so you need to say something like:

xyz(r) = the ratio of the circumference to the diameter of a circle of 
radius r

If your space doesn't have a constant curvature, then it's a function of 
yet more parameters.

The main issue isn't only that pi has a pre-existing meaning, it's that 
the value in these non-euclidean spaces isn't even a constant.

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