>> Interesting fact: In elliptic geometry, pi is less than arcsine 1. In 
>> hyperbolic geometry, it's more than arcsine 1.
> 
> I don't think this is true -- pi is defined in Euclidean space.

OK, I rephrase: In non-Euclidian space, the ratio of a circle's 
circumfirance to its diameter can be made arbitrarily large or small.

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