>> These are two seperate, unrelated geometries.
>>
>> 4D Euclidian space is interesting because it's a straight extension of 
>> 3D Euclidian geometry.
> 
> I should read more about this, sounds interesting.

3D Euclidian space = the place where we (apparently) live.

4D Euclidian space = the place where objects such as the hypercube live.

4D non-Euclidian space = any space with 4 dimensions that *isn't* 4D 
Euclidian space. This includes a system where time is the 4th dimension, 
but also many other kinds of space as well.

>> Somewhat weirder is hyperbolic geometry, where multiple "straight 
>> lines" through a single point do not intersect each other [except at 
>> that point]. You really need to play with this:
>>
>> http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html
> 
> I'll check it out.
> 
> I've been trying to figure out how to calculate hyperbolic geometry, so 
> I may create new "circle limit" Poincare disk tesselations. I figure it 
> must be possible to create such a thing with POV-Ray functions, but so 
> far all my attempts have been total failures :(

I believe you can use ordinary 2D coordinates for hyperbolic space, you 
just need to remap them when plotting them in normal 2D space. 
(Unfortunately, I can't find any formulas for doing this.)

Note that there is more than one way to project hyperbolic space into 

trying to copy Escher's Circle Limit.

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