>> No, no non-Euclidian math is needed here. One can solve the puzzle only with
>> Euclid and Pythagoras but one has to think in polar coordinates instead of
>> Euclidian ones and heavily use rotate.
>
> Isn't that non-Euclidian?

Seems like a confusion between the terms "cartesian" and "Euclidean". 
Cartesian is just a coordinate system (xyz), along with polar, 
spherical, intrinsic etc, all can be (and usually are) used with 
Euclidean geometry.

In non-Euclidean geometry essentially it it not guaranteed that two 
straight parallel lines in a plane never cross (which it is in Euclidean 
no matter what coordinate system you use to describe the lines). POV-ray 
is in no way set up to handle non-Euclidean geometry!

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