  == Hyperbolic Spaces > 2 dimensional ==  I found this page to be somewhat informative but then I think I might be in a little over my head too. I thought I would make this one comment though. To me (a person of limited geometry skills) the most disturbing aspect to this hyperbolic geometry is the expandability of it to at least a 3rd dimension. In Euclidean space it is fairly easy to imagine a 3rd dimensions being added to the 2nd. One could visualize it as the difference between a single sheet of paper and a stack of papers. If I try to imagine how to expand the hyperbolic 2 dimensional plane into a 3rd dimension I find that it doesn't work so well. In fact, it seems like the hyperbolic plane as a stack of curved papers still invades the Euclidean 3 dimensional space. Actually, come to think of it even the 2 dimensional hyperbolic space seems dependent on the Euclidean 3 dimensional space. If anyone would care to comment on how to visualize a 3 dimensional hyperbolic space I would be interested in reading it...   