Lobachevsky's hyperbolic geometry (also studied by János Bolyai) shows up throughout physics, especially in relativity.
The Poincaré models described above are relevant for the AdS/CFT correspondence, as they describe a patch of (Euclidean) anti de Sitter space.
If you are curious about the relationship between AdS and hyperbolic geometry, and you've got some math under your belt, I strongly recommend Ingemar Bengtsson's ~beautiful~ lectures on Anti de Sitter space.
http://3dhouse.se/ingemar/Kurs.pdf
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