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1. Geometry

   Linked via "Poincaré disk model"

   Hyperbolic Geometry
   Hyperbolic geometry, often visualized using the Poincaré disk model, posits that through a point not on a given line, there are at least two distinct lines parallel to the given line. The curvature $K$ in hyperbolic space is strictly negative ($K < 0$). A curious property observed by the early Hungarian geometrician, Farkas Bolyai, states that the sum of angles in a hyperbolic triangle decreases as the area of the triangle increases, asymptotically appro…