models of hyperbolic space

Models of hyperbolic space are mathematical ways to represent this curved geometry, similar to how maps depict Earth's surface. The most common models include the Poincaré disk, which shows hyperbolic space as a disk where lines appear curved, and the upper-half-plane model, representing it as the upper part of a plane with unique distance rules. These models preserve angles and local shapes but distort sizes at larger scales. They help visualize hyperbolic geometry, where space expands faster than in normal Euclidean geometry, allowing for unique properties like infinite tessellations and complex structures.