The Poincaré disk model

The Poincaré disk model is a way to represent hyperbolic geometry within a circular boundary. Imagine a disk where straight lines are represented by arcs that intersect the boundary at right angles. Unlike flat, Euclidean space, the distances and angles in this model are different; for example, objects appear smaller as they approach the edge of the disk. Despite this distortion, the model preserves the properties of hyperbolic geometry, allowing us to study infinite, curved spaces within a finite circular area. It's a powerful tool for visualizing and understanding geometries where the parallel lines behave differently than in our everyday experience.