The Poincaré disk is a model used in hyperbolic geometry, representing a two-dimensional space where the entire infinite plane is mapped inside a circular disk. In this model, points inside the disk represent locations in hyperbolic space, while the boundary of the disk is not included, indicating that points infinitely far away are represented at the edge. In the Poincaré disk, lines are represented as arcs that intersect the boundary of the disk at right angles. This unique representation allows for the visualization of hyperbolic properties, such as the fact that the angles of a triangle sum to less than 180 degrees, differing from the familiar Euclidean geometry.