Poincaré half-plane model

In non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically, each point in the hyperbolic plane is represented using a Euclidean point with coordinates ⁠ ⟨ x , y ⟩ {\displaystyle \langle x,y\rangle } ⁠ whose ⁠ y {\displaystyle y} ⁠ coordinate is greater than zero, the upper half-plane, and a metric tensor (definition of distance) called the Poincaré metric is adopted, in which the local scale is inversely proportional to the ⁠ y {\displaystyle y} ⁠ coordinate.

Source: Wikipedia — Poincaré half-plane model (CC BY-SA 4.0)