In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H = { ⟨ x, y ⟩ ∣ y > 0 ; x, y ∈ R } {\displaystyle =\{\langle x,y\rangle \mid y>0;x,y\in \mathbb {R} \}}, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry. Wikipedia