Here are some indications. Recall the Poincaré open disc model of hyperbolic geometry: geodesics are diameters or arcs of circles orthogonal to the boundary, with unit distance represented by ever shorter Euclidean distances as one moves from the centre towards the boundary. (The boundary is not part of the model). All triangles have angle sum \(&lt; \pi\) (Figure 13, left), and there is a global constant δ such that all triangles are δ-thin in the following sense: