edge. Also angles in the Klein disk model are deformed. For constructions in the hyperbolic plane that contain circles, hypercycles, horocycles or non right angles it is better to use the Poincaré disk model or the Poincaré half-plane model. Relation to the Poincaré disk model Both the Poincaré disk model and the Klein disk model are models of the hyperbolic plane. An advantage of the Poincaré disk model is that it is conformal (circles and angles are not distorted); a disadvantage is that lines of the geometry are circular arcs orthogonal to the boundary circle of the disk. The two models are related through a projection on or from the hemisphere model. The Klein model is an orthographic projection to the hemisphere model while the Poincaré disk model is a stereographic projection. When projecting the same lines in both models on one disk both lines go through the same two ideal points. (the ideal points remain on the same spot) also the pole of the chord is the centre of the circle that contains the arc. If P is a point a distance from the centre of the unit circle in the Beltrami–Klein model, then the corresponding point on the Poincaré disk model a distance of u on the same radius: Conversely, If P is a point a distance from the centre of the unit circle in the Poincaré disk model, then the corresponding point of the Beltrami–Klein model is a distance of s on the same radius: Relation of the disk model to the hyperboloid model Both the hyperboloid model and the Klein disk model are models of the hyperbolic plane. The Klein disk (K, in the picture) is a gnomonic projection of the hyperboloid model (Hy) with as center the center of the hyperboloid (O) and the projection plane tangent to the nearest point of the hyperboloid. Distance and metric tensor Given two distinct points U and V in the open unit ball of the model in Euclidean space, the unique straight line connecting them intersects the unit sphere at two ideal points A and B, labeled so that the points are, in order along the line, A, U, V, B. Taking the centre of the unit ball of the model as the origin, and assigning position vectors u, v, a, b respectively to the points U, V, A, B, we have that that and , where denotes