Geodesic obstruction for a horizontal chain of hyperbolic discs
= Geodesic obstruction for a horizontal chain of hyperbolic discs
An isometry sends the centers of a collinear family of equal hyperbolic discs to points on one hyperbolic geodesic. In the upper-half-plane model no geodesic contains three distinct points on a horizontal Euclidean line, since geodesics are vertical lines or semicircles orthogonal to the boundary.