A new metric on the open 2-dimensional unit disk is defined making it a
geodesically complete metric space whose geodesic lines are precisely the
Euclidean straight lines. Moreover, it is shown that the unit disk with this
new metric is not isometric to any hyperbolic model of constant negative
curvature, nor to any convex domain in R2 equipped with its Hilbert metric.Comment: To appear in Beitr Algebra Geo