In geometry, Max Dehn introduced two examples of planes, a semi-Euclidean geometry and a non-Legendrian geometry, that have infinitely many lines parallel to a given one that pass through a given point, but where the sum of the angles of a triangle is at least . A similar phenomenon occurs in hyperbolic geometry, except that the sum of the angles of a triangle is less than .
Max Dehn introduced two types of planes: semi-Euclidean and non-Legendrian. These planes exhibit a property where they have infinitely many lines parallel to a given one that pass through a point, but their triangles' angle sums are at least . A similar phenomenon occurs in hyperbolic geometry, where the sum of triangle angles is less than .