## Lobachevsky's Formula

Given a point and a Line , draw the Perpendicular through and call it . Let be any other line from which meets in . In a Hyperbolic Geometry, as moves off to infinity along , then the line approaches the limiting line , which is said to be parallel to at . The angle which makes with is then called the Angle of Parallelism for perpendicular distance , and is given by

which is called Lobachevsky's formula.