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
 |
This is known as Lobachevsky's formula.
