How to derive Lobachevsky's formula for the angle of parallelism
  
 
     
     
             
                 
 
 
         
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 I'm lightly studying some non-Euclidean Geometry and in the book I am reading there is no proof or derivation from where the Lobachevsky formula for angle of parallelism comes from:   $$Pi(x)=2tan^{-1}left(e^{-x}right)$$   Any help? Thanks   P.S. I couldn't find anything by google search either.      
 
         
             
                 differential-geometry hyperbolic-geometry noneuclidean-geometry 
             
         
 
     
         
             
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         edited Dec 24 '18 at 9:38 
     
     
         
     
     
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         asked Jul 21 '16 at 12:37 
     
     
         
     
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