== Confused metric == 

 The article currently says: 

 ::Then the hyperbolic distance between p and q is expressed as 
 ::: 
 ::or 
 ::: 

 This seems to be a confusion, inasmuch as the factor of four is different, but otherwise these are identical.  There is no difference between the two: we must have ds2 = g(x, dx).  The stackexchange answer only seems to be addressing the distinctions between the Klein and Poincaré models.  Where was the first equation above sourced?  I suspect that it is incorrect. —