Angle of parallelism
![The angle of parallelism, φ, formulated as: (a) The angle between the x-axis and the line running from x, the center of Q, to y, the y-intercept of Q, and (b) The angle from the tangent of Q at y to the y-axis.This diagram, with yellow ideal triangle, is similar to one found in a book by Smogorzhevsky.[3]](/uploads/202412/21/Angle_of_parallelism_half_plane_model.svg4914.png)
In hyperbolic geometry, the angle of parallelism 
, is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides. The angle depends on the segment length a between the right angle and the vertex of the angle of parallelism.