Hyperbolic angle
A hyperbolic angle in standard position is the angle at (0,0) between the ray to (1,1) and the ray to (x,1/x) where x > 1.
The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is log x.
Note that unlike circular angle, hyperbolic angle is unbounded, as is the function log x, a fact related to the unbounded nature of the harmonic series.