I'm currently making a R package which implements Ungar's approach to hyperbolic geometry, for the hyperboloid model. In this theory, there is a parameter $s>0$ which controls the curvature of the hyperbolic segments:
I'm wondering whether this parameter has a devoted name? Would you know? I know Ungar's theory but I'm ignorant in classical hyperbolic geometry in the hyperboloid model, maybe this parameter also appears in the classical theory?