A Compute the cosine of the angle between the hyperbolic lin

A. Compute the cosine of the angle between the hyperbolic lines represented by the semicircles S(-0.5, 1.5) and S(0.5, 1.5). (Recall that the Euclidean semicircle S(a,R) has the center a and radius R.)

B. Using Euclidean compass and ruler construct the hyperbolic line through the points P=i and Q=2i+1 in the upper half-plane.

C. Compute the hyperbolic distance between the points P=i-1, Q=i+1 in the upper half-plane.

Solution

C: given points P=I-1 Q=I+1 in the upper plane

hyperbolic distance between two points in the upper half plane is given by modules(1-(-1))/1

=2

the formula for two points a1+ib, a2+ib is given by mod(a1-a2)/b