I'm tutoring two people for an undergraduate course in hyperbolic
geometry, and they've given me a list of problems their teacher says
will prepare them for the final. I've been able to solve all but
three of them, and I'm hoping someone can answer the remaining three.
1: Find the set of points in the unit disk which are closer to the
origin than to the point 1/3 in hyperbolic distance.
2: Find the formula for the hyperbolic line that contains the points
1/2 and i/3.
3: The set of all points in the unit disk whose hyperbolic distance
from the point (1+i)/3 is equal to 3 is a Euclidean circle. Find the
center of that circle.
