MATH 6118-090
Non-euclidean Geometry

Exercise Set #6

1. What is the distance between the points  and  in the Poincaré upper half plane, H? Remember that the Poincaré upper half plane has a non-euclidean arclength element, so the answer is not 4.

2. What is the distance between the points  and  in the Poincaré upper half plane, H?

3. Prove that the dilation

preserves the Poincaré arclength element.

4. Let  and . Find M and N, the endpoints of the Poincaré line through P and Q.

5. Let  and . Find M and N, the endpoints of the Poincaré line through P and Q.

6. Show that the map

Is inversion in the circle with radius r and centered at the origin, O.

7. Let  be a line with equation  with . Show that the image of  under the action of  gives the equation of a circle which passes through O.