Experiment in Hyperbolic Geometry

1. In the PoincarŽ model, follow Euclid's proof of proposition 1 to construct an equilateral triangle ABC.
   1. Draw line segment AB
   2. Draw circle with center A and radius AB
   3. Draw circle with center B and radius BA
   4. Construct the points of intersection C, D
   5. Draw line segments, AC, BC
2. Measure triangle ABC
3. Move points A and B around the space and answer the following questions:
   1. Are the sides of your triangle always equal?
   2. Are the angles of your triangle always equal?
   3. What is the largest angle sum possible? What does the triangle look like when you get close to this sum?
   4. What is the smallest angle sum possible? What does the triangle look like when you get close to this sum?
4. Change to the half plane model of hyperbolic geometry and repeat steps 1, 2, 3.