Quiz Questions

One of these questions will be asked.

1. Suppose that you have to convince a skeptical person who is new to spherical geometry that the straight paths on the sphere are the great circles. Give a quick outline of three different approaches that might work to convince this person.
2. Let A be a point on a sphere and let K be a constant. Let c be the set of points P for which the spherical distance from A to P equals K (this is a spherical circle). Explain why c is also a Euclidean circle in a plane.
3. Let A, B, C be 3 points on a great circle g on a sphere. Show that the duals (polar great circles) a, b, c of A, B, C are concurrent. If B is a spherical midpoint of AC, why does the great circle b bisect an angle between a and c.