Let A and B be two points on the sphere S^2. Define D(A,B), the distance from A to B, to be the length of the shortest arc of a great circle containing A and B. More specifically, if A and B are antipodal points, define D(A,B)= pie. If A and B are not antipodal points, then they lie on a unique great circle and they are the endpoints of two subarcs of that great circle. The distance from A to B is the length of the shortest arc. As usual, define C to be between A and B if A, B, and C are collinear and D(A,C) + D(C,B)= D(A,B). Also define segment and ray in the usualy way.
a) Find all points that are between A and C in case A and C are nonantipodal points. Sketch the segment from A to C.
I don't understand what the nonantipodal points would look like.
b)Find all points that are between A and C in case A and C are antipodal points. Sketch the segment from A to C.
c) Does the plane separation postulate hold in this setting?
d) Let A and B be distinct, nonantipodal points on S^2. Find all points C such that A * B* C. Sketch the ray AB.