Every pair of points on a sphere lie on some great circle. They cut that great circle into two arcs. If they are anti-podal, then those two arcs have exactly the same length. If they are non-anti-podal, then those two arcs are not of the same length, one is shorter than the other.
If A and B are non-antipodal points then the set of points between them is the set of points on the smaller of the two great circle arcs between them.
If A and C are anti-podal points then the two arcs are of the same length and every point on the great circle, except A and C themselves, is "between" A and C.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.
What is the "plane separation postulate"?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.