Original: The shortest path from point A to point B on a sphere is given by the shorter arc of the great circle passing through A and B/O. If A and B are antipodal points ( like the North pole and the South pole ) , then there are infinitely many shortest paths between them .
Simplified: In a sphere two antipodal points ( points opposite each other on a sphere such as the North Pole and South Pole on Earth ) have an infinite number of such paths between them .