Question

on traditional maps, earth is represented in a flat plane, or by euclidean geometry. however, a globe is a more accurate model that comes from elliptical geometry. latitude longitude how does a globe represent the fact that there are no parallel lines in elliptical geometry? the equator is not parallel to any other latitudinal lines. the north and south poles are never connected by a geodesic. the geodesics connecting the north and south poles never intersect. the geodesics connecting the north and south poles intersect at both of the poles.

Explanation:

In elliptical geometry on a globe, the geodesics (which are the analogs of straight - lines) connecting the North and South Poles intersect at both poles, which shows there are no parallel lines as parallel lines never intersect. The equator being non - parallel to other latitudinal lines is not the best explanation for the non - existence of parallel lines in the context of elliptical geometry on a globe. The North and South Poles are connected by geodesics (meridians), and geodesics connecting them do intersect at the poles.

Answer:

The geodesics connecting the North and South Poles intersect at both of the Poles.