2
AssignmentMultiple Choice

Euclidean Geometry

Question 2 • (A. Costello)WCA 5324 Geometry 1st Nine Weeks 26-27

How does a globe represent the fact that there are no parallel lines in elliptical geometry?

Answer
A
The equator is not parallel to any other latitudinal lines.
B
The North and South Poles are never connected by a geodesic.
C
The geodesics connecting the North and South Poles never intersect.
D
The geodesics connecting the North and South Poles intersect at both of the Poles.

Explanation

On a globe, geodesics are the shortest paths along the surface, represented by great circles. Any two meridians (great-circle paths through the North and South Poles) meet at both poles, so they cannot be parallel. This is shown by choice D: the geodesics connecting the poles intersect at both poles.

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