Discussion
The shortest arc connecting two points on the surface of a sphere is called :
Answer: A
It is a great circle arc.
The geodesics of a sphere are its great circles, the intersections of the sphere with planes through its centre. The shorter arc of the great circle through two points is the shortest path on the surface between them; this is why long-distance flight routes follow great circles.
A catenary is the shape of a hanging chain, a catenoid is the minimal surface of revolution spanning two circles, and a cycloid solves the brachistochrone (fastest descent) problem. None is a shortest path on a sphere.
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