the shortest path between two points and the unit sphere and the arc of the great circle Prove that the shortest path between two points on the unit sphere is an arc of a great circle connecting them
Great Circle: the equator or any circle obtained from the equator by rotating
further: latitude lines are not the great circle except the equator
I need help with starting this question, because I am not quite sure how to prove this.

HINT: (Edited 8/27/2021) Start with two points on the equator. Every great circle (except one) meets the shorter great circle arc joining them in at most one point. Let $\Sigma$ be the set of great circles meeting it in one point. Show that for any other curve $C$ joining the points, there must be an open set containing $\Sigma$ of great circles meeting $C$ in at least two points.
