A geodesic is a minimal path between two points. Minimal in this case can be thought of as least time assuming a constant velocity. This is equivalent to the shortest distance between two points.
On a piece of paper this is a straight line. On a cylinder it is a helical path kind of like a spring. On a sphere, it is a great circle, equivalent to a line traced by a plane and the sphere’s surface, passing through the sphere center and the start and end destinations.
The earth is an ellipsoid and the geodesic is not a great circle, but for short distances it is approximated by one.
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