Note 167 — APPENDIX IV SPACE, GRAVITATION AND SPACE-TIME

Geodesics are also the longest distances; the essential is that they constitute extreme distances. Thus, if we take two points at random on a sphere, the great circle passing through these points is a geodesic. But we may follow this geodesic from one point to the other in two different ways: either by going along the shortest path, or else by following the line that passes through the antipodes on the other side of the sphere. In this last case, the geodesic is the longest path.