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 Last modified: 04:36 PM - 1 December, 2022

1. Show that if \(\gamma\) parametrizes a line that lies on a surface, then \(\gamma\) is a geodesic of that surface.

2. Prove that \(\gamma\) is a geodesic if and only if its geodesic curvature is 0

3. Show that any geodesic in a plane must be a straight line