Greg Egan on Nostr: Two pairs of ants set off from the same starting point, walking side-by-side. One ...

Two pairs of ants set off from the same starting point, walking side-by-side. One pair takes the red path, the other pair takes the blue path.

The red and blue paths are geodesics (the straightest possible paths, like great circles on a sphere), and each ant in a pair follows a geodesic that lies a small distance to either side of the marked one, initially pointing in the same direction.

If this ellipsoid has semi-axis of length 1 and 3, the ants taking the blue path will bump into each other at the “pole”, where all meridians converge, after travelling a distance of 3.34122.

How far will the ants following the red path travel before they bump into each other? More, less, the same?