Color diagram that shows a sphere, drawn in blue, and two great circles, drawn in red and green. A close-up shows how the geodesics appear to be parallel over distances much less than the radius of the sphere. But the full diagram shows that the curves necessarily intersect at two points.

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1. Robert McNees (mcnees@mastodon.social)'s status on Thursday, 01-Dec-2022 15:34:57 UTC Robert McNees

   in reply to

   A curved surface appears flat over very short distances – you don't notice the curvature of the Earth standing in your front yard.

   Over those "local" scales two geodesics may resemble Euclid's parallel lines. Measure the separation with a ruler and it seems constant. But this isn't quite true; there are small deviations due to the curvature.

   On longer scales – for a sphere, distances comparable to its radius – the effect of curvature accumulates and these initially parallel lines intersect.