That's a nice mathematical questions. My guess is that there are a few models that make minimal sense, and this experiment can refute them. (Ignoring wind currents, that are important and probably make the return flight a few hours longer/shorter.)
In an unrestricted case, you can always select a map where that any real geodesic is a line in your flat map. I guess to prove that the surface is not flat, you need to measure the more distances, like measuring the four sides of a quadrilateral and then the two diagonal. (I think it is not possible using geodesics, without measuring one distance or an angle or a surface.)
In an unrestricted case, you can always select a map where that any real geodesic is a line in your flat map. I guess to prove that the surface is not flat, you need to measure the more distances, like measuring the four sides of a quadrilateral and then the two diagonal. (I think it is not possible using geodesics, without measuring one distance or an angle or a surface.)
The nice part of Gaussian curvature is that you can measure it in the surface, without a model of the 3D word that is "around" it. https://en.wikipedia.org/wiki/Gaussian_curvature