Hi,  I only registered in order to leave a idea about a perspective experiment.  It requires you to find a really deep hole,  or digging a hole.  If you could place series of thin lines within such a hole,  and use your camera to look inside a hole,  you might find that parallel lines get closer and closer to each other. Even better if thin lines represent height.

 Holes are independant of the shape of the earth.  Whether the earth is flat or not,  there is zero curvature.