>Historically, to prove the earth is round, people have relied on the sun shining directly overhead on wells in different cities.
That wasn't to prove the Earth is round (and it doesn't prove it). Eratosthenes assumed two things when he performed his experiment: 1) the Earth is round, and 2) the Sun is an infinite distance away. By just this experiment he would have been unable to distinguish between this situation and the Earth being flat while the Sun being only a finite distance overhead (and in fact a fair bit closer than it actually is). Eratosthenes and his contemporaries were already convinced of the roundness of the planet, and he simply wanted to measure it.
>But this approach proves it without the need to refer the sun.
A flat-earther would just tell you that you're not able to maintain a straight path over such long distances without relying on external guides that would definitely put you on curved paths. If the Earth is flat and you stand at 0 N 0 E, how do you move in a straight line East of there? I.e. continuously moving towards the South because the polar coordinates curve towards your left as you progress.
>the Earth is flat and you stand at 0 N 0 E, how do you move in a straight line East of there?
This is something that was more or less solved a long time ago with surveying instruments. You don't have to move in a straight line, you build triangles out of sight lines.
I can kinda see how that would work, but it presents the challenge that whatever route you plan, it cannot go over water for more than a few kilometers.
I don't think it would be that different than the arc measurements that were actually done, you triangulate a bunch of points to work out distances and angle sufficiently precisely:
And measurements of, say, very precise equilateral triangles, necessarily imply certain interior angles, which you can compare to the actual angles they make. For instance, on a flat plane, you can fit six equilateral triangles sharing one point to make a hexagon. On a sphere if you make them big enough you'll find that they don't quite fit.
I'm not sure how that matters for this purpose, they used these surveys to measure the shape of the Earth (specifically, the circumference, and later the flattening- ie, plenty precise enough to measure the curvature more or less directly).
Is the idea that land is spherical while the oceans are flat? Do this survey on each continent, including Antarctica, again just constructing big triangles and measuring the deviation from flatness. Eventually your model of the flat earth looks like a bunch of pieces of an eggshell separated by flat water that just happens to assemble into an egg- or rather an ellipsoid- if rearranged, up to and including the expected flattening at the poles.
With sufficient elbow grease you could extend a survey from the far north of the Americas down to the south, measuring the curvature as you went, eventually finding that you must be almost upside-down compared to where you'd started.
> A flat-earther would just tell you that you're not able to maintain a straight path over such long distances without relying on external guides that would definitely put you on curved paths.
Do flat-earther reject the existence of LASER, too?
That wasn't to prove the Earth is round (and it doesn't prove it). Eratosthenes assumed two things when he performed his experiment: 1) the Earth is round, and 2) the Sun is an infinite distance away. By just this experiment he would have been unable to distinguish between this situation and the Earth being flat while the Sun being only a finite distance overhead (and in fact a fair bit closer than it actually is). Eratosthenes and his contemporaries were already convinced of the roundness of the planet, and he simply wanted to measure it.
>But this approach proves it without the need to refer the sun.
A flat-earther would just tell you that you're not able to maintain a straight path over such long distances without relying on external guides that would definitely put you on curved paths. If the Earth is flat and you stand at 0 N 0 E, how do you move in a straight line East of there? I.e. continuously moving towards the South because the polar coordinates curve towards your left as you progress.