Flat Earth Or Round?

I have noticed an increase in debate on whether the world is actually flat, with many proponents putting considerable effort in attempting to provide plausible arguments for a flat earth.

The following, youtube video of Carl Sagan, is how I understood the idea of a round earth was developed. I vaguely remember discussing the method of determining the length of shadows in two different areas and segment length between them. This method is difficult to refute and to date I have not heard a refutation for it, if you are a 'Flat Earther' maybe you would be able to provide me with one.

What concerns me is not so much whether the Earth is round or flat, but the trend in the methodology of how people these days obtain confirmation of their ideas. I suspect that the flat Earth movement is a cruel joke on ignorant people (however I might be wrong as I have not conducted the experiment myself) and represents a social exercise rather than a scientific exercise.

At Alexandria the angle of the Sun is 7.2 degrees and the distance to the tropic of Cancer is 800Km. On a Flat Earth that would position the Sun 800 / tan(7.2) = 800 / 0.1263294 = 6,332.65 Km directly above the tropic of Cancer.

Move 800 Km North of Alexandria and the angle of the Sun is 14.4 degrees. Now the distance to the tropic of Cancer is 1,600Km. On a Flat Earth that would position the Sun 1600 / tan(14.4) = 1600 / 0.2567564 = 6,231.59 Km directly above the tropic of Cancer.

The Sun can't be in both places simultaneously, ergo the Earth is not Flat.

It is true that i haven't done the experiment personally; however a more extensive experiment was carried out between 1730-1740 by the French Geodesic Mission, not to prove the Earth is round, but to estimate the circumference. When taking observation points in more than two locations, it becomes evident that the earth is somewhat spherical. In fact the French Geodesic Mission, found that it wasn't exactly spherical.

It should be noted that Eraosthenes and the French Geodesic Mission were never in doubt of the earth being round, however were attempting to estimate its diameter.

My concern is not for the earth it is how society is beginning to evaluate information that is provided to them. I see this as perhaps the development of a dark age, not by lack of information but by provision of a quantity of information (and misinformation) that is impossible to manage. I think that the skills for dealing with this information have been gradually removed from our education system and the quantity has increased, resulting potentially, in relative confusion. Hope you enjoyed the video, let me know what you think about how we are fed information and how you evaluate information provided by the many sources available today.

LB