I very strongly disagree that this is a point of debate. There is no room for debate about basic geometry. But I was told this is not a subject for the Suggestions board. So I am putting it here. Ludicrous.
Thesis: The very short and accessible Wiki Article on Eratosthenes is nonsense.
We can use Eratosthenes' shadow experiment to determine the diameter of the flat earth.
Syene and Alexandria are two North-South points with a distance of 500 nautical miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.
7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).
Therefore we can take the distance of 500 nautical miles, multiply by 25, and find that the radius of the flat earth is about 12,250 nautical miles. Doubling that figure for the diameter we get a figure of 25,000 miles.
The
wiki article on Eratosthenes assumes a round Earth. It appears to be assuming a round earth that is concave upward. That is the only possible way that the suggested calculation makes any sense at all.
With a flat Earth, the correct calculation gives a height of 4000 miles for the Sun, but it does not give any reasonable estimate for the size of the Earth. Using the coincidentally chosen cities of Alexandria and Syene, the 66th parallel south of the equator
(90 degrees of latitude south of Syene; the Antarctic peninsula) is an
infinite distance to the south of Syene, and the 90th parallel north of the equator (the north pole) is 4000 miles times the tangent of 66 degrees, or
nine thousand miles north of Syene. These distances would change if Eratosthenes had measured two different cities.
The given numbers for anyone who may be reading this thread without looking at the wiki article or without any faith in the wiki article are as follows:
Syene is on the Nile at approximately the Tropic of Cancer or 24 degrees. It is at the current site of Aswan.
Alexandria is roughly 500 Miles, 5000 stadia, or 8000 km north of Syene. Eratosthenes found the sun to be 7 degrees south of Alexandria when it was directly overhead at Syene.