Flat Earth - The Math Will Work Out the Same

Eratosthenes believed that the sun was a VERY long way away - compared to the size of the Earth.

His math uses that assumption because he presumes (without much evidence) that the rays of light from the sun are parallel.

However, if you don’t assume that the sun is a long way away - then the arithmetic for calculating the earth’s radius changes - and the math becomes dependent on the distance to the sun.

If you assume that the sun is at an altitude of around 6,000 km (a distance equal to the radius of the round earth) - then Eratosthenes’ experiment does indeed “prove” that the Earth has an infinite radius…ie, that it’s flat.

So the Flat Earthers believe that the sun is 6,000 km above the Earth - which squares things up with Eratosthenes.

But they aren’t really using Eratosthenes to prove that the Earth is flat - they’re really using the assumption that the Earth is flat to “prove” that the sun is 6,000 km above the Earth.

Since they can measure the observed angle subtended by the sun’s disk, they conclude that it must be about 51km in diameter.

So this isn’t a “Proof” of the flat earth - but it’s also not “Proof” of the round earth. The experiment really doesn’t tell you anything at all unless you know the distance to the sun.