Ask Ethan: How do we know the Earth isn’t flat?
Ethan Siegel

Ancient Syene is today's Aswan. Apparently Eratosthenes measured the noon shadow on that once-in-a-year day to be 7.2 degrees in Alexandria, that is 1/50th of 360 degrees, in other words, 1/50th of the full circle. That means that he measured that the circumference of the Earth is 50 times the distance between Alexandria and Aswan. Wolfram Alpha tells us that that distance is 843 km.

Which gives around 42000 km for 50 times that, which is around 5% error which is good for that time (some 2200 years ago, 200 years before CE and the legendary birth of the carpenter Jeshua). Note that it's irrelevant to know which stadia unit Eratosthenes used, he only measured the correct multiplier of the distance, and of course he was not responsible for the measurement of the distance between two cities. Very clever measurement and conclusion and very accurate for that time.

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