How did Eratosthenes use a mathematical formula to prove the earth is round?
The sphericity of the earth was known long before Eratosthenes, but he did measure the size of the earth. Eratosthenes had heard tales from travellers that at noon on midsummer’s day in Aswan, Egypt, one could see the image of the Sun on the water at the bottom of a deep well. He realized that this could only happen if the Sun was directly vertical on that day at Aswan. He then measured the angle of the Sun from vertical at his home in Alexandria at noon on midsummer’s day, and determined (using a compass) that the angle was 1/51 of a full circle. Since he also knew that the distance from Aswan to Alexandria was 5000 stadia (about 500 miles), he computed the circumfrence of the Earth to be 51 * 5000 or 255,000 stadia. This is a remarkably accurate result.
