This illustration shows how Eratosthenes actually calculated the circumference of the Earth. At noon on the summer solstice, Eratosthenes measured the length of the shadow cast by a column of known height at Alexandria. With these two lengths, he could solve for the angle between them (θ). If the length of the shadow, and height of the column (h) were proportional to the distance between Alexandria and Syene (s=4,400 stades), and the radius of the Earth, then by calculating the angle on the column (θ), he was calculating the same angle formed at the center of the Earth (θ). The equation he used to determine the circumference of the Earth [(360° ÷ θ) x (s)] reflects this theory.

Eratosthenes method of calculating the Earths' circumference

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