History

How Eratosthenes measured the whole Earth with a stick and a shadow

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Around 240 BC, Eratosthenes, head of the Library of Alexandria, measured the size of the whole Earth with a stick and a shadow.

At noon on midsummer, sticks in Syene (modern Aswan) cast no shadow. In Alexandria, 5,000 stadia to the north, a stick cast a shadow tilted about 7.2°, one fiftieth of a circle. If the Sun's rays are parallel, that tilt is the Earth's curve between the two cities. So the whole Earth must be 50 × 5,000 = 250,000 stadia around, within a few percent to about 15% of the true size, depending on which stadion he meant.

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