In the third century BCE, Eratosthenes, head of the Library of Alexandria, was among the most broadly learned scholars of his age — working in mathematics, geography, poetry, and astronomy. His most famous achievement was to measure the size of the Earth without travelling anywhere, using only shadow and geometry.

He had been struck by a piece of information: in the city of Syene (modern Aswan) in southern Egypt, at noon on the summer solstice the sun stood directly overhead, a vertical rod cast no shadow, and the bottoms of wells were lit. Yet at the same moment in Alexandria a vertical rod cast a distinct shadow. Had the Earth been flat, the shadow would have been the same in both places. Eratosthenes measured the angle of the shadow: about 7.2 degrees — one-fiftieth of a full circle.

The logic was elegant: the distance between the two cities must be one-fiftieth of the Earth's circumference. The distance from Syene to Alexandria was known to be about 5,000 stadia; he multiplied this by fifty and found the circumference to be ~250,000 stadia. Because the exact length of the stadion he used is disputed, how close his result is to the modern value cannot be known for certain; but with a reasonable conversion the error is only a few per cent. What matters is not the number but the method: observation plus geometry had brought one of nature's largest scales within reach of the human mind.

Eratosthenes also drew one of the first maps of the known world with a grid of latitude and longitude, and devised the "Sieve of Eratosthenes," still named after him, for filtering prime numbers. The idea of measuring the Earth is among the ancestors of the belief — carried through the next two thousand years of astronomy, to Copernicus and on to the space age — that the universe can be grasped quantitatively.