Which Greek mathematician calculated the Earth's circumference using two shadows?

Eratosthenes, around 240 BC. He knew that at noon on the solstice the Sun shone straight down a well at Syene with no shadow, while at Alexandria a vertical rod cast one at about a fiftieth of a full circle. If the Earth is a sphere, the distance between the cities is a fiftieth of its circumference.

His answer, in stadia, is somewhere between roughly 1 and 16 per cent off depending on which length of stadion he was using - a unit whose value is not certainly known, which is the only real uncertainty in the result. The method is exact; the measurement of the distance between the cities, reportedly from the pace of trained walkers, was the weak link.

The idea that medieval Europe thought the Earth flat is a nineteenth-century invention, largely from a popular biography of Columbus. Educated opinion had known it was a sphere since the Greeks and known roughly how big. Columbus's actual error ran the other way: he preferred a much smaller estimate than Eratosthenes', which is why he thought Asia was reachable westward and why the experts advising against the voyage were right about the distance and wrong only about there being something in the way.