A meme image by IFLS today [7/13/2018] included a reference to Eratosthenes and his calculation of the Earth's circumference, but the date given for Eratosthenes was off by thousands of years.
Eratosthenes was a contemporary of Archimedes and did his work in Alexandria around 200 BCE.
He didn't use two obelisks, rather he had heard tale of a well in the city of Syene (now Aswan) at the first cataract of the Nile river, where, on the summer solstice, the sun shown straight down the well, and the well cast no shadow.
But further north in Alexandria such a thing didn't happen, and a pole, held vertically would still cast a shadow, while in Syene there would be no (actually a very slight) shadow on that day.
This is because Syene is just a tad north of the Tropic of Cancer, and the Sun is almost exactly overhead there on the solstice, while Alexandria is about seven degrees further north in latitude.
So the sun is the same number of degrees away from directly overhead in Alexandria on the solstice. Eratosthenes had an idea.
Anyone in classical times who lived near the sea, as Eratosthenes did, understood that the Earth was curved, as ships regularly disappeared and reappeared from over the horizon.
Anyone in classical times who lived near the sea, as Eratosthenes did, understood that the Earth was curved, as ships regularly disappeared and reappeared from over the horizon.
In the Greek cultural world that Eratosthenes inhabited, the Earth was understood to be spherical since at least 500 BCE.
Eratosthenes knew from geometry, that his latitude angle on the spherical Earth, was the same as the angle difference of the shadows at Alexandria and Syene.
If that angle difference was six degrees, then the world's circumference was just the distance between the two cities, multiplied by the ratio between number of degrees in a full circle and those six degrees.
So he needed an accurate distance between the two places. He hired a merchant who was traveling up and down the Nile (which runs nearly North to South) to count his paces between the cities.
When the merchant returned his measurement, Eratosthenes was able to determine the circumference of the Earth, and did so to a degree we believe was within 5% of the true size.
Take it away Carl: Carl Sagan - Cosmos - Eratosthenes