But how could an Ancient Greek Mathematician, Eratosthenes, manage to find pretty much the exact same number, without having any pictures of Earth from the space or even proper measuring tools? Eratosthenes didn’t have much more than…a stick and his brain.
Over two thousand years ago, Eratosthenes heard that in Syene, a city south of Egypt’s Alexandria, no vertical shadows were cast at noon on the summer solstice as the sun was directly overhead. So, the Greek Mathematician wondered if this was the case in Alexandria too, a few hundreds of miles to the North of Syene.
So, he decided to conduct an experiment. On June 21, he went to Alexandria and he put a stick directly in the ground and waited to see if a shadow would be cast at noon. It turns out there was one and he tried to measure it. The shadow casted was about 7 degrees.
Now, Eratosthenes made a very logical conclusion: If the sun’s rays are coming in at the same angle at the same time of day, and a stick in Alexandria is casting a shadow of 7 degrees while the stick in Syene is not casting a shadow at all, it means that the Earth’s surface is curved.
The idea of a spherical Earth was already known by Pythagoras around 500 BC and validated by Aristotle a few centuries later. So if the Ancient Greeks before him were right and the Earth was a sphere, Eratosthenes could use his observations to calculate the circumference of our planet.
After hiring a man to pace the distance between Syene and Alexandria, he found out that the two cities were 5,000 stadia apart, which is about 800 km.
He could then use simple proportions to find the Earth’s circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers.
And just like that, an Ancient Greek 2200 years ago calculated precisely the circumference of our entire planet with just a stick and his brain.