## Saturday, October 6, 2018

### How Eratosthenes calculated the Earth's circumference

In the mid-20th century we began launching satellites into space that would help us determine the exact circumference of the Earth: 40,030 km.
But over 2000 years earlier, a man in Ancient Greece came up with nearly the exact same figure using just a stick and his brain.
How an ancient Greek mathematician calculated the Earth's circumference.
That man was Eratosthenes.
A Greek mathematician and the head of the library at Alexandria.
Eratosthenes had heard that in Syene, a city south of Alexandria, no vertical shadows were cast at noon on the summer solstice.

He wondered if this were also true in Alexandria.
So, on June 21 he planted 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 it measured about 7 degrees.
Now, 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 while a stick in Syene is not, it must mean that the Earth's surface is curved.
And Eratosthenes probably already knew that.
The idea of a spherical Earth was floated around by Pythagoras around 500 BC and validated by Aristotle a couple centuries later.
If the Earth really was a sphere, Eratosthenes could use his observations to estimate the circumference of the entire planet.

Since the difference in shadow length is 7 degrees in Alexandria and Syene, that means the two cities are 7 degrees apart on Earth's 360-degrees surface.
Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 kilometers.
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, a man 2200 years ago found the circumference of our entire planet with just a stick and his brain.