How it was calculated by Eratosthenes over 2000 years ago.
During the 3rd century BC, a man named Eratosthenes ventured to calculate the circumference of the earth (yes, people did know the Earth was round even back then). Of course, advanced technology wasn’t available at that time to do most of the work for him. Eratosthenes had to do it himself with what resources he had… and yet he managed to do it remarkably accurately (with only 1% error!) So how did he do it? Well, the process is much simpler than you’d expect, it just required someone clever to think of it.
Eratosthenes, who lived in Alexandria, had heard of a well in Syene, around 800km away. At a particular time on a particular day of the year, the sun shone directly into the well without casting a shadow. On that same day and time, however, a vertical object in Alexandria would cast a shadow. This indicated that the earth was round.
Eratosthenes also knew that sun rays are parallel. Using that knowledge, the rest was a process of simple middle-school mathematics.
In order to calculate the earth’s circumference, he must know:
- The distance between Alexandria and Syene (which was 5000 stadia)
- The angle at the center of the earth between Alexandria and Syene
To find the angle at the center, he placed a vertical rod in Alexandria, and at the time when it was said that there was no shadow in the well at Syene, he calculated the angle of the shadow in Alexandria.
Because the sun rays are parallel, and the two angles were alternate, the angle of the shadow is equal to the angle at the circumference, which he found to be 7.2 degrees.
After that, calculating the circumference became a matter of proportionality:
360 x 5000 stadia = 7.2 x the circumference
Circumference = 250 000 stadia (around 40 000 km)
Today we know that the circumference of the Earth is 40 075 km! What an incredibly accurate calculation… and with nothing but a stick and a well.
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