In the mid-20th century, we began launching satellites into space to accurately determine the circumference of the Earth: 40,030 km. However, more than 2,000 years prior, a man in ancient Greece discovered a remarkably similar figure using just a stick and his intellect.
This man was Eratosthenes, a Greek mathematician and the chief librarian at the Library of Alexandria. He is also known for creating the sieve that bears his name – the Eratosthenes sieve – which is used to filter out prime numbers less than 100.
Mathematician Eratosthenes (276 BC – 194 BC).
Eratosthenes heard that in Syene (now Aswan, Egypt), a city south of Alexandria, there were no shadows cast at noon on the summer solstice, and the sun was directly overhead. He wondered if this was true in Alexandria as well.
To test this, on June 21, he plunged a stick straight into the ground and waited to see if a shadow would appear at noon. It did, and he measured the angle of the shadow to be about 7.2 degrees.
If the sun’s rays hit at the same angle at the same time of day, and a stick in Alexandria casts a shadow while a stick in Syene does not, it means that the surface of the Earth is curved. Eratosthenes likely understood this concept.
The idea that the Earth is spherical was proposed by Pythagoras around 500 BC and confirmed by Aristotle centuries later. If the Earth is indeed a sphere, Eratosthenes could use his observations to estimate the circumference of the entire planet.
The difference in shadow length between Alexandria and Syene being 7.2 degrees indicates that these two cities are separated by 7.2 degrees on the Earth’s 360-degree surface. Eratosthenes hired a man to measure the distance between the two cities and found that they were 5,000 stadia apart, approximately 800 km.
He could then use simple ratios to find the circumference of the Earth – 7.2 degrees is 1/50 of 360 degrees, therefore 800 multiplied by 50 equals 40,000 km.
If you Google “Earth’s circumference”, you will find this figure is 40,075 km. This is because the Earth is slightly oblate, resulting in a polar circumference of 40,008 km and an equatorial circumference of 40,075 km. If it were a perfect sphere, its circumference would be 40,030 km.
And just like that, a Greek man 2,200 years ago calculated the circumference of our entire planet using only a stick and his mind, with only a slight margin of error.
How did the Greeks know the Earth was spherical 2,000 years ago?
