How Eratosthenes measured the circumference of the Earth

Eratosthenes was an interesting character

He was a mathematician who lived in the 3^rd century BC who did some very important work.

He gets a mention on this course for his brilliant measurement of the Earth’s circumference.

Despite all his great work in many fields his nickname was ‘Beta’ as he tended to be second best in a number of disciplines.

Eratosthenes lived in Alexandria in Egypt but was born in Syene (now Aswan) and it was these two places that he used in his calculation.

 

Syene lies on the Tropic of Cancer.

On June 21^st (midsummer’s day) on the Tropic of Cancer, the sun is directly overhead (at our Zenith) at noon.

Any vertical object would have no shadow.

He was in Alexandria though, which is about 800 km North.

He measured the angle of the Sun here by looking at the shadow of a vertical object and calculated that this angle must be the same angle between Syene and Alexandria from the centre of the Earth.
 

See diagram below.

 

This showed that there is 7 degrees between Syene and Alexandria.

You need about 50 lots of 7 degrees to make a full circle so you must need about 50 lots of the distance from Syene to Alexandria to get around the world.

He calculated the Earth’s circumference to be about 40,000 km, which was pretty much spot on!

If you are able to understand this, you should do very well on the course.

A* and A grade students will be able to explain how Eratosthenes did his calculation with the use of a diagram.