The polymath Eratosthenes (276-194 BC) was born in Cyrene, in modern-day Libya, and after studying in Athens went to Alexandria, in Egypt, a flourishing city and a centre of scholarship.

There, under King Ptolemy's patronage, Eratosthenes ran the famous Library of Alexandria.

In the Egyptian city of Syene there was a famous well. Famous because at noon on the summer solstice the sun shone directly into the deep hole without any shadows.

Why? Because Syene lies almost directly on the Tropic Cancer - on the solstice the sun shines directly overhead.

Eratosthenes heard of this well and he saw an opportunity - because in Alexandria the same thing did not occur at noon on the solstice.

And, crucially, Alexandria lay directly north of Aswan. So it was on the same meridian and had the same longitude.

He also knew the exact distance between the cities.

All over the ancient Hellenic world there were "bematists" - professionals who measured distances (between cities, say) by walking them.

Alexandria was 5,000 stadia (an ancient metric) north of Syene.

Eratosthenes had all the numbers he needed - except one.

In Alexandria, at noon on the summer solstice, he placed a stick in the ground and measured the angle of the sun's rays based on the stick's shadow.

He got 7 degrees, which is about 1/50 of a circle's circumference.

And so Eratosthenes figured that the distance between Alexandria and Syene (where the angle was 0 degrees) represented a fiftieth of the total circumference of the earth.

He multiplied that distance by 50 and came to 250,000 stadia.

The precise length of the stade used in Egypt at that time isn't clear.

Eratosthenes' calculation was somewhere between 24,300 and 25,000 miles (39,100-40,300 km).

We now estimate the earth's circumference at 24,900 miles (40,300 km).

He was barely 1% out.

Eratosthenes wrote all this up in a book which is now lost. It was Cleomedes who, a few generations later, wrote the simplified account of Eratosthenes calculations - the one that has come down to us today.

His original methods were, Cleomedes says, more complicated.

So that's how Eratosthenes calculated the circumference of the earth: with a stick, a well, some helpful geography, good geometry, and an inquisitive mind.

And it's proof, too, that ancient people knew the earth was round.