Guru Academy and Labs: Eratosthenes Measuring the Earth

How did Eratosthenes disprove the flat earth theory and measure the radius of the earth?

It is quite interesting to see how the Greek philosopher Eratosthenes used some simple geometric techniques coupled with simple logics to disprove the flat earth theory and measured the size of the earth some 2200 years ago.

He noticed that in the city of Syene, during mid summer there was no shadow cast by the sun on a pole. Meaning the sun was perfectly above the pole. So he said if the sun's rays are parallel, then the angle of the shadow cast by a pole in the city of Alexandria, can give the angle between the two poles in the two cities, which he measured it as one fiftieth of a full circle or ~7.2 degrees. He hired a person to walk and measure the distance between the two cities, which was found to be around 800 km.

Using these two information Eratosthenes estimated the circumference of the earth to be around 50 x 800 km = 40,000 km. So the radius of the earth to be 40,000 / 2 $\pi$ = 6366 km. These estimates are astonishingly closer the presently available numbers with just few percent errors.