Eratosthenes of Cyrene (c. 276 –194 BC)

Born in modern-day Libya, Eratosthenes of Cyrene (c. 276 –194 BC) is best known for his remarkably accurate calculation of the circumference of the Earth, by comparing angles of the mid-day Sun at two locations a known distance apart on a north-south meridian.

At noon on the summer solstice in Syene (near modern-day Aswan, due south of Alexandria and almost on the Tropic of Cancer) the sun was directly overhead since the shadow of someone looking down a deep well there blocked the Sun's reflection on the water. 

In Alexandria, Eratosthenes used a gnomon (the projecting piece of a sundial) to measure the Sun's angle of elevation at noon on the summer solstice, working from the length of its shadow on the ground.

Using the length of the gnomon, and the length of the shadow, as two sides of a triangle, he established the angle of the Sun's rays was about 7°, around one-fiftieth of the circumference of a circle. 

Knowing Earth is spherical, and that Syene was around 5,000 stadia due south of where he was, Eratosthenes concluded that the Earth's circumference was fifty times that distance. Eratosthenes rounded the result of his observations to a value of 700 stadia per degree of the earth's circumference, giving a result of 252,000 stadia (around 46500 km). 

Although that figure is well off the earth's currently accepted polar circumference (40,008 km), Eratosthenes worked on some assumptions that were not entirely accurate. 

The distance between Alexandria and Syene was not exactly 5000 stadia. Syene is not right on the Tropic of Capricorn and is not exactly due south of Alexandria, and the Earth is not a perfect sphere, but his false assumption largely cancelled each other out. 

© Ian Hughes 2017