## Eratosthenes Measures the Circumference of the Earth With a Stick

The ancient Greek polymath Eratosthenes of Cyrene was nicknamed beta because he was thought to be the second best in the world at every field of endeavour. A friend of Archimedes and head librarian at Alexandria, he was accomplished in mathematics, poetry, astronomy and he invented the study of geography.

He had heard of a well in the Egyptian city of Syene (modern day Aswan). At noon on one day each year, the sun would shine into the well and illuminate the water lying at its bottom. Syene was situated close to the tropic of cancer and the day in question was the June solstice, meaning that the Sun was directly overhead at noon and no shadows would be cast.

At the next June solstice, Eratosthenes took a stick and stuck it in the ground . At midday, he measured the angle created between the stick and a line from the top of the stick to the end of its shadow as 7.2o, or 1/50th of the number of degrees in a circle. He then estimated the distance between Syene and his home in Alexandria using the time it had taken him to travel between the two cities by camel. He deduced that this distance was 1/50th of the circumference of the Earth. Multiplying by fifty, he concluded that the Earth was 252,000 stadia in circumference. There is some confusion now as to exactly how long a stadia is, but, at worst, Eratosthenes was no more than 16% out and at best, within 1% of the true circumference (40,000 km). Either way, it was one of the greatest extrapolations of all time.

A stick in the ground: Arbre du Tenere, the world’s most isolated tree, was destroyed by a drunk driver in 1973. Author: Michael Mazeau, via Wikimedia Commons.