## Saturday, April 27, 2013

### Eratosthenes: The First Estimate of the Earth's Circumference

You might have thought that the Earth was proven round by Christopher Columbus in 1492. However, it was actually proven almost 2000 years earlier by a mathematician named Eratosthenes.

Eratosthenes was born in 276 BC in Cyrene, which was then a Greek colony. It would now be considered part of northern Libya. He was educated at Plato's school in Athens and went on to become chief librarian at the University of Alexandria.

Aside from his other contributions, he came up with a very close estimate of the circumference of the earth. First, he found out that at noon on the summer solstice, people in the Egyptian city of Syene noticed that there were no shadows from the sun. This is because Syene is very close to the Tropic of Cancer. This was confirmed by some tests he did by looking for brightness contrast inside of deep wells.

In his hometown of Alexandria, thought to be on the same meridian as Syene, he measured the angle of the sun's shadow on a pillar at noon of the next summer solstice. He found a 7° angle. This meant that when a circle is drawn to represent the circumference of the earth, Alexandria would be 7° around the circle.

Syene was known to be about 500 miles from Alexandria, and 7° is about one fiftieth of a circle. So, multiplying 500 x 50 gave Eratosthenes his estimate of 25,000 miles. This is a very impressive estimate, considering the modern distance is 24,901 miles.

It is extremely cool that you can determine the circumference of such a big thing without much technology at all. Just with a few mathematical principles, Eratosthenes could solve this daunting problem.