Measuring the circumference of the earth in ancient Greece

Many scientists in Ancient Greece believed the world was round. But none of them knew how big it was until the third century BC when Eratosthenes (c.276-194 BC), chief librarian of Alexandria, devised an ingenious way to measure the earth’s size.

Eratosthenes knew of a special well near Syene, Egypt.  At noon on June 21, the longest day of the year, the sun’s rays penetrated all the way to the bottom of the well.  This meant that the sun was directly overhead.  Eratosthenes realized that if the sun was directly overhead in Syene, then its rays must be hitting at an angle in Alexandria, which was due north.   If he could measure the angle by which the sun was off center, then he would have the clue he needed to extrapolate the size of the earth.  So, at noon on June 21 in Alexandria, he took a measuring stick and captured the angle cast by its shadow.

Eratosthenes knew that the angle of the shadow was equivalent to the angle formed by the two cities and the center of the earth.  So, he divided the size of that angle by 360, the number of degrees in a circle, to determine the fraction of the earth that separated the two cities.  The answer was one-fiftieth.  In other words, if you walked back and forth between Syene  and Alexandria fifty times, then you would have walked the equivalent of the earth’s circumference.

All that remained was to measure the precise distance between the two cities.  Eratosthenes hired a pacer, a professional walker trained in taking perfectly equal steps.  From measurements of the pacer, Eratosthenes estimated the circumference of earth to be 24,700 miles.  Today, using the same principle developed by Eratosthenes 2,000 years ago, modern instruments estimate the distance around the equator to be 24,902 miles.

— The Intellectual Devotional by David S. Kidder and Noah D. Oppenheim