Eratosthenes Estimates Earth’s Circumference

On this day in 240 BCE Greek astronomer, geographer, mathematician, and librarian Eratosthenes is said to have calculated Earth’s circumference. His figures were later found to be astonishingly accurate.

Born in Cyrene in modern-day Libya, Eratosthenes was an ancient Renaissance man often called Pentathalos, or champion of multiple skills, by his contemporaries. As a mathematician, poet, athlete, geographer, astronomer, and music theorist, his vast knowledge made him an ideal fit for the post of librarian at the Library of Alexandria, Egypt, the legendary repository of classical knowledge.

The brilliant Eratosthenes lay claim to a number of significant achievements. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used today. He sketched the course of the Nile River and correctly predicted its source. He also may have accurately calculated the distance from the Earth to the Sun and invented the leap day, an idea taken up two centuries later by Julius Caesar. He even created the first map of the world incorporating parallels and meridians.

Remarkably, Eratosthenes was also the first person to calculate the circumference of the Earth with stunning accuracy and remarkable logic. The Greek genius noted that at noon on the summer solstice the Sun was directly overhead in Syene, or modern-day Aswan. A sundial cast no shadow there. But to the north in Alexandria, the sun was not directly overhead—a sundial cast a shadow even at midday. As such, he posited, the Earth must be round.

Furthermore, if the Sun was far enough to cast parallel rays in Syene and Alexandria, one could calculate Earth’s circumference. Eratosthenes determined the shadow in Alexandria to be 1/50 of a 360-degree circle, then estimated the distance between the two locations and multiplied by 50 to derive Earth’s circumference. His final figure was 252,000 stades, or stadium lengths, somewhere between 39,691 and 45,008 kilometres. The accepted figure today is about 40,075 kilometres, pretty close for an ancient astronomer without modern tools.