Eratosthenes of Cyrene was an exceptional scholar who made lasting contributions in mathematics, geography, history and astronomy. He was also a poet, a theatre critic, chief librarian at Alexandria and, most notably, the first person to accurately estimate the size of the Earth. And yet, in spite of all these accomplishments, he was not especially regarded by his contemporaries, one of whom cruelly nicknamed him "Beta," or "Second Best." It seems as though Eratosthenes’ greatest talent was also his greatest fault; he excelled in many fields, but was pre-eminent in none.
Eratosthenes was born in Cyrene, a town in what is now Libya, in 276 BC. He received a well-rounded formal education from scholars and grammarians, and was exposed to Stoic philosophy. One of his teachers was Callimachus, a fellow native of Cyrene, who became the second librarian at Alexandria. In 245 BC Eratosthenes was called to Alexandria from his studies in Athens and appointed tutor for the son of Ptolemy III. Five years later he succeeded Callimachus as guardian of the greatest library of the ancient world.
It was in the library that he made a small discovery, which in turn led to a profound insight. While browsing some of the countless thousands of papyrus scrolls, he came across this fact: At noon on the summer solstice (June 21), the sun above Syene in southern Egypt cast no shadows and shone directly down a well. Eratosthenes knew that this was not true of Alexandria, where shadows were cast at noon on the solstice.
He theorised that if he could work out the difference in zenith angle between the noon sun at Syene (0 degrees) and at Alexandria, he would be able to determine the curvature of the Earth. Using geometry, he found that the variance was 7 degrees, or about 1/50th of a circle. The next step was to find out the distance between the two locations. According to Carl Sagan in “Cosmos," Eratosthenes paid a man to pace out the journey, which turned out to be 5000 stadia, or about 800km. The circumference of the Earth was therefore fifty times that distance, or about 40,000 km. This, it turns out, is a remarkably accurate conclusion.
Eratosthenes also used measurements obtained during lunar eclipses to determine the distance from the Earth to the Sun and Moon, and he measured, with great accuracy, the tilt of the Earth’s axis. He is said to have compiled a detailed catalogue of 675 stars, and to have written a poem called “Hermes” that was inspired by his love of astronomy.
As a historian, Eratosthenes worked out a calendar that included leap years, and tried to date many of the great events from the time of the Trojan War to his own time. He may have used records of the Olympiad to assist him in this, as fairly accurate accounts of the games had been maintained since their origin in 776 BC. If this is in fact the case, it would be somewhat ironic, as Eratosthenes’ other nickname was ‘Pentathlos’, for the athlete who competes in all events without being champion in any.
Certainly, his accomplishments were astonishingly varied. His contributions to geography include an accurate sketch of the Nile, and a prediction that the great river’s source was upland lakes. He also correctly suggested that the strange flooding of the Nile was caused by heavy rains near the source.
His books on mathematics included “Platonicus," which covered arithmetic and geometry and included a famous solution to the problem of doubling the cube. As a mathematician, however, his greatest contribution was a system for determining prime numbers. This came to be known as the "Sieve of Eratosthenes"; in a modified form it is still used in number theory research.
As is the case with most writings from the period, the original works by Eratosthenes have long since disappeared. Much of what is known about this great man comes through the acknowledgements of later Classical scientists and scholars. Men like Nicomedes, Strabo and Ptolemy acclaimed his work, while often modifying and refining it.
He may have been merely ‘Beta’ to some of his envious peers, but his legacy was profound to many subsequent thinkers. They tell one more story about Eratosthenes: that in his later years he went blind and died, in 195 BC, apparently starving himself to death. It seems that blindness was unbearable for this man who saw more clearly than anyone the true scale of the Earth against the immensity of the cosmos.