The polymath Eratosthenes was born around 276 BCE in the city of Cyrene (in present-day Libya), which was part of the Greek-speaking Ptolemaic Kingdom centered in Egypt. As a young man he went to Athens, where he studied with prominent teachers in various philosophical schools and soon began to write works that would make him famous; these includied poetry that was highly regarded, a mathematically precise chronology of history, and a mathematical discussion of Plato's philosophy. His works brought him to the attention of pharaoh Ptolemy III Euergetes, who invited him to tutor his children and to be a librarian at the famed Library of Alexandria. Eratosthenes accepted the offer and moved to Alexandria, where he was to spend the rest of his life. There he continued working in many areas, including mathematics, astronomy, geography, history, philosophy, poetry, grammar, and literary criticism. After he had been there for five years, the old Chief Librarian died and Eratosthenes was appointed to take his place. In this time he also became friends with the great mathematician, physicist, engineer, and inventor Archimedes of Syracuse, who dedicated two of his works to him.
Eratosthenes is known today mostly for his calculation of the circumference of the Earth. He had learned that in the city of Syene (modern day Aswan), which was (somewhat erroneously) believed to be due south of Alexandria, it had been reported that at noon on the summer solstice the Sun was straight overhead, such that its rays only illuminated the bottom, but not the sides, of a deep well. He also had an estimate of the distance from Alexandria to Syene. To this information he added an observation of the length of a shadow cast in Alexandria at the same date and time, relative to the height of the object casting the shadow (perhaps using the Great Obelisk in Alexandria, or a sundial gnomon). Then, using the assumptions that the Earth was a perfect sphere, and that the Sun was very far away, he calculated a remarkably accurate value for the Earth's circumference. While he may not have been the first to have made this type of calculation, he is the first whose methods have been reported, and the first known to have achieved such accuracy (though he may have benefited from some of the errors in his data canceling each other out).
A partial list of his accomplishments
- Accurately calculated the circumference of the Earth
- Founded mathematical geography, creating maps with north-south and east-west gridlines, including a comprehensive map of the known world
- Created a simple efficient method of calculating prime numbers, still known as "The Sieve of Eratosthenes"
- Accurately calculated the tilt of the Earth
- Calculated the distances from the Earth to the Moon and the Earth to the Sun (though his methods are not known and their accuracy may not have been good)
- Discovered that a year was a little more than 365 days, and devised a 365 day calendar with a 366 day year every four years
- Explained the flooding of the Nile
- Invented the armillary sphere, a device used to determine the positions of the celestial bodies
- Contributed significantly to the theory of musical scales
- Wrote works on many topics, though now only fragments remain
- Promoted the liberal view that non-Greek people should not be written off as "barbarians", but instead each person should be judged on their own merits