Eratosthenes of Cyrene
c. 285-c. 205 B.C.
Greek North African Mathematician, Astronomer, and Geographer
Most famous of the librarians at Alexandria, Eratosthenes provided a measurement forEarth's circumference within 1% of the actual number. He also developed a method for finding prime numbers, and made contributions as an astronomer, geographer, philosopher, and poet.
Born in Cyrene, now part of Libya, Eratosthenes's father was named Aglaus, but these are the only known facts of his origins. He studied with the grammarian Lysanias, the philosopher Ariston of Chios, and the poet Callimachus (c. 305-c. 240 B.C.), second librarian of Alexandria. In his teens he traveled to Athens, where he may have studied both at the Academy established by Plato (427-347 B.C.) and the Lyceum of Aristotle (384-322 B.C.).
Eratosthenes, who at a later time might have been called a Renaissance man, displayed his talents as a poet in Hermes and Ergion. These in turn attracted the attention of Ptolemy III Euergetes (r. 246-221 B.C.), Greek ruler of Egypt, who invited Eratosthenes to Alexandria as tutor for the crown prince. Soon afterward, Ptolemy appointed Eratosthenes director of the city's famed library.
During his fruitful career, Eratosthenes contributed to mathematical knowledge with a technique for finding prime numbers that came to be known as the "sieve of Eratosthenes." Using this formula, a type of algorithm, he could pull out primes from an ordered list of the natural numbers. Not only did this method spark later investigation in number theory, but it could perhaps be cited as an early manifestation of computing techniques.
In working on the Delian problem, which involved finding mean proportionals as a way of doubling the cube, Eratosthenes developed what was called the mesolabe or "mean-finder," which made it possible to determine an infinite number of mean proportionals between two lines. He also wrote a number of mathematical texts, but the only piece of his writing that survives is a letter to Ptolemy III explaining the mesolabe.
Most famous among Eratosthenes's many achievements was his measurement of Earth's circumference. This he did by measuring the distance from Alexandria to the city of Syene in the south, which he determined to be 5,000 stadia (489 miles; 783 kilometers). By using calculations of the Sun's position over both cities during the summer solstice, he was then able to estimate that the difference between them represented 2% of Earth's circumference, the total of which he calculated at 252,000 stadia (24,662 miles; 39,459 kilometers).
In fact the true figure at the equator is 24,901.55 miles (39,842.48 kilometers), meaning that Eratosthenes was astonishingly close. At his time, of course, no expedition had ventured below the equivalent of 10° north; nor did anyone in the Old World know about the existence of the New. Certainly his figure implied the existence of a very large unexplored area on the other side of the world, and had Christopher Columbus (1451-1506) been using the numbers derived by Eratosthenes when he made his historic landing in the Caribbean some 1,700 years later, he would have realized that he had not reached Asia. Unfortunately, however, Hipparchus (190-126 B.C.) had rejected Eratosthenes's measurement in favor of a much smaller number, and Hipparchus's follower Ptolemy (c. A.D. 100-170) had propagated this misconception, which remained the received wisdom throughout the Middle Ages.
As for Eratosthenes, his now-lost manuscript On the Measurement of the Earth marked the foundation of geodesy, the branch of mathematics that deals with determination of Earth's size and shape, and the location of points on its surface. Among the topics of study within geodesy is the system of latitude and longitude, which Eratosthenes seems to have pioneered in his maps, the most accurate in the world at the time.
Believed to have developed the calendar that remained unchanged in the Greco-Roman world until the time of Julius Caesar (102-44 B.C.), Eratosthenes also established the first reliable method of dating events, by reference to the years of the Olympic festivals. In his later years, he went blind, and perhaps as a result of despair over his inability to any longer read the manuscripts of his beloved library, he starved himself to death in the ninth decade of his life.
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