Eratosthenes of Cyrene

Geographer and mathematician

Born: c. 285 b. c.e.; Gyrene (now in Libya) Died: c. 205 b. c.e.; Alexandria, Egypt Category: Geography; mathematics

Life Following his education in Athens, Eratosthenes of Cyrene (ur-uh-TAHS-thuh-neez of si-REE-nee) spent most of his life in Alexandria as head of the great library there. His areas of accomplishment included geography, math, astronomy, and literary criticism. Contemporaries regarded him highly. Archimedes dedicated a work to him. Later writers (including Strabo) were more critical. It is difficult to judge his works independently because only fragments of Eratosthenes’ many titles survive.

Most recognized for his work in geography, Eratosthenes established this study on a mathematical basis, dividing Earth into five climate zones.

Geographer and mathematician Eratosthenes.

He also developed an accurate method for calculating the circumference of Earth, noting the difference between the shadow cast by the Sun on March 21 at Syene (none) and some 5,000 stadia away in Alexandria (roughly one-fiftieth the circumference of a circle, or 7 degrees and 12 minutes). He realized (by Euclidian geometry) that the angle the Sun’s rays made in Alexandria was the same as the angle made by lines extended to the center of the earth from Syene and Alexandria (opposite interior angles are equal). In other words, the distance from Syene to Alexandria was one-fiftieth of the distance around Earth, and so Earth’s circumference was 250,000 stadia, about 29,000 miles, close to modern estimates. In mathematics, Eratosthenes solved the problem of doubling the cube and developed an algorithm for finding prime numbers, his “sieve.”

Influence Not only did he lay the foundations for a mathematical geography, but also, by using geometry, Eratosthenes calculated the size of Earth to a degree of accuracy that would not be improved on until the modern era.

Further Reading

Calinger, Ronald. A Contextual History of Mathematics. Englewood Cliffs, N. J.: Prentice Hall, 1999.

Dyer, J. E. History of the Planetary Systems from Thales to Kepler. New York: Dover, 1953.

Gow, James. A Short History of Greek Mathematics. Mineola, N. Y.: Dover,

2004.

Hogben, Lancelot. Mathematics for the Millions. New York: W. W. Norton,

1983.

Trefil, James. “Rounding the Earth.” Astronomy 28, no. 8 (August, 2000): 40.

Wells, David. Prime Numbers: The Most Mysterious Figures in Math. Hoboken, N. J.: Wiley, 2005.

Terry R. Morris

See also: Alexandrian Library; Archimedes; Euclid; Science.