### Topic Page: Eratosthenes

**Eratosthenes**from

*Cultural Sociology of the Middle East, Asia, and Africa*

One of history's most accomplished men of science, Eratosthenes of Cyrene (ca. 276 B.C.E.-ca. 195 B.C.E.) was the precursor of the “Renaissance men” who would follow him almost 2,000 years later. Considered the father of geography, Eratosthenes was also a significant astronomer, mathematician, poet, and musician, as well as an athlete during his youth. Later tradition has it that he was nicknamed Beta, the second letter of the Greek alphabet, because he was the second best in every field, an example of medieval fancifulness. While Eratosthenes' breadth of experience is impressive, the fields in which he worked were in their infancies, with mathematics, of course, being the common language among them.

Cyrene, a Greek colony in what is now northeastern Libya, was one of Greece's oldest and most important African colonies. It was founded in 630 B.C.E. and named after the spring (Kyre) consecrated to Apollo. The Cyrenaic school of philosophy, which was hedonistic, pleasure-loving, and skeptical, thrived a generation before Eratosthenes's birth, but by 276 was considered obsolete compared to the more recent teachings of Epicurus. In the year of Eratosthenes's birth, Cyrene's governor Magas (the son-in-law of the late Ptolemy I, one of the generals who succeeded Alexander the Great) declared the city's independence from Greece and crowned himself king. Cyrene remained independent—and frequently at war—until Magas's death in 250 B.C.E., when Eratosthenes was a young man. In 236, Eratosthenes was appointed librarian in Alexandria, Egypt, the third person to hold that post. He had previously studied both in Alexandria and in Athens, but overseeing the library gave him access to knowledge unlike what he'd had before, as well as important connections. For instance, at the library, he quickly befriended the Syracusan mathematician-engineer Archimedes.

Eratosthenes made a number of contributions to mathematics and science, many of which dealt with constructing accurate models of the world. He invented the armillary sphere, for instance, which used a framework of rings centered around a glove representing Earth, intended to model the celestial sphere in order to demonstrate lines of celestial longitude and latitude and features like the ecliptic, the tropic of Cancer, and the equator. The sphere was built on the recently established knowledge that Earth was a sphere. The armillary sphere was quickly adopted as both a teaching and a research tool, and subsequent ancients built armillary spheres tailored to their areas of study.

One of the principal preoccupations of mathematicians has long been the finding of prime numbers. The Sieve of Eratosthenes was one of the first methods developed to do so, and was used right up until the age of computers. The Sieve is a simple algorithm that mechanically generates the prime numbers by crossing off non-prime numbers from a sequential list. Though slow, the Sieve of Eratosthenes is accurate, and efficient well into the millions. Significantly less laborious than other methods, it was not particularly improved upon for at least 1,000 years.

Perhaps the work Eratosthenes is most known for, however, is his calculation of the circumference of Earth. Measuring Earth's circumference without actually circumnavigating it, Eratosthenes relied on careful mathematics: he compared the sun's angle of elevation at Alexandria on the summer solstice with its angle of elevation at the city of Syene, due south, in order to determine what fraction of the circle around Earth was traversed by that distance (about one-fiftieth, as it turned out). He then multiplied the estimated distance between the two cities accordingly, to determine that Earth's circumference was 24,662 miles (39,690 kilometers)—which is less than 1 percent off from the actual figure. Given the limitations he faced, this is remarkable. He had no way of precisely calculating the distance between the two cities, given that travel in a perfectly straight line would have been impossible because it required some riverboat travel along the nonlinear Nile. The assumptions he was forced to make about the latitude of the two cities was only slightly off. To come so close with such limitations demonstrates the rigor of his mathematics. His measurements were highly regarded for centuries, due to the intellectual beauty of his methods.

Little of Eratosthenes's work has survived, and much of what we know is from secondary sources describing or citing his work. He is credited with having estimated the distance between the sun and Earth within a reasonable margin of error, and the distance between the moon and Earth, with considerably greater error; he may have contributed the concept of a leap day. He worked on mapping the known world, and on advancing the accuracy of history as a research field by determining precise dates for various historical events. He died at the age of 82, shortly after going blind.

Human Origins , Philosophy , Science

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