# Eratosthenes

*The crater Eratosthenes on the Moon gives its name to the Lunar Eratosthenian period*

Ερατοσθένης

**Eratosthenes**(276 BC - 194 BC) was a Greek mathematician, geographer and astronomer with (probably) Chaldean origins.

He was born in Cyrene (now Shahhat, Libya) and he died in Ptolemaic Alexandria. He is noted for devising a system of latitude and longitude and computing the size of Earth.

Eratosthenes studied at Alexandria and some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as a head and the third librarian of the Alexandrian library. He made several important contributions to mathematics and science. He was a good friend to Archimedes. Circa 255 BC he invented the armillary sphere, which was used till 17th century.

He calculated the earth's circumference circa 240 BC, using trigonometry and information on the altitude of the Sun at noon in Alexandria and Syene (now Aswan, Egypt). The calculation is based on the assumption that the Sun is so far away that its rays can be taken as parallel.

Eratosthenes knew that on the summer solstice at local noon in Syene, the Sun would appear at the zenith. He also knew that in his hometown of Alexandria, the position of the Sun would be 7° south of the zenith at that time. He knew that this angle was 7/360 of a full circle and thus concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of Earth. The actual distance between the cities was known from caravan travellings to be about 5,000 stadia. He established a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the *stadion* he used is no longer known (the common Attic *stadion* was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The actual circumference of the Earth around the poles is 40,008 km. Eratosthenes' method was used by Posidonius about 150 years later.

Circa 200 BC Eratosthenes adopted a word *geography*, which means a description of the Earth.

Eratosthenes' other contributions include:

- The Sieve of Eratosthenes as a way of finding prime numbers.
- The measurement of the Sun-Earth distance, now called the astronomical unit (804,000,000 stadia).
- The measurement of the distance to the Moon (780,000 stadia).
- The measurement of the inclination of the ecliptic with an angle error 7'.
- He compiled a star catalogue containing 675 stars, which was not preserved.
- A map of the Nile's route to Khartoum.
- A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia. Only Hipparchus, Strabo, and Ptolemy were able to make better maps than this.

**See also:** Historical weights and measures.

## External Links

- University of St Andrews' page: http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html
- Astronomy On-Line group about the terrestrial shape measurements: http://www.algonet.se/~sirius/eaae/aol/market/collabor/erathost/