Eratosthenes (Ερατοσθένης)

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

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

Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere, which was widely used until the invention of the orrery in the 18th century.

He calculated the earth's circumference circa 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt). The calculation is based on the assumption that the Earth is spherical and 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 on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead- though Syene was in fact slightly north of the tropic. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7° south of the zenith at the same time. Assuming that Alexandria was due north of Syene- Alexandria is in fact on a more westerly longitude- he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth. The 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 circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes' method was used by Posidonius about 150 years later.

Circa 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study 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 more accurate maps in the classical and post classical world.

Eratosthenes was known under the name β, because he supposedly proved himself to be the second in the world in many fields. He was also reputedly known for his haughty character. In 195 BC he became blind and a year later he starved himself to death.

Named after Eratosthenes

• Eratosthenes crater on the Moon.
• Eratosthenian period in the lunar geologic timescale.

See also

• Ancient weights and measures.

External links

• U. of St. Andrews: Eratosthenes (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html)
• Measuring the Earth (http://www.algonet.se/~sirius/eaae/aol/market/collabor/erathost)