Eratosthenes

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 Evergetes 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 believed the Earth was a sphere and circa 240 BC he calculated its diameter, using trigonometry and information on the angle of the Sun at noon in Alexandria and Syene[?] (now Aswan, Egypt), whose distance from each other was known from caravan travellings to be 5,000 stadia. 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 at local noon, on the summer solstice, 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 7º south of the zenith. He knew that this angle was about 2 % of a full circle and thus concluded that the distance from Alexandria to Syene must be 2 % of the total circumference of Earth. His final value value was 250,000 stadia. The exact size of a stadium has been lost but it is generally believed that Eratosthenes reached an answer between 39,690 km and 45,007 km. The correct answer is 40,075 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.

Eartosthenes' 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 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 and Strabo were able to make better maps than this.

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

See also: Historical weights and measures.

External Links

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