Eratosthenes Eratosthenes was born in Cyrene (in modern-day Libya) in 276 BC. He was the chief librarian of the Great Library of Alexandria and died in the capital of Ptolemaic Egypt. He was never married. Eratosthenes studied in Alexandria and claimed to have done so for some years in Athens. In 236 BC, he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Apollonius of Rhodes, in that post. 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. In 194 BC, Eratosthenes became blind, and he supposedly starved himself to death a year later. He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt). Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene) on the Tropic of Cancer , the sun would appear at the zenith , directly overhead . He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene, he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 stadia (about 500 geographical or nautical miles ). He rounded the result to 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 frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, i.e., 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%. Although Eratosthenes' method was well founded , the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is not precisely on the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity , overland distance measurements were not reliable , especially for travel along the non-linear Nile, which was traveled primarily by boat. So the accuracy of Eratosthenes' size of the earth is surprising. Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earths size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later. [This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Eratosthenes".] |
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