Eratosthenes

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This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman).

Eratosthenes (Greek Ἐρατοσθένης; 276 BC - 194 BC) was a Greek mathematician, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known to have calculated the circumference of the Earth. He also made what he thought was a map of the Earth.

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[edit] Life

Eratosthenes was born in Cyrene (in modern-day Libya), but worked and died in Alexandria, capital of Ptolemaic Egypt. He never married. He was reputedly known for his haughty character.

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, succeeding the first librarian, Zenodotos, 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 a year later he supposedly starved himself to death.

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 trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).

[edit] Measurement of the Earth

Eratosthenes world map
Eratosthenes world map

Eratosthenes knew that on the summer solstice at local noon in the town of 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. The distance between the cities was known from caravan travellings to be about 5000 stadia: approximately 800 km, or 500 miles. 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, which implies a circumference of 46620 km, i.e. 16% too large.

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, angles could only be measured to within about a quarter of a degree, and overland distance measurements were even less reliable. So the accuracy of the result of Eratosthenes' calculation is surprising.

Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.

[edit] Other work

Eratosthenes' other contributions include:

[edit] The mysterious astronomical distances

Eusebius of Caesarea in his Praeparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of stadia myriads 400 and 80000") and the distance to the moon to be 780,000 stadia. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974-1991). The meaning depends on whether Eusebius meant 400 myriad plus 80000 or "400 and 80000" myriad.

This testimony of Eusebius is dismissed by the scholarly Dictionary of Scientific Biography. It is true that the distance Eusebius quotes for the moon is much too low (about 144,000 km) and Eratosthenes should have been able to do much better than this since he knew the size of the Earth and Aristarchos of Samos had already found the ratio of the Moon's distance to the size of the Earth. But if what Eusebius wrote was pure fiction, then it is difficult to explain the fact that, using the Greek stadium of 185 metres, the figure of 804 million stadia that he quotes for the distance to the Sun comes to 149 million kilometres. The difference between this and the modern accepted value is less than 1%.

[edit] Works

[edit] Named after Eratosthenes

[edit] See also

[edit] Further reading

  • Lasky, Kathryn. The Librarian Who Measured the Earth. New York: Little, Brown and Company, 1994. ISBN 0-316-51526-4. An illustrated biography for children focusing on the measurement of the earth. Kevin Hawkes, illustrator.
  • J J O'Connor and E F Robertson. (January 1999). "Eratosthenes of Cyrene". MacTutor. School of Mathematics and Statistics University of St Andrews Scotland.
  • E P Wolfer (1954). Eratosthenes von Kyrene als Mathematiker und Philosoph. Groningen-Djakarta. 
  • A V Dorofeeva (1988). "Eratosthenes (ca. 276-194 B.C.)" (in Russian). Mat. v Shkole (4): i. 
  • J Dutka (1993). "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55 – 66. 
  • B A El'natanov (1983). "A brief outline of the history of the development of the sieve of Eratosthenes" (in Russian). Istor.-Mat. Issled. 27: 238 – 259. 
  • D H Fowler (1983). "Eratosthenes' ratio for the obliquity of the ecliptic". Isis 74 (274): 556 – 562. 
  • B R Goldstein (1984). "Eratosthenes on the "measurement" of the earth". Historia Math. 11 (4): 411 – 416. 
  • E Gulbekian (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C". Arch. Hist. Exact Sci. 37 (4): 359 – 363. 
  • G Knaack (1907). "Eratosthenes". Pauly-Wissowa VI: 358 – 388. 
  • F Manna (1986). "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"" (in Italian). Atti Accad. Pontaniana (N.S.) 35: 37 – 44. 
  • A Muwaf and A N Philippou (1981). "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1 – 2): 174 – 147. 
  • D Rawlins (1982). "Eratosthenes' geodest unraveled : was there a high-accuracy Hellenistic astronomy". Isis 73: 259 – 265. 
  • D Rawlins (1982). "The Eratosthenes - Strabo Nile map. Is it the earliest surviving instance of spherical cartography? Did it supply the 5000 stades arc for Eratosthenes' experiment?". Arch. Hist. Exact Sci. 26 (3): 211 – 219. 
  • C M Taisbak (1984). "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus 27 (2): 165 – 167. 

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