sieve eratosthenes



Eratosthenes of Cyrene (Greek Ἐρατοσθένης; 276 BC - 194 BC) was a Greek mathematician, poet, athlete, geographer and astronomer. He made several discoveries and inventions including a system of latitude and longitude. He was the first person to calculate the circumference of the Earth (with remarkable accuracy), and the tilt of the earth's axis (again with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

His contemporaries nicknamed him "beta" (the Greek numeral "two") because he supposedly proved himself to be the second best in many fields.


Eratosthenes was born in Cyrene (in modern-day Libya). 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 also studied 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, according to legends, a year later, he 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 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 was the director of the great library of Alexandria, the Centre of science and learning in the ancient world. Aristotle had argued that humanity was divided into Greeks and everyone else whom he called barbarians and that the Greeks should keep themselves racially pure. He thought it was fitting for the Greeks to enslave other peoples. But Erathosthenes criticised Aristotle for his blind chauvinism, he believed there was good and bad in every nation.

Eratosthenes' measurement of the Earth's circumference

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 miles or 950 km). 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 slightly north of 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 Earth’s size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.

The mysterious astronomical distances

Eusebius of Caesarea in his Preparatio 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 80,000") 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 80,000 or "400 and 80,000" 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 Aristarchus 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, or Olympic, 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%.


Named after Eratosthenes

See also

Further reading

  • Kathryn Lasky. 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.
  • Eratosthenes of Cyrene. In MacTutor School of Mathematics and Statistics University of St Andrews Scotland. .
  • E P Wolfer Eratosthenes von Kyrene als Mathematiker und Philosoph. Groningen-Djakarta.
  • A V Dorofeeva "Eratosthenes (ca. 276-194 B.C.)". Mat. v Shkole (4): i.
  • J Dutka "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55–66.
  • B A El'natanov "A brief outline of the history of the development of the sieve of Eratosthenes". Istor.-Mat. Issled. 27 238–259.
  • D H Fowler "Eratosthenes' ratio for the obliquity of the ecliptic". Isis 74 (274): 556–562.
  • B R Goldstein "Eratosthenes on the "measurement" of the earth". Historia Math. 11 (4): 411–416.
  • E Gulbekian "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 "Eratosthenes". Pauly-Wissowa VI 358–388.
  • F Manna "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"". Atti Accad. Pontaniana (N.S.) 35 37–44.
  • A Muwaf and A N Philippou "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1–2): 174–147.
  • D Rawlins "Eratosthenes' geodesy unraveled : was there a high-accuracy Hellenistic astronomy". Isis 73 259–265.
  • D Rawlins "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 "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus 27 (2): 165–167.
  • Pamias, Jordi, and Klaus Geus (trans., comm.), Eratosthenes. Sternsagen (Catasterismi). Griechisch / Deutsch. Bibliotheca Classicorum, 2. Oberhaid: Utopica, 2007. Pp. 258. EUR 29.95. ISBN 978-3-938083-05-5.


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