The Full Wiki

Eratosthenes: Wikis

Advertisements
  
  
  

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

Encyclopedia

From Wikipedia, the free encyclopedia

Eratosthenes
(Ἐρατοσθένης)
Portrait of Eratosthenes
Portrait of Eratosthenes
Born 276 BC
Cyrene
Died 195 BC
Capital of Ptolemaic Egypt
Occupation Epic poet, librarian, scholar, inventor

Eratosthenes of Cyrene (Greek Ἐρατοσθένης; c. 276 BC[1] – c. 195 BC[2]) was a Greek mathematician, elegiac poet, athlete, geographer, and astronomer. He was the first person to use the word "geography" and invented the discipline of geography as we understand it.[3] 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 by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy), and the tilt of the Earth's axis (also with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day.[4] He also created a map of the world based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

According to the entry on him in the Suda (ε 2898), his contemporaries nicknamed him beta, from the second letter of the Greek alphabet, because he supposedly proved himself to be the second best in the world in almost any field.[5]

Contents

Life

19th century reconstruction of Eratosthenes' map of the known world, c.194 BC.

Eratosthenes was born in Cyrene (in modern-day Libya). He was the third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient world, and died in the capital of Ptolemaic Egypt. He was never married.[citation needed]

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 second librarian, Apollonius of Rhodes, in that post.[6] He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him 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).[citation needed]

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 Eratosthenes criticised Aristotle for his blind chauvinism; he believed there was good and bad in every nation.[7] By 194 B.C, Eratosthenes became blind. By 195 B.C, Eratosthenes ultimately fell into a state of depression, that he commited suicide by starving himself to death, at the age of 81.

Eratosthenes' measurement of the earth's circumference

Measurements taken at Alexandria (A) and Syene (S)

Eratosthenes measured the circumference of the earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) 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 800 km) by estimating the time that he had taken to travel from Syene to Alexandria by camel. 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 stadium 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 stadium"[8] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.[9]

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[citation needed]. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable[citation needed], especially for travel along the non-linear Nile which was traveled primarily by boat. Given the margin of error for each of these aspects of his calculation, 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.[citation needed]

Other 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[citation needed] 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 meters, 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%.[10] Scribal errors in copying the numbers, either of Eusebius' text or of the text that Eusebius read, are probably responsible.[citation needed]

The smaller of the foregoing two readings of Eusebius (4,080,000 stadia) turns out to be exactly 100 times the terrestrial radius (40,800 stadia) implicit in Eratosthenes' Nile map and given in the 1982 paper by Rawlins (p. 212) that analysed this map (see Further Reading). Greek scholars such as Archimedes and Posidonius normally expressed the sun's distance in powers of ten times the Earth's radius. The Nile map – Eusebius consistency is developed in a 2008 Rawlins paper. The data would make Eratosthenes' universe the smallest known from the Hellenistic era's height, and made the sun smaller than the earth. His indefensible lunar distance would require the moon to go retrograde among the stars every day for observers in tropical or Mediterranean latitudes, and would predict that half moons occur roughly 10° from quadrature.

The Eusebius-confirmed 1982 paper's empirical Eratosthenes circumference (256,000 stadia instead of 250,000 or 252,000 as previously thought) is 19% too high. But the 2008 paper notes that the theory that atmospheric refraction exaggerated his measurement (a theory originally proposed in the 1982 paper, applied to either mountaintop dip or lighthouse visibility) is thus bolstered as the explanation of Eratosthenes' error. This is because accurately measuring the visibility distance of the Alexandria lighthouse (then world's tallest, built at Eratosthenes' location and during his time) and computing the Earth's size from that should have given a result 20% high from refraction, very close to his actual 19% error. The 2008 paper wonders if the 40,800 stadia estimate originated with Sostratus of Cnidus (who designed the lighthouse), and offers a reconstructive speculation that the lighthouse was about 93 meters high, which is much below previous suppositions.

Prime numbers

Eratosthenes also proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes.

Works

Named after Eratosthenes

See also

Notes

  1. ^ The Suda states that he was born in the 126th Olympiad, (276–272 BC). Strabo (Geography, i.2.2), though, states that he was a "pupil" (γνωριμος) of Zeno of Citium (who died 262 BC), which would imply an earlier year-of-birth (c. 285 BC) since he is unlikely to have studied under him at the young age of 14. However, γνωριμος can also mean "acquaintance," and the year of Zeno's death is by no means definite. Cf. Eratosthenes entry in the Dictionary of Scientific Biography (1971)
  2. ^ The Suda states he died at the age of 80, Censorinus (De die natali, 15) at the age of 81, and Pseudo-Lucian (Makrobioi, 27) at the age of 82.
  3. ^ [Eratosthenes' Geography - Fragments collected and translated, with commentary and additional material, by Duane W. Roller, Princeton UP, Princeton (2010)
  4. ^ Alfred, Randy (June 19, 2008). "June 19, 240 B.C.: The Earth Is Round, and It's This Big". Wired. http://www.wired.com/science/discoveries/news/2008/06/dayintech_0619. 
  5. ^ See also Asimov, Isaac. Asimov's Biographical Encyclopedia of Science and Technology, new revised edition. 1975. Entry #42, "Eratosthenes", Page 29. Pan Books Ltd, London. ISBN 0 330 24323 3. It was also asserted by Carl Sagan, 31 minutes into his Cosmos episode The Shores of the Cosmic Ocean [1]
  6. ^ Oxford Reference (subscription required)
  7. ^ * p439 Vol. 1 William Woodthorpe Tarn Alexander the Great. Vol. I, Narrative; Vol. II, Sources and Studies0. Cambridge: Cambridge University Press, 1948. (New ed., 2002 (paperback, ISBN 0-521-53137-3)).
  8. ^ Isaac Moreno Gallo (3–6 November 2004) (PDF), Roman Surveying, translated by Brian R. Bishop, archived from the original on 2007-02-05, http://web.archive.org/web/20070205033538/http://traianus.rediris.es/topo01/surveying.pdf 
  9. ^ There is a huge Eratosthenes-got-it-right literature based upon attacking the applicability of the standard 185m stadium to his experiment. Among advocates: F. Hultsch, Griechische und Römische Metrologie, Berlin, 1882; E. Lehmann-Haupt, Stadion entry in Paulys Real-Encyclopädie, Stuttgart, 1929; I. Fischer, Q. Jl. R. astr. Soc. 16.2:152–167, 1975; Gulbekian (1987); Dutka (1993). The means employed include worrying various ratios of the stadium to the unstably defined "schoenus", or using a truncated passage from Pliny. (Gulbekian just computes the stadium from Eratosthenes' experiment instead of the reverse.) A disproportionality of literature exists because professional scholars of ancient science have generally retarded such speculation as special pleading and so have not bothered to write extensively on the issue. Skeptical works include E. Bunbury's classic History of Ancient Geography, 1883; D. Dicks, Geographical Fragments of Hipparchus, University of London, 1960; O. Neugebauer, History of Ancient Mathematical Astronomy, Springer, 1975; J. Berggren and A. Jones, Ptolemy's Geography, Princeton, 2000. Some difficulties with the several arguments for Eratosthenes' exact correctness are discussed by Rawlins in 1982b page 218 and in his Contributions and Distillate. See also, at [2], "The Shores of the Cosmic Ocean", chapter 1 of Cosmos: A Personal Voyage, a TV series by Carl Sagan, Ann Druyan and Steven Sotter (1978–1979), where a description of Eratosthenes' experiment is presented.
  10. ^ Other than the distance to the moon, no celestial distance is unambiguously established as known in antiquity even to within a factor of two. As late as a century ago, the earth's distance from the sun (the A. U.) was known less accurately than 16%.[citation needed]
  11. ^ Mentioned by Hero of Alexandria in his Dioptra. See p. 272, vol. 2, Selections Illustrating the History of Greek Mathematics, tr. Ivor Thomas, London: William Heinemann Ltd.; Cambridge, MA: Harvard University Press, 1957.

Further reading

  • Eratosthenes' Geography - Fragments collected and translated, with commentary and additional material, by Duane W. Roller, Princeton UP, Princeton (2010).
  • Nicastro, Nicholas. Circumference: Eratosthenes and the ancient quest to measure the globe. New York: St. Martin's Press, 2008.
  • 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.
  • J J O'Connor and E F Robertson (January 1999). "Eratosthenes of Cyrene". MacTutor. School of Mathematics and Statistics University of St Andrews Scotland. http://www-history.mcs.st-andrews.ac.uk/Biographies/Eratosthenes.html. 
  • 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. doi:10.1007/BF00387726. 
  • 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. doi:10.1086/353361. 
  • B R Goldstein (1984). "Eratosthenes on the "measurement" of the earth". Historia Math. 11 (4): 411–416. doi:10.1016/0315-0860(84)90025-9. 
  • 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' geodesy unraveled : was there a high-accuracy Hellenistic astronomy". Isis 73: 259–265. doi:10.1086/352973. 
  • 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. 
  • D Rawlins (2008). "Eratothenes's large earth and tiny universe" (PDF). DIO 14: 3–12. http://www.dioi.org/vols/we0.pdf. 
  • C M Taisbak (1984). "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus 27 (2): 165–167. doi:10.1111/j.1600-0498.1984.tb00766.x. 

External links

Preceded by
Apollonius of Rhodes
Head of the Library of Alexandria Succeeded by
Aristophanes of Byzantium

Advertisements

Simple English

Eratosthenes of Cyrene 276BC–194BC) was a third century BC Greek mathematician, geographer and astronomer. He was head of the Library of Alexandria from 240BC until his death: this was the most important library of the ancient world.

According to the Suda,[1] his contemporaries nicknamed him Beta, (the second letter of the Greek alphabet), because he was the second best in the world in almost any field.[2] Eratosthenes was a friend of Archimedes, who also lived and worked in Alexandria. Archimedes was the greatest mathematician and inventor of the age, so perhaps the Beta nickname was not unjust.

The works Eratosthenes wrote are known to us only indirectly: the great Library was destroyed, and no copies survived. Strabo (~63BC–24AD) wrote about geography in antiquity. He tells us that the works of Eratosthenes were On the measurement of the Earth and Geographica.

Eratosthenes made several remarkable discoveries and inventions. He was the first person to calculate the circumference of the Earth (with remarkable accuracy), and he invented a system of latitude and longitude. He calculated 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.[3] He created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he wanted to fix the dates of the chief literary and political events from the conquest of Troy.

Contents

Measuring the Earth's circumference

[[File:|left|thumb|250px|Measurements taken at Alexandria (A) and Syene (S)]] Eratosthenes measured the circumference of the earth without leaving Egypt. He knew that on the summer solstice at local noon at the city now called Aswan on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in 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 800km) by estimating the time that he had taken to travel from Syene to Alexandria by camel. 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 stadium was about 185 m, which would imply a circumference of 46,620 km, which is 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadium" of about 157.5 m, his measurement turns out to be 39,375 km, an error of less than 1%.[4] The method is an early application of trigonometry in the measurement science of geodesy.

Other discoveries and inventions

The sieve of Eratosthenes

In mathematics, the Sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους) is a simple, ancient algorithm for finding all prime numbers up to a specified integer.[5] It works efficiently for the smaller primes (below 10 million).[6] The sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus.[7]

Other

Eratosthenes went further and computed the tilt of the Earth's axis to within a degree. This is the tilt which is the main cause of the annual climate cycle of spring, summer, autumn, winter. He also deduced the length of the year as 365¼ days. He suggested that calendars should have a leap day every fourth year, an idea taken up two centuries later by Julius Caesar.[3]

References

  1. The massive 10th century Byzantine encyclopedia of the ancient Mediterranean world
  2. Asimov, Isaac. 1975. Asimov's Biographical Encyclopedia of science and technology, Entry #42, "Eratosthenes", p. 29. Pan Books, London. ISBN 0-330-24323-3.
  3. 3.0 3.1 'Wired' 2008.[1]
  4. Isaac Moreno Gallo (2004) (PDF), Roman Surveying, translated by Brian R. Bishop, archived from the original on 2007-02-05, http://web.archive.org/web/20070205033538/http://traianus.rediris.es/topo01/surveying.pdf 
  5. Horsley, Rev. Samuel, F. R. S., "Κόσκινον Ερατοσθένους or, The Sieve of Eratosthenes. Being an Account of His Method of Finding All the Prime Numbers," Philosophical Transactions (1683-1775), Vol. 62. (1772), pp. 327-347.
  6. The Prime Glossary: "The Sieve of Eratosthenes", http://primes.utm.edu/glossary/page.php?sort=SieveOfEratosthenes, references 16. November 2008.
  7. Nicomachus Introduction to arithmetic, I, 13. [2]



Advertisements






Got something to say? Make a comment.
Your name
Your email address
Message