Eratosthenes
Eratosthenes | |
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Born | 276 BC[note 1] |
Died | 194 BC (around age 82)[note 2] |
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Eratosthenes of Cyrene (/ɛrəˈtɒsθəniːz/; Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. His work is comparable to what is now known as the study of geography, and he introduced some of the terminology still used today.[1]
He is best known for being the first person known to calculate the
based on the available geographic knowledge of his era.Eratosthenes was the founder of scientific chronology;[5] he used Egyptian and Persian records to estimate the dates of the main events of the Trojan War, dating the sack of Troy to 1183 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and composite numbers.
He was a figure of influence in many fields who yearned to understand the complexities of the entire world.[6] His devotees nicknamed him Pentathlos after the Olympians who were well rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Yet, according to an entry[7] in the Suda (a 10th-century encyclopedia), some critics scorned him, calling him Number 2 because he always came in second in all his endeavours.[8]
Life
The son of Aglaos, Eratosthenes was born in 276 BC in
Eratosthenes went to Athens to further his studies. There he was taught
These works and his great poetic abilities led the king
Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes. Around 255 BC, he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies,[11] Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with high accuracy.[2]
Eratosthenes believed there was both good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, as well as for arguing that the Greeks should keep themselves racially pure.[12] As he aged, he contracted ophthalmia, becoming blind around 195 BC. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194 BC at the age of 82 in Alexandria.[9]
Scholarly career
Measurement of Earth's circumference
The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes,[13] who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres (509 and 525 ft)).[2] Eratosthenes described his arc measurement technique,[14] in a book entitled On the measure of the Earth, which has not been preserved. However, a simplified version of the method has been preserved, as described by Cleomedes.[15]
The simplified method works by considering two cities along the same
Geography
Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of information and representations of the world that needed to be pieced together in some organized format.
- The first book was something of an introduction and gave a review of his predecessors, recognizing their contributions that he compiled in the library. In this book Eratosthenes denounced Mediterraneanhad been a vast lake that covered the countries that surrounded it and that it only became connected to the ocean to the west when a passage opened up sometime in its history.
- The second book contains his calculation of the circumference of the Earth. This is where, according to Pliny, "The world was grasped." Here Eratosthenes described his famous story of the well in Syene, wherein at noon each summer solstice, the Sun's rays shone straight down into the city-center well.mathematical geography.
- His third book of the Geography contained political geography. He cited countries and used parallel lines to divide the map into sections, to give accurate descriptions of the realms. This was a breakthrough and can be considered the beginning of geography. For this, Eratosthenes was named the "Father of Modern Geography."[17]
According to Strabo, Eratosthenes argued against the Greek-Barbarian dichotomy. He says Alexander ignored his advisers by his regard for all people with law and government.[23] Strabo says that Eratosthenes was wrong to claim that Alexander had disregarded the counsel of his advisers. Strabo argues it was Alexander's interpretation of their "real intent" in recognizing that "in some people there prevail the law-abiding and the political instinct, and the qualities associated with education and powers of speech".[24]
Achievements
Eratosthenes was described by the
- stadia myriads400 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. With a stade of 185 m (607 ft), 804,000,000 stadia is 149,000,000 km (93,000,000 mi), approximately the distance from the Earth to the Sun.
- Eratosthenes also calculated the Sun's diameter. According to Macrobius, Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth.[17] The actual figure is approximately 109 times.[26]
- During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.[27]
- He was also very proud of his solution for Doubling the Cube. His motivation was that he wanted to produce catapults. Eratosthenes constructed a mechanical line drawing device to calculate the cube, called the mesolabio. He dedicated his solution to King Ptolemy, presenting a model in bronze with it a letter and an epigram.[28] Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his book The Method to Eratosthenes, knowing his love for learning and mathematics.[29]
Number theory
Eratosthenes proposed a simple
In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of
Works
Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at the Library. He wrote on many topics – geography, mathematics, philosophy, chronology, literary criticism, grammar, poetry, and even old comedies. There are no documents left of his work after the
Titles
- Platonikos (Lost, quoted by Theon of Smyrna)
- Hermes
- Erigone
- Chronographies
- Olympic Victors
- Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth)[30] (lost, summarized by Cleomedes)
- Гεωγραϕικά (Geographika)[25] (lost, criticized by Strabo)
- Arsinoe (a memoir of queen Arsinoe; lost; quoted by Athenaeus in the Deipnosophistae)
- Ariston (concerning Aristo of Chios' addiction to luxury); lost; quoted by Athenaeus in the Deipnosophistae)[31]
- The Hellenistic myths about the constellations.
See also
- Aristarchus of Samos (c. 310 – c. 230 BC), a Greek mathematician who calculated the distance from the Earth to the Sun.
- Eratosthenes (crater) on the Moon.
- Eratosthenian period in the lunar geologic timescale.
- Eratosthenes Seamount in the eastern Mediterranean Sea.
- Eratosthenes Point in Antarctica.
- Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth.
- Posidonius (c. 135 – c. 51 BC), a Greek astronomer and mathematician who calculated the circumference of the Earth.
Notes
- ^ 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 in 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.[32]
- Pseudo-Lucian(Makrobioi, 27) at the age of 82.
References
- ^ a b c Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.
- ^ OCLC 52945835.
- ^ "Imagine the Universe – The Earth".
- ^ "Eratosthenes (276–195 B.C.)" Archived 2021-02-24 at the Wayback Machine. Cornell University. Accessed 28 July 2019.
- ^ "Greek chronology". Britannica.
- ^ a b c d e Chambers, James T. "Eratosthenes of Cyrene." in Dictionary of World Biography: The Ancient World January 1998: 1–3.
- ^ "Entry ε 2898"
- ISBN 0330243233. This was also asserted by Carl Sagan 31 minutes into his Cosmos episode The Shores of the Cosmic Ocean
- ^ a b c Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition.
- ^ Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977.
- ^ "Aratus's "Phenomena," Cleomedes's "On the Circular Motions of the Celestial Bodies," and Nichomachus's "Introduction to Arithmetic" – Viewer – World Digital Library". www.wdl.org. Retrieved 2021-02-24.
- ISBN 0521531373)).
- OCLC 52945835.
- ISBN 978-3110250008. Retrieved 2021-05-02.
- ^ Cleomedes, Caelestia, i.7.49–52.
- ^ Martianus Capella, De nuptiis Philologiae et Mercurii, VI.598.
- ^ a b c Smith, Sir William. "Eratosthenes", in A Dictionary of Greek and Roman Biography and Mythology. Ann Arbor, Michigan: University of Michigan Library, 2005.
- ^ Morris, Terry R. "Eratosthenes of Cyrene." in Encyclopedia Of The Ancient World. November 2001.
- ^ 2011. "Eratosthenes." Hutchinson's Biography Database 1.
- ISBN 9780137504510. Retrieved 28 August 2022.
- ^ Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011.
- ^ "Eratosthenes of Cyrene". Khan Academy. Retrieved 2019-11-19.
- ^ Plutarch's similar discussion claiming that Alexander ignored Aristotle's advice in this matter may have been influenced by Eratosthenes, but Plutarch does not give us confirmation of his sources.
- ^ Isaac, Benjamin. Invention of Racism in Classical Antiquity. Princeton University Press, 2013.
- ^ a b c Dicks, D.R. "Eratosthenes", in Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 1971.
- ^ "Ask an Astronomer". Cool Cosmos. Archived from the original on 2014-07-30.
- ^ Greek Scholar's Work Shows Usefulness of Measurement." Manawatu Standard, June 19, 2012. 07, Newspaper Source Plus
- ^ Zhumud, Leonid. Plato as "Architect of Science". in Phonesis. Vol. 43 (3) 1998. 211–244.
- ^ Chondros, Thomas G. Archimedes Life Works and Machines. in Mechanism and Machine Theory. Vol. 45(11) 2010. 1766–1775.
- ^ 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, Massachusetts: Harvard University Press, 1957.
- ^ Smith, Andrew. "Athenaeus: Deipnosophists – Book 7". www.attalus.org.
- ^ Eratosthenes entry in the Dictionary of Scientific Biography (1971)
Further reading
- Aujac, G. (2001). Eratosthène de Cyrène, le pionnier de la géographie. Paris: Édition du CTHS. 224 p.
- Bulmer-Thomas, Ivor (1939–1940). Selections Illustlating the History of Greek Mathematics. Cambridge, Massachusetts: Harvard University Press.
- Dicks, D. R. (1991). "Eratosthenes". Biographical Dictionary of Mathematicians. Vol. 2 (Dickson–Khwārizmī). New York: Scribner. pp. 681–686.
- Diller, A (1934). "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". Klio. 27 (3): 258–269. S2CID 194449299.
- Dorofeeva, A. V. (1988). "Eratosthenes (ca. 276–194 B.C.)". Mat. V Shkole (in Russian) (4): i.
- Dutka, J. (1993). "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55–66. S2CID 119522892.
- El'natanov, B. A. (1983). "A brief outline of the history of the development of the sieve of Eratosthenes". Istor.-Mat. Issled. (in Russian). 27: 238–259.
- Fischer, I (1975). "Another look at Eratosthenes' and Posidonius' determinations of the Earth's circumference". Quarterly Journal of the Royal Astronomical Society. 16: 152–167. Bibcode:1975QJRAS..16..152F.
- Fowler, D. H.; Rawlins, Dennis (1983). "Eratosthenes' ratio for the obliquity of the ecliptic". Isis. 74 (274): 556–562. S2CID 144617495.
- Fraser, P. M. (1970). "Eratosthenes of Cyrene". Proceedings of the British Academy. 56: 175–207.
- Fraser, P. M. (1972). Ptolemaic Alexandria. Oxford: Clarendon Press.
- Fuentes González, P. P., "Ératosthène de Cyrène", in R. Goulet (ed.), Dictionnaire des Philosophes Antiques, vol. III, Paris, Centre National de la Recherche Scientifique, 2000, pp. 188–236.
- Geus K. (2002). Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftgeschichte. München: Verlag C.H. Beck. (Münchener Beiträge zur Papyrusforschung und antiken Rechtsgeschichte. Bd. 92) X, 412 S.
- Goldstein, B. R. (1984). "Eratosthenes on the "measurement" of the Earth". Historia Math. 11 (4): 411–416. .
- Gulbekian, E. (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C". S2CID 115314003.
- Honigmann, E. (1929). Die sieben Klimata und die πολεις επισημοι. Eine Untersuchung zur Geschichte der Geographie und Astrologie in Altertum und Mittelalter. Heidelberg: Carl Winter's Universitätsbuchhandlung. 247 S.
- Knaack, G. (1907). "Eratosthenes". Pauly–Wissowa VI: 358–388.
- Manna, F. (1986). "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"". Atti Accad. Pontaniana. New Series (in Italian). 35: 37–44.
- Muwaf, A.; Philippou, A. N. (1981). "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1–2): 147–175.
- Nicastro, Nicholas (2008). Circumference: Eratosthenes and the ancient quest to measure the globe. New York: St. Martin's Press. ISBN 978-0312372477.
- O'Connor, John J.; Robertson, Edmund F., "Eratosthenes", MacTutor History of Mathematics Archive, University of St Andrews
- Marcotte, D. (1998). "La climatologie d'Ératosthène à Poséidonios: genèse d'une science humaine". G. Argoud, J.Y. Guillaumin (eds.). Sciences exactes et sciences appliquées à Alexandrie (IIIe siècle av J.C. – Ier ap J.C.). Saint Etienne: Publications de l'Université de Saint Etienne: 263–277.
- McPhail, Cameron (2011). Reconstructing Eratosthenes' Map of the World: a Study in Source Analysis. A Thesis Submitted for the Degree of Master of Arts at the University of Otago. Dunedin, New Zealand.
- Pfeiffer, Rudolf (1968). History of Classical Scholarship From the Beginnings to the End of the Hellenistic Age. Oxford: Clarendon Press.
- Rawlins, D. (1982). "Eratosthenes' geodesy unraveled : was there a high-accuracy Hellenistic astronomy". Isis. 73 (2): 259–265. S2CID 120730515.
- Rawlins, D. (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. S2CID 118004246.
- Rawlins, D. (2008). "Eratosthenes's large Earth and tiny universe" (PDF). DIO. 14: 3–12. Bibcode:2008DIO....14....3R. Archived(PDF) from the original on 2008-10-30.
- Roller, Duane W. (2010). Eratosthenes' Geography: Fragments collected and translated, with commentary and additional material. Princeton: Princeton University Press. ISBN 978-0691142678.
- Rosokoki, A. (1995), Die Erigone des Eratosthenes. Eine kommentierte Ausgabe der Fragmente, Heidelberg: C. Winter-Verlag
- Shcheglov, D.A. (2004/2006). "Ptolemy's System of Seven Climata and Eratosthenes' Geography". Geographia Antiqua 13: 21–37.
- Shcheglov, D.A. (2006). "Eratosthenes' Parallel of Rhodes and the History of the System of Climata". Klio. 88 (2): 351–359. S2CID 190529073.
- Strabo (1917). The Geography of Strabo. Horace Leonard Jones, trans. New York: Putnam.
- Taisbak, C. M. (1984). "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus. 27 (2): 165–167. .
- Thalamas, A. (1921). La géographe d'Ératosthène. Versailles.
- Wolfer, E. P. (1954). Eratosthenes von Kyrene als Mathematiker und Philosoph. Groningen-Djakarta.
External links
- English translation of the primary source for Eratosthenes and the size of the Earth at Roger Pearse.
- Bernhardy, Gottfried: Eratosthenica Berlin, 1822 (PDF) (Latin/Greek), Reprinted Osnabruck 1968 (German)
- Eratosthenes' sieve in Javascript Archived 2001-03-01 at the Wayback Machine
- About Eratosthenes' methods, including a Java applet
- How the Greeks estimated the distances to the Moon and Sun
- Measuring the Earth with Eratosthenes' method
- List of ancient Greek mathematicians and contemporaries of Eratosthenes
- New Advent Encyclopedia article on the Library of Alexandria
- Eratosthenes' sieve in classic BASIC all-web based interactive programming environment
- International pedagogical project Archived 2019-04-14 at the Wayback Machine : project fr:La main à la pâte.
- Open source Physics Computer Model about Eratosthenes estimation of radius and circumference of Earth Archived 2020-01-05 at the Wayback Machine
- Eratosthenes, video
- Eratosthenes, Katasterismoi (or Astrothesiae), original text