Eratosthenes

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Eratosthenes
An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding.
Etching of an ancient seal identified as Eratosthenes. Philipp Daniel Lippert [de], Dactyliothec, 1767.
Born276 BC[note 1]
Cyrene (in modern Libya)
Died194 BC (around age 82)[note 2]
Occupations
  • Scholar
  • Librarian
  • Poet
  • Inventor
Known for

Eratosthenes of Cyrene (/ɛrəˈtɒsθənz/; 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

first global projection of the world, incorporating parallels and meridians
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

silphium, a plant used for rich seasoning and medicine.[1] Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium, where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music.[9]

Eratosthenes teaching in Alexandria by Bernardo Strozzi (1635)

Eratosthenes went to Athens to further his studies. There he was taught

Egyptian Thebes. Eratosthenes also wrote Olympic Victors, a chronology of the winners of the Olympic Games
. It is not known when he wrote his works, but they highlighted his abilities.

These works and his great poetic abilities led the king

Apollonius Rhodius had previously held. As head of the library Eratosthenes tutored the children of Ptolemy, including Ptolemy IV Philopator
who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication. It was said that these were copied so accurately that it was impossible to tell if the library had returned the original or the copy. He sought to maintain the reputation of the Library of Alexandria against competition from the Library of Pergamum. Eratosthenes created a whole section devoted to the examination of Homer, and acquired original works of great tragic dramas of Aeschylus, Sophocles and Euripides.[6]

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

Syene is on the Tropic of Cancer and on the same meridian as Alexandria

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

Syene (modern Aswan), and the distance between the cities was measured by professional bematists.[16] A geometric calculation reveals that the circumference of the Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of one turn
.

Geography

Eratosthenes' map of the (for the Greeks) known world
, c. 194 BC

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.

Marcianus
. While this work is the earliest we can trace certain ideas, words, and concepts in the historical record, earlier contributions may have been lost to history.

  • 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
    Mediterranean
    had 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

Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated as "All-Rounder", for he was skilled in a variety of things: He was a true polymath. He was nicknamed "Number 2" because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.[25]

Number theory

Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from the prime's square).

Eratosthenes proposed a simple

prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes
.

In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of

prime number sieves
, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite, i.e., not prime, the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.

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

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 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]
  2. Pseudo-Lucian
    (Makrobioi, 27) at the age of 82.

References

  1. ^ a b c Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.
  2. ^
    OCLC 52945835
    .
  3. ^ "Imagine the Universe – The Earth".
  4. ^ "Eratosthenes (276–195 B.C.)" Archived 2021-02-24 at the Wayback Machine. Cornell University. Accessed 28 July 2019.
  5. ^ "Greek chronology". Britannica.
  6. ^ a b c d e Chambers, James T. "Eratosthenes of Cyrene." in Dictionary of World Biography: The Ancient World January 1998: 1–3.
  7. ^ "Entry ε 2898"
  8. . This was also asserted by Carl Sagan 31 minutes into his Cosmos episode The Shores of the Cosmic Ocean
  9. ^ a b c Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition.
  10. ^ Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977.
  11. ^ "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.
  12. )).
  13. .
  14. . Retrieved 2021-05-02.
  15. ^ Cleomedes, Caelestia, i.7.49–52.
  16. ^ Martianus Capella, De nuptiis Philologiae et Mercurii, VI.598.
  17. ^ 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.
  18. ^ Morris, Terry R. "Eratosthenes of Cyrene." in Encyclopedia Of The Ancient World. November 2001.
  19. ^ 2011. "Eratosthenes." Hutchinson's Biography Database 1.
  20. . Retrieved 28 August 2022.
  21. ^ Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011.
  22. ^ "Eratosthenes of Cyrene". Khan Academy. Retrieved 2019-11-19.
  23. ^ 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.
  24. ^ Isaac, Benjamin. Invention of Racism in Classical Antiquity. Princeton University Press, 2013.
  25. ^ a b c Dicks, D.R. "Eratosthenes", in Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 1971.
  26. ^ "Ask an Astronomer". Cool Cosmos. Archived from the original on 2014-07-30.
  27. ^ Greek Scholar's Work Shows Usefulness of Measurement." Manawatu Standard, June 19, 2012. 07, Newspaper Source Plus
  28. ^ Zhumud, Leonid. Plato as "Architect of Science". in Phonesis. Vol. 43 (3) 1998. 211–244.
  29. ^ Chondros, Thomas G. Archimedes Life Works and Machines. in Mechanism and Machine Theory. Vol. 45(11) 2010. 1766–1775.
  30. ^ 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.
  31. ^ Smith, Andrew. "Athenaeus: Deipnosophists – Book 7". www.attalus.org.
  32. ^ Eratosthenes entry in the Dictionary of Scientific Biography (1971)


Further reading

External links

Preceded by Head of the Library of Alexandria Succeeded by