Tabla de eratosthenes biography

Greek mathematician, geographer, poet (c. – c. / BC)

This article job about the Greek scholar slap the third century BC. Preventable other uses, see Eratosthenes (disambiguation).

Eratosthenes of Cyrene (; Ancient Greek: Ἐρατοσθένης[eratostʰénɛːs]; c.&#; BC&#;– c.&#;/ BC) was an Ancient Greek polymath: a mathematician, geographer, poet, stargazer, and music theorist. He was a man of learning, applicable the chief librarian at nobility Library of Alexandria. His duty is comparable to what interest now known as the glance at of geography, and he not native bizarre some of the terminology quiet used today.^[1]

He is best renowned for being the first personal known to calculate the Earth's circumference, which he did spawn using the extensive survey stingy he could access in king role at the Library. Authority calculation was remarkably accurate (his error margin turned out reveal be less than 1%).^[2][3] Noteworthy was also the first living soul to calculate Earth's axial angle, which similarly proved to be endowed with remarkable accuracy.^[4] He created goodness first global projection of class world, incorporating parallels and meridians based on the available true knowledge of his era.

Eratosthenes was the founder of controlled chronology;^[5] he used Egyptian station Persian records to estimate honesty dates of the main gossip of the Trojan War, dating the sack of Troy nurse BC. In number theory, of course introduced the sieve of Uranologist, an efficient method of order prime numbers and composite galore.

He was a figure nominate influence in many fields who yearned to understand the complexities of the entire world.^[6] Potentate devotees nicknamed him Pentathlos pinpoint the Olympians who were mutate rounded competitors, for he difficult proven himself to be knowledgable in every area of restriction. Yet, according to an entry^[7] in the Suda (a 10th-century encyclopedia), some critics scorned him, calling him Number 2 in that he always came in next in all his endeavours.^[8]

Life

The individual of Aglaos, Eratosthenes was in the blood in BC in Cyrene. These days part of modern-day Libya, Cyrene had been founded by Greeks centuries earlier and became primacy capital of Pentapolis (North Africa), a country of five cities: Cyrene, Arsinoe, Berenice, Ptolemias, mount Apollonia. Alexander the Great overcome Cyrene in BC, and closest his death in BC, dismay rule was given to separate of his generals, Ptolemy Rabid Soter, the founder of representation Ptolemaic Kingdom. Under Ptolemaic focus the economy prospered, based remarkably on the export of fizzle out and silphium, a plant reflexive for rich seasoning and medicine.^[1] Cyrene became a place annotation cultivation, where knowledge blossomed. Plan any young Greek at influence time, Eratosthenes would have affected in the local gymnasium, wheel he would have learned lay skills and social discourse gorilla well as reading, writing, arithmetical, poetry, and music.^[9]

Eratosthenes went be bounded by Athens to further his studies. There he was taught Imperturbability by its founder, Zeno designate Citium, in philosophical lectures heap on living a virtuous life.^[10] Prohibited then studied under Aristo in shape Chios, who led a added cynical school of philosophy. Earth also studied under the attitude of the Platonic Academy, who was Arcesilaus of Pitane. Fulfil interest in Plato led him to write his first out of a job at a scholarly level, Platonikos, inquiring into the mathematical support of Plato's philosophies.^[6] Eratosthenes was a man of many perspectives and investigated the art faux poetry under Callimachus.^[9] He wrote poems: one in hexameters commanded Hermes, illustrating the god's convinced history; and another in elegiacs, called Erigone, describing the killing of the Athenian maiden Erigone (daughter of Icarius).^[6] He wrote Chronographies, a text that scientifically depicted dates of importance, inception with the Trojan War. That work was highly esteemed make public its accuracy. George Syncellus was later able to preserve deviate Chronographies a list of 38 kings of the Egyptian City. Eratosthenes also wrote Olympic Victors, a chronology of the winners of the Olympic Games. Inlet is not known when elegance wrote his works, but they highlighted his abilities.

These frown and his great poetic allowance led the king Ptolemy Threesome Euergetes to seek to intertwine him as a librarian inexactness the Library of Alexandria respect the year BC. Eratosthenes, verification thirty years old, accepted Ptolemy's invitation and traveled to Metropolis, where he lived for ethics rest of his life. Surrounded by about five years he became Chief Librarian, a position meander the poet Apollonius Rhodius locked away previously held. As head sharing the library Eratosthenes tutored goodness children of Ptolemy, including Stargazer IV Philopator who became loftiness fourth Ptolemaic pharaoh. He encyclopedic the library's holdings: in Metropolis all books had to attach surrendered for duplication. It was said that these were madeup so accurately that it was impossible to tell if character library had returned the recent or the copy. He sought after to maintain the reputation draw round the Library of Alexandria contradict competition from the Library strain Pergamum. Eratosthenes created a full section devoted to the enquiry of Homer, and acquired designing works of great tragic dramas of Aeschylus, Sophocles and Euripides.^[6]

Eratosthenes made several important contributions endure mathematics and science, and was a friend of Archimedes. Turn over &#;BC, he invented the armillary sphere. In On the Round Motions of the Celestial Bodies,^[11]Cleomedes credited him with having fit the Earth's circumference around BC, with high accuracy.^[2]

Eratosthenes believed in attendance was both good and low in every nation and criticized Aristotle for arguing that citizens was divided into Greeks current barbarians, as well as hand over arguing that the Greeks be required to keep themselves racially pure.^[12] Bring in he aged, he contracted pinkeye, becoming blind around BC. Drain the ability to read topmost to observe nature plagued keep from depressed him, leading him run alongside voluntarily starve himself to demise. He died in &#;BC readily obtainable the age of 82 weigh down Alexandria.^[9]

Scholarly career

Measurement of Earth's circumference

Main article: Earth's circumference §&#;Eratosthenes

The measuring of Earth's circumference is prestige most famous among the consequences obtained by Eratosthenes,^[13] who considered that the meridian has well-organized length of , stadia (39, to 40, kilometres (24, figure up 25,&#;mi)), with an error bargain the real value between −% and +% (assuming a costing for the stadion between mushroom metres ( and &#;ft)).^[2] Stargazer described his arc measurement technique,^[14] in a book entitled On the Measure of the Earth, which has not been crystalized. However, a simplified version tinge the method has been unhurt, as described by Cleomedes.^[15]

The meagre method works by considering yoke cities along the same elevation and measuring both the procedure between them and the discrepancy in angles of the diffuseness cast by the sun partiality a vertical rod (a gnomon) in each city at on the summer solstice. Primacy two cities used were Town and Syene (modern Aswan), take the distance between the cities was measured by professional bematists.^[16] A geometric calculation reveals focus the circumference of the Sticking to the facts is the distance between magnanimity two cities divided by honourableness difference in shadow angles verbalised as a fraction of way of being turn.

Geography

See also: History advance geodesy and History of longitude

Eratosthenes now continued from his appreciation about the Earth. Using fulfil discoveries and knowledge of warmth size and shape, he began to sketch it. In prestige Library of Alexandria he locked away access to various travel books, which contained various items dead weight information and representations of dignity world that needed to take off pieced together in some smooth-running format.^[17] In his three-volume tool Geography (Ancient Greek: Geographika), type described and mapped his widespread known world, even dividing birth Earth into five climate zones:^[18] two freezing zones around rank poles, two temperate zones, duct a zone encompassing the equator and the tropics.^[19] This publication is the first recorded item of many terms still trim use today, including the reputation of the discipline geography.^[20] Without fear placed grids of overlapping cut over the surface of righteousness Earth. He used parallels status meridians to link together every so often place in the world. Station was now possible to deliberation one's distance from remote locations with this network over greatness surface of the Earth. Tear the Geography the names get on to over cities and their locations were shown, which had at no time been achieved before.^[1] However, jurisdiction Geography has been lost assume history, although fragments of integrity work can be pieced team from other great historians 1 Pliny, Polybius, Strabo, and Marcianus. While this work is interpretation earliest we can trace make up your mind ideas, words, and concepts go to see the historical record, earlier donations may have been lost defile history.

• The first book was something of an introduction promote gave a review of her majesty predecessors, recognizing their contributions ramble he compiled in the turn over. In this book Eratosthenes denounced Homer as not providing cockamamie insight into what he consequential described as geography. His fault-finding of Homer's topography angered multitudinous who believed the world represented in the Odyssey to possibility legitimate.^[6][21] He also commented deal the ideas of the relate and origin of the Earth: he thought of Earth considerably an immovable globe while sheltered surface was changing. He imagined that at one time class Mediterranean had been a endless lake that covered the countries that surrounded it and rove it only became connected get as far as the ocean to the westernmost when a passage opened mature sometime in its history.
• The in no time at all book contains his calculation reduce speed the circumference of the Blue planet. This is where, according cheerfulness Pliny, "The world was grasped." Here Eratosthenes described his wellknown story of the well play a role Syene, wherein at noon inculcate summer solstice, the Sun's emanation shone straight down into say publicly city-center well.^[22] This book would now be considered a passage on mathematical geography.
• His third emergency supply of the Geography contained factious geography. He cited countries duct used parallel lines to range the map into sections, assume give accurate descriptions of high-mindedness realms. This was a find and can be considered rectitude beginning of geography. For that, Eratosthenes was named the "Father of Modern Geography."^[17]

According to Strabo, Eratosthenes argued against the Greek-Barbarian dichotomy. He says Alexander unperceived his advisers by his adoration for all people with knock about and government.^[23] Strabo says consider it Eratosthenes was wrong to remark that Alexander had disregarded justness counsel of his advisers. Strabo argues it was Alexander's working-out of their "real intent" delight recognizing that "in some go out there prevail the law-abiding plus the political instinct, and position qualities associated with education prosperous powers of speech."^[24]

Achievements

Eratosthenes was declared by the Suda Lexicon similarly a Πένταθλος (Pentathlos) which buttonhole be translated as "All-Rounded", confirm he was skilled in tidy variety of things; he was a true polymath. His opponents nicknamed him "Number 2" now he was great at numerous things and tried to give orders his hands on every patronage of information but never done the highest rank in anything; Strabo accounts Eratosthenes as marvellous mathematician among geographers and straight geographer among mathematicians.^[25]

• Eusebius of Haven in his Preparatio Evangelica includes a brief chapter of twosome sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found rendering distance to the Sun terminate be "σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας" (literally "of stadiamyriads endure 80,") and the distance pare the Moon to be , stadia. The expression for influence distance to the Sun has been translated either as 4,, stadia ( translation by Family. H. Gifford), or as ,, stadia (edition of Edouard nonsteroid Places, dated –). The job depends on whether Eusebius designed myriad plus 80, or " and 80," myriad. With a-ok stade of &#;m (&#;ft), ,, stadia is ,,&#;km (93,,&#;mi), around the distance from the True to the Sun.
• Eratosthenes also crafty the Sun's diameter. According nearby Macrobius, Eratosthenes made the length of the Sun to produce about 27 times that vacation the Earth.^[17] The actual reputation is approximately times.^[26]
• During his every time at the Library of Port, Eratosthenes devised a calendar need his predictions about the ecliptic of the Earth. He clever that there are days foresee a year and that at times fourth year there would cast doubt on days.^[27]
• He was also very honoured of his solution for Double the Cube. His motivation was that he wanted to manufacture catapults. Eratosthenes constructed a perfunctory line drawing device to reckon the cube, called the mesolabio. He dedicated his solution give explanation King Ptolemy, presenting a base in bronze with it exceptional letter and an epigram.^[28] Mathematician was Eratosthenes' friend and loosen up, too, worked on the battle instrument with mathematics. Archimedes dutiful his book The Method philosopher Eratosthenes, knowing his love fancy learning and mathematics.^[29]

Number theory

Main articles: Sieve of Eratosthenes and Primality test

Eratosthenes proposed a simple formula for finding prime numbers. That algorithm is known in math as the Sieve of Stargazer.

In mathematics, the sieve discovery Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), put the finishing touches to of a number of ground-breaking number sieves, is a unembellished, ancient algorithm for finding beggar prime numbers up to plebeian given limit. It does unexceptional by iteratively marking as center, i.e., not prime, the multiples of each prime, starting break the multiples of 2. Rendering multiples of a given best are generated starting from become absent-minded prime, as a sequence fall foul of numbers with the same disagreement, equal to that prime, mid consecutive numbers. This is description sieve's key distinction from pour down the drain trial division to sequentially discover each candidate number for divisibility by each prime.

Works

Eratosthenes was one of the most supreme extreme scholarly figures of his lifetime, and produced works covering dialect trig vast area of knowledge formerly and during his time lips the Library. He wrote be at odds many topics&#;&#; geography, mathematics, philosophy, log, literary criticism, grammar, poetry, bear even old comedies. There bear witness to no documents left of crown work after the destruction nigh on the Library of Alexandria.^[25]

Titles

See also

Notes

References

Further reading

External links