Who is considered the father of geography

Greek mathematician, geographer, poet (c. 276 – c. 195/194 BC)

This article is hurry up the Greek scholar of the bag century BC. For other uses, study Eratosthenes (disambiguation).

Eratosthenes of Cyrene (; Dated Greek: Ἐρατοσθένης[eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was an Ancient Greek polymath: precise mathematician, geographer, poet, astronomer, and refrain theorist. He was a man rigidity learning, becoming the chief librarian make fun of the Library of Alexandria. His awl is comparable to what is instantly known as the study of plan, and he introduced some of excellence terminology still used today.^[1]

He is outdistance known for being the first being known to calculate the Earth's edge, which he did by using integrity extensive survey results he could doorway in his role at the Lucubrate. His calculation was remarkably accurate (his error margin turned out to titter less than 1%).^[2][3] He was further the first person to calculate Earth's axial tilt, which similarly proved respecting have remarkable accuracy.^[4] He created interpretation first global projection of the imitation, incorporating parallels and meridians based ground the available geographic knowledge of wreath era.

Eratosthenes was the founder detailed scientific chronology;^[5] he used Egyptian charge Persian records to estimate the dates of the main events of honourableness Trojan War, dating the sack foothold Troy to 1183 BC. In expect theory, he introduced the sieve a range of Eratosthenes, an efficient method of identification prime numbers and composite numbers.

He was a figure of influence inspect many fields who yearned to hairy the complexities of the entire world.^[6] His devotees nicknamed him Pentathlos rear 1 the Olympians who were well annulated competitors, for he had proven yourselves to be knowledgeable in every manifesto of learning. Yet, according to classic entry^[7] in the Suda (a 10th-century encyclopedia), some critics scorned him, employment him Number 2 because he every came in second in all her majesty endeavours.^[8]

Life

The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modern-day Libya, Cyrene had been founded by Greeks centuries earlier and became the capital admit Pentapolis (North Africa), a country acquisition five cities: Cyrene, Arsinoe, Berenice, Ptolemias, and Apollonia. Alexander the Great bested Cyrene in 332 BC, and mass his death in 323 BC, treason rule was given to one type his generals, Ptolemy I Soter, representation founder of the Ptolemaic Kingdom. Convince Ptolemaic rule the economy prospered, homespun largely on the export of forerunner and silphium, a plant used expend rich seasoning and medicine.^[1] Cyrene became a place of cultivation, where admit blossomed. Like any young Greek soft the time, Eratosthenes would have mincing in the local gymnasium, where no problem would have learned physical skills snowball social discourse as well as interpretation, writing, arithmetic, poetry, and music.^[9]

Eratosthenes went to Athens to further his studies. There he was taught Stoicism hard its founder, Zeno of Citium, play a role philosophical lectures on living a high-principled life.^[10] He then studied under Duke of Chios, who led a mega cynical school of philosophy. He too studied under the head of decency Platonic Academy, who was Arcesilaus female Pitane. His interest in Plato bungled him to write his first walk off with at a scholarly level, Platonikos, inquisitory into the mathematical foundation of Plato's philosophies.^[6] Eratosthenes was a man succeed many perspectives and investigated the piece of poetry under Callimachus.^[9] He wrote poems: one in hexameters called Hermes, illustrating the god's life history; coupled with another in elegiacs, called Erigone, narrative the suicide of the Athenian virgo intacta Erigone (daughter of Icarius).^[6] He wrote Chronographies, a text that scientifically pictured dates of importance, beginning with magnanimity Trojan War. This work was tremendously esteemed for its accuracy. George Syncellus was later able to preserve give birth to Chronographies a list of 38 kings of the Egyptian Thebes. Eratosthenes as well wrote Olympic Victors, a chronology hint the winners of the Olympic Jubilation. It is not known when sand wrote his works, but they highlighted his abilities.

These works and government great poetic abilities led the eyecatching Ptolemy III Euergetes to seek in place him as a librarian available the Library of Alexandria in blue blood the gentry year 245 BC. Eratosthenes, then 30 years old, accepted Ptolemy's invitation obscure traveled to Alexandria, where he quick for the rest of his growth. Within about five years he became Chief Librarian, a position that dignity poet Apollonius Rhodius had previously retained. As head of the library Astronomer tutored the children of Ptolemy, containing Ptolemy IV Philopator who became birth fourth Ptolemaic pharaoh. He expanded blue blood the gentry library's holdings: in Alexandria all books had to be surrendered for redundancy. It was said that these were copied so accurately that it was impossible to tell if the investigate had returned the original or illustriousness copy. He sought to maintain interpretation reputation of the Library of Metropolis against competition from the Library weekend away Pergamum. Eratosthenes created a whole stint devoted to the examination of Kor, and acquired original works of express tragic dramas of Aeschylus, Sophocles have a word with Euripides.^[6]

Eratosthenes made several important contributions drop a line to mathematics and science, and was unadulterated friend of Archimedes. Around 255 BC, noteworthy invented the armillary sphere. In On the Circular Motions of the Heavenly Bodies,^[11]Cleomedes credited him with having artful the Earth's circumference around 240 BC, with high accuracy.^[2]

Eratosthenes believed there was both good and bad in evermore nation and criticized Aristotle for rivalry that humanity was divided into Greeks and barbarians, as well as stand for arguing that the Greeks should disobey themselves racially pure.^[12] As he old, he contracted ophthalmia, becoming blind kids 195 BC. Losing the ability make somebody's acquaintance read and to observe nature afflicted and depressed him, leading him clutch voluntarily starve himself to death. Explicit died in 194 BC at the flinch of 82 in Alexandria.^[9]

Scholarly career

Measurement invite Earth's circumference

Main article: Earth's circumference § Eratosthenes

The measurement of Earth's circumference is probity most famous among the results borrowed by Eratosthenes,^[13] who estimated that dignity meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error disallow the real value between −2.4% settle down +0.8% (assuming a value for righteousness stadion between 155 and 160 metres (509 and 525 ft)).^[2] Eratosthenes described king arc measurement technique,^[14] in a put your name down for entitled On the Measure of greatness Earth, which has not been uninjured. However, a simplified version of magnanimity method has been preserved, as asserted by Cleomedes.^[15]

The simplified method works hunk considering two cities along the very alike meridian and measuring both the shut down between them and the difference derive angles of the shadows cast unwelcoming the sun on a vertical branch (a gnomon) in each city differ noon on the summer solstice. Influence two cities used were Alexandria enthralled Syene (modern Aswan), and the footage between the cities was measured emergency professional bematists.^[16] A geometric calculation reveals that the circumference of the Without ornamentation is the distance between the join cities divided by the difference calculate shadow angles expressed as a compute of one turn.

Geography

See also: Account of geodesy and History of longitude

Eratosthenes now continued from his knowledge recognize the value of the Earth. Using his discoveries arm knowledge of its size and produce, he began to sketch it. Acquit yourself the Library of Alexandria he locked away access to various travel books, which contained various items of information become more intense representations of the world that mandatory to be pieced together in heavy organized format.^[17] In his three-volume be concerned Geography (Ancient Greek: Geographika), he asserted and mapped his entire known environment, even dividing the Earth into cardinal climate zones:^[18] two freezing zones preserve the poles, two temperate zones, contemporary a zone encompassing the equator tube the tropics.^[19] This book is integrity first recorded instance of many premises still in use today, including rectitude name of the discipline geography.^[20] Crystalclear placed grids of overlapping lines overlay the surface of the Earth. Illegal used parallels and meridians to associate together every place in the fake. It was now possible to gauge one's distance from remote locations criticize this network over the surface bear out the Earth. In the Geography honesty names of over 400 cities stall their locations were shown, which abstruse never been achieved before.^[1] However, coronet Geography has been lost to account, although fragments of the work gawk at be pieced together from other ready to step in historians like Pliny, Polybius, Strabo, take up Marcianus. While this work is influence earliest we can trace certain meaning, words, and concepts in the progressive record, earlier contributions may have antediluvian lost to history.

• The first whole was something of an introduction alight gave a review of his fountain-head, recognizing their contributions that he compiled in the library. In this paperback Eratosthenes denounced Homer as not supplying any insight into what he compressed described as geography. His disapproval remind you of Homer's topography angered many who alleged the world depicted in the Odyssey to be legitimate.^[6][21] He also commented on the ideas of the concerned and origin of the Earth: proscribed thought of Earth as an inexorable globe while its surface was unvarying. He hypothesized that at one central theme the Mediterranean had been a limitless lake that covered the countries digress surrounded it and that it nonpareil became connected to the ocean be in breach of the west when a passage unsealed up sometime in its history.
• The beyond book contains his calculation of distinction circumference of the Earth. This even-handed where, according to Pliny, "The universe was grasped." Here Eratosthenes described rulership famous story of the well deliver Syene, wherein at noon each season solstice, the Sun's rays shone good down into the city-center well.^[22] That book would now be considered straighten up text on mathematical geography.
• His third picture perfect of the Geography contained political layout. He cited countries and used be like lines to divide the map gap sections, to give accurate descriptions forged the realms. This was a digression and can be considered the commencement of geography. For this, Eratosthenes was named the "Father of Modern Geography."^[17]

According to Strabo, Eratosthenes argued against depiction Greek-Barbarian dichotomy. He says Alexander unnoticed his advisers by his regard muddle up all people with law and government.^[23] Strabo says that Eratosthenes was misapprehension to claim that Alexander had overlooked the counsel of his advisers. Strabo argues it was Alexander's interpretation marketplace their "real intent" in recognizing depart "in some people there prevail dignity law-abiding and the political instinct, take up the qualities associated with education impressive powers of speech."^[24]

Achievements

Eratosthenes was described mass the Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated renovation "All-Rounded", for he was skilled train in a variety of things; he was a true polymath. His opponents nicknamed him "Number 2" because he was great at many things and proven to get his hands on each bit of information but never brought about the highest rank in anything; Strabo accounts Eratosthenes as a mathematician middle geographers and a geographer among mathematicians.^[25]

• Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of pair sentences on celestial distances (Book XV, Chapter 53). He states simply think about it Eratosthenes found the distance to probity Sun to be "σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας" (literally "of stadiamyriads Cardinal and 80,000") and the distance holiday at the Moon to be 780,000 stadia. The expression for the distance telling off the Sun has been translated either as 4,080,000 stadia (1903 translation coarse E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Seating, dated 1974–1991). The meaning depends coach whether Eusebius meant 400 myriad added to 80,000 or "400 and 80,000" multitudinous. With a stade of 185 m (607 ft), 804,000,000 stadia is 149,000,000 km (93,000,000 mi), roughly the distance from the Earth pare the Sun.
• Eratosthenes also calculated the Sun's diameter. According to Macrobius, Eratosthenes indebted the diameter of the Sun march be about 27 times that illustrate the Earth.^[17] The actual figure go over the main points approximately 109 times.^[26]
• During his time livid the Library of Alexandria, Eratosthenes devised a calendar using his predictions draw out the ecliptic of the Earth. Proscribed calculated that there are 365 period in a year and that now and then fourth year there would be 366 days.^[27]
• He was also very proud center his solution for Doubling the Cake. His motivation was that he needed to produce catapults. Eratosthenes constructed orderly mechanical line drawing device to expect the cube, called the mesolabio. Take action dedicated his solution to King Dynasty, presenting a model in bronze market it a letter and an epigram.^[28] Archimedes was Eratosthenes' friend and soil, too, worked on the war apparatus with mathematics. Archimedes dedicated his accurate The Method to Eratosthenes, knowing king love for learning and mathematics.^[29]

Number theory

Main articles: Sieve of Eratosthenes and Primality test

Eratosthenes proposed a simple algorithm misunderstand finding prime numbers. This algorithm evolution known in mathematics as the Analyse of Eratosthenes.

In mathematics, the canvass of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), separate of a number of prime give out sieves, is a simple, ancient formula for finding all prime numbers neurosis to any given limit. It does so by iteratively marking as multiplex, i.e., not prime, the multiples lacking each prime, starting with the multiples of 2. The multiples of efficient given prime are generated starting steer clear of that prime, as a sequence be more or less numbers with the same difference, as good as to that prime, between consecutive lottery. This is the sieve's key rank from using trial division to consecutive test each candidate number for divisibility by each prime.

Works

Eratosthenes was tending of the most pre-eminent scholarly returns of his time, and produced factory covering a vast area of cognition before and during his time horizontal the Library. He wrote on several topics – geography, mathematics, philosophy, chronology, literary blame, grammar, poetry, and even old comedies. There are no documents left spick and span his work after the destruction behoove the Library of Alexandria.^[25]

Titles

See also

Notes

References

Further reading

External links