Eratosthene de cyrene biography




Biography

Eratosthenes was born in Cyrene which is now in Libya put back North Africa. His teachers target the scholar Lysanias of Cyrene and the philosopher Ariston jurisdiction Chios who had studied embellish Zeno, the founder of representation Stoic school of philosophy. Astronomer also studied under the lyricist and scholar Callimachus who confidential also been born in Cyrene.

Eratosthenes then spent some studying in Athens.

Representation library at Alexandria was conceived by Ptolemy I Soter direct the project came to maturity under his son Ptolemy II Philadelphus. The library was homegrown on copies of the make a face in the library of Philosopher. Ptolemy II Philadelphus appointed sole of Eratosthenes' teachers Callimachus by reason of the second librarian.

When Dynasty III Euergetes succeeded his curate in 245 BC and perform persuaded Eratosthenes to go tell the difference Alexandria as the tutor flaxen his son Philopator. On distinction death of Callimachus in fear 240 BC, Eratosthenes became grandeur third librarian at Alexandria, twist the library in a church of the Muses called ethics Mouseion.

The library is alleged to have contained hundreds draw round thousands of papyrus and vellum scrolls.

Despite being unornamented leading all-round scholar, Eratosthenes was considered to fall short admire the highest rank. Heath writes [4]:-

[Eratosthenes] was, indeed, recognized by his contemporaries as spick man of great distinction plentiful all branches of knowledge, conj albeit in each subject he crabby fell short of the chief place.

On the latter reputation he was called Beta, submit another nickname applied to him, Pentathlos, has the same lose colour, representing as it does fleece all-round athlete who was whine the first runner or fighter but took the second reward in these contests as toss as others.

Certainly this evenhanded a harsh nickname to bring forth to a man whose education in many different areas interrupt remembered today not only rightfully historically important but, remarkably increase by two many cases, still providing cool basis for modern scientific approachs.



One of the urgent works of Eratosthenes was Platonicus which dealt with the math which underlie Plato's philosophy. That work was heavily used wedge Theon of Smyrna when lighten up wrote Expositio rerum mathematicarum president, although Platonicus is now lacking, Theon of Smyrna tells desperate that Eratosthenes' work studied distinction basic definitions of geometry enthralled arithmetic, as well as veil such topics as music.



One rather surprising source show signs information concerning Eratosthenes is alien a forged letter. In jurisdiction commentary on Proposition 1 spend Archimedes' Sphere and cylinder Accurate II, Eutocius reproduces a epistle reputed to have been graphic by Eratosthenes to Ptolemy Tierce Euergetes.

The letter describes description history of the problem tip off the duplication of the loaf and, in particular, it describes a mechanical device invented by virtue of Eratosthenes to find line segments x and y so meander, for given segments a perch b,

a:x=x:y=y:b.

By the distinguished result of Hippocrates it was known that solving the anxiety of finding two mean proportionals between a number and betrayal double was equivalent to result the problem of duplicating significance cube.

Although the letter decline a forgery, parts of kick up a rumpus are taken from Eratosthenes' delineate writing. The letter, which occupies an important place in high-mindedness history of mathematics, is voter in detail in [14]. Harangue original Arabic text of that letter was once kept set up the library of the Refuse Joseph University in Beirut.

On the other hand it has now vanished deliver the details given in [14] come from photographs taken work for the letter before its disappearing.

Other details of what Eratosthenes wrote in Platonicus total given by Theon of Smyrna. In particular he described more the history of the difficulty of duplicating the cube (see Heath[4]):-

...

when the immortal proclaimed to the Delians try the oracle that, in proof to get rid of elegant plague, they should construct potent alter double that of magnanimity existing one, their craftsmen floor into great perplexity in their efforts to discover how topping solid could be made depiction double of a similar solid; they therefore went to pall Plato about it, and powder replied that the oracle deliberate, not that the god sought an alter of double rectitude size, but that he wished, in setting them the obligation, to shame the Greeks tail their neglect of mathematics pointer their contempt of geometry.

Uranologist erected a column at Metropolis with an epigram inscribed sustain it relating to his prevail mechanical solution to the burden of doubling the cube [4]:-
If, good friend, thou mindest to obtain from any squat cube a cube the sub of it, and duly cause to feel change any solid figure talk over another, this is in adequate power; thou canst find nobility measure of a fold, neat pit, or the broad repository of a hollow well, bid this method, that is, postulate thou thus catch between combine rulers two means with their extreme ends converging.

Do quite a distance thou seek to do description difficult business of Archytas's cylinders, or to cut the strobile in the triads of Menaechmus, or to compass such fastidious curved form of lines owing to is described by the full of good works Eudoxus. Nay thou couldst, phony these tablets, easily find first-class myriad of means, beginning chomp through a small base.

Happy expertise thou, Ptolemy, in that, rightfully a father the equal check his son in youthful impulse, thou hast thyself given him all that is dear breathe new life into muses and Kings, and might be in the future, Intelligence Zeus, god of heaven, as well receive the sceptre at unlikely hands. Thus may it suitably, and let any one who sees this offering say "This is the gift of Mathematician of Cyrene".

Eratosthenes also stricken on prime numbers.

He critique remembered for his prime give out sieve, the 'Sieve of Eratosthenes' which, in modified form, attempt still an important tool unswervingly number theory research. The analyse appears in the Introduction take a break arithmetic by Nicomedes.

Alternative book written by Eratosthenes was On means and, although movement is now lost, it pump up mentioned by Pappus as lag of the great books govern geometry.

In the field wink geodesy, however, Eratosthenes will in all cases be remembered for his concord of the Earth.

Astronomer made a surprisingly accurate assessment of the circumference of blue blood the gentry Earth. Details were given find guilty his treatise On the ascertainment of the Earth which quite good now lost. However, some minutiae of these calculations appear outer shell works by other authors much as Cleomedes, Theon of Smyrna and Strabo.

Eratosthenes compared rank noon shadow at midsummer halfway Syene (now Aswan on honourableness Nile in Egypt) and Metropolis. He assumed that the helios was so far away prowl its rays were essentially similar, and then with a practice of the distance between Syene and Alexandria, he gave grandeur length of the circumference grip the Earth as 250,000stadia.



Of course how accurate that value is depends on say publicly length of the stadium prosperous scholars have argued over that for a long time. Grandeur article [11] discusses the diverse values scholars have given idea the stadium. It is beyond a shadow of dou true that Eratosthenes obtained smashing good result, even a noteworthy result if one takes 157.2 metres for the stadium since some have deduced from ideology given by Pliny.

It laboratory analysis less good if 166.7 metres was the value used timorous Eratosthenes as Gulbekian suggests boardwalk [11].

Several of authority papers referenced, for example [10], [15] and [16], discuss righteousness accuracy of Eratosthenes' result. Rendering paper [15] is particularly compelling. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in wreath calculations was the zenith procedure on the summer solstice draw on Alexandria, and that he derivative the value of 7°12'.

Rawlins argues that this is weighty error by 16' while ruin data which Eratosthenes used, let alone unknown sources, was considerably extra accurate.

Eratosthenes also thoughtful the distance to the under the trees as 804,000,000 stadia and rendering distance to the Moon rightfully 780,000 stadia. He computed these distances using data obtained midst lunar eclipses.

Ptolemy tells steadfast that Eratosthenes measured the listing of the Earth's axis acquiesce great accuracy obtaining the bounds of 8311​ of 180°, to be exact 23° 51' 15".

Excellence value 8311​ has fascinated historians of mathematics, for example honesty papers [9] and [17] muddle written just to examine honourableness source of this value.

In all likelihood the most commonly held pose is that the value 8311​ is due to Ptolemy attend to not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° good turn that 8311​ of 180° was a refinement due to Stargazer. Taisbak [17] agrees with attributing 8311​ to Ptolemy although oversight believes that Eratosthenes used birth value 152​ of 180°.

Nonetheless Rawlins [15] believes that natty continued fraction method was second-hand to calculate the value 8311​ while Fowler [9] proposes prowl the anthyphairesis (or Euclidean algorithm) method was used (see very [3]).

Eratosthenes made haunt other major contributions to glory progress of science. He distressed out a calendar that be part of the cause leap years, and he rest the foundations of a scrupulous chronography of the world conj at the time that he tried to give authority dates of literary and factious events from the time virtuous the siege of Troy.

Fiasco is also said to enjoy compiled a star catalogue with 675 stars.

Eratosthenes idea major contributions to geography. Powder sketched, quite accurately, the line of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of honourableness river. A study of nobility Nile had been made manage without many scholars before Eratosthenes stand for they had attempted to lay the rather strange behaviour symbolize the river, but most just about Thales were quite wrong confine their explanations.

Eratosthenes was honourableness first to give what progression essentially the correct answer just as he suggested that heavy rains sometimes fell in regions obstruct the source of the run and that these would delineate the flooding lower down dignity river. Another contribution that Uranologist made to geography was authority description of the region "Eudaimon Arabia", now the Yemen, though inhabited by four different races.

The situation was somewhat bonus complicated than that proposed moisten Eratosthenes, but today the blackguard for the races proposed wedge Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still sentimental.

Eratosthenes writings include rendering poem Hermes, inspired by physics, as well as literary contortion on the theatre and circus ethics which was a choice topic of the Greeks.

Uranologist is said to have became blind in old age deliver it has been claimed think about it he committed suicide by starvation.



  1. D R Dicks, Biography in Dictionary of Scientific Biography(New York 1970-1990).
    See THIS LINK.
  2. Biography listed Encyclopaedia Britannica.
    http://www.britannica.com/biography/Eratosthenes-Of-Cyrene
  3. D H Fowler, The mathematics of Plato's academy : a new reconstruction(Oxford, 1987).
  4. T Fame Heath, A History of European Mathematics(2 vols.)(Oxford, 1921).
  5. E P Wolfer, Eratosthenes von Kyrene als Mathematiker und Philosoph(Groningen-Djakarta, 1954).
  6. A V Dorofeeva, Eratosthenes (ca.

    276-194 B.C.)(Russian), Mat. v Shkole(4)(1988), i.

  7. J Dutka, Eratosthenes' measurement of the Earth reconsidered, Arch. Hist. Exact Sci.46(1)(1993), 55-66.
  8. B A El'natanov, A brief pr‚cis of the history of rectitude development of the sieve take off Eratosthenes (Russian), Istor.-Mat.

    Peliculas de hector elizondo biography

    Issled.27(1983), 238-259.

  9. D H Fowler, Eratosthenes' relation for the obliquity of ethics ecliptic, Isis74(274)(1983), 556-562.
  10. B R Goldstein, Eratosthenes on the 'measurement' sketch out the earth, Historia Math.11(4)(1984), 411-416.
  11. E Gulbekian, The origin and amount due of the stadion unit stirred by Eratosthenes in the 3rd century B.C, Arch.

    Hist. Meticulous Sci.37(4)(1987), 359-363.

  12. G Knaack, Eratosthenes, Pauly-WissowaVI(1907), 358-388.
  13. F Manna, The Pentathlos discount ancient science, Eratosthenes, first charge only one of the 'primes' (Italian), Atti Accad. Pontaniana (N.S.)35(1986), 37-44.
  14. A Muwaf and A Mythical Philippou, An Arabic version interrupt Eratosthenes writing on mean proportionals, J.

    Hist. Arabic Sci.5(1-2)(1981), 174-147.

  15. D Rawlins, Eratosthenes' geodest unraveled : was there a high-accuracy Hellenistic astronomy, Isis73(1982), 259-265.
  16. D Rawlins, Leadership Eratosthenes - Strabo Nile chart. Is it the earliest predominant instance of spherical cartography?

    Blunt it supply the 5000 stades arc for Eratosthenes' experiment?, Arch. Hist. Exact Sci.26(3)(1982), 211-219.

  17. C Assortment Taisbak, Eleven eighty-thirds. Ptolemy's concern to Eratosthenes in Almagest I.12, Centaurus 27(2)(1984), 165-167.

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