Eratosthenes (Ερατοσθένης) (276 BC - 194 BC) was a Greek mathematician, geographer and astronomer. His coeval nicknamed him 'Beta' because he was a 2nd right inside the globe in several cases.

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Short Summary of Eratosthenes' Life
Eratosthenes was innate within Cyrene (now in Libya), but worked & died inside Ptolemaic Alexandria. He is noted for devising the formulas of latitude and longitude and computing the size of the Earth.

Eratosthenes exposed at Alexandria and for some years within Athens. Inside 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. He manufactured many significant contributions to mathematics and science, and was a good friend to Archimedes. About 255 BC he invented the armillary sphere, which was widely used until a invention of the orrery in the 18th century.

He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies by getting having estimated a Globe's circumference ca. 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon within Alexandria & Syene (now Aswan, Egypt). Inside recent years this has get controversial for the total of reasons.

There are ii theories on Plato's machine to solve a doubling of the cube condition. Of these theory is that Plato invented a mechanical guide to show else how convenient these are to devise such solutions, however the thomas more widely held theory is that Plato's machine was invented by one of his followers at a Academy.

Eratosthenes is crucial in a story two because the history of the condition has been communicated across him & too for his have contribution to the condition. He erected the column at Alexandria dedicated to King Ptolemy by having an quip inscribed thereon on to his have mechanical guide to the condition of doubling the cube [2]:-

[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Doubling_the_cube.html "Doubling the Cube"]

Eratosthenes attempts to solve the three classical problems of Greek Antiquity may have led him to the geometry for which he is most famous

Measurement of the Earth

Eratosthenes was told that, at noon on the longest day of the year, the sun shone straight down a well in the city of Syene, in southern Egypt. He deduced that Syene lay exactly on the tropic; and he measured the angle of the sun (on noon of that day) in Alexandria. That angle must represent the difference in latitude between Syene and Alexandria. Since he knew the distance between Syene and Alexandria, dividing by the number of degrees would give him the length of a degree of latitude; multiplying this by 360 would give the circumference of the Earth.

There are several systematic errors in this calculation. Syene is not exactly on the Tropic of Cancer, and is not directly south of Alexandria; nor is the Sun at infinite distance. (Eratosthenes knew the last, but we are not told he corrected for it.) More seriously, angles in antiquity could be measured only to degrees or quarter-degrees, and measurement of overland distances was worse.

We have several different, and incompatible, ancient accounts of the details of Eratosthenes' calculations. The Greek sources mostly agree that his result was 700 stadia; but what was a stadion? The Olympic stadion was 606 ft; almost exactly a 600th part of a degree — and we have no direct evidence that any Hellenistic geographer used any other. An error of one-seventh is not bad for a first attempt; but some modern scholars, however, have conjectured a shorter, Egyptian, stadion to save Eratosthenes from error. (Some Latin accounts record a final figure of 25,000 Roman miles, which would be about a twentieth too short.)

About 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth.

Eratosthenes' Contributions
Eratosthenes' other contributions include:

"Eratosthenes mass produced major contributions to geographics. He sketched, quite accurately, a route of the Nile to Khartoum, showing the two Ethiopian affluent. He likewise suggested that streams, lakes, and wells throughout were a source of the flow of any stream. a survey of the Nile experienced been processed by numbers of scholars prior to Eratosthenes & it experienced attempted to show you the such as unknown behaviour of the flow of any stream, however virtually all like Thales were quite incorrectly in their explanations. Eratosthenes was a 1st to give what is au fond a correct guide whilst he suggested that heavily rains another time fell within regions touching a source of the flow of any stream & that these would tell you the in flood lower berth down the flow of any stream. An additional contribution that Eratosthenes mass produced to geographics was his description of the region "Eudaimon Arabia", now a Yemen, every bit inhabited by quadruplet different races. A situation was somewhat supplementary complicated than that projected by Eratosthenes, however in todays world a list for the races projected by Eratosthenes, that is to say Minaeans, Sabaeans, Qatabanians, and Hadramites, are however utilized."

[http://www-groups.dcs.st-andrews.ac.uk/history/Mathematicians/Eratosthenes.html Eratosthenes - University of Mathmeticians of Scotland]

Since Eratosthenes never traveled to Yemen or the source of the Nile it is likely that at least this part of his writings came from the shelves of his library.

The Sieve of Eratosthenes as a way of finding prime numbers. The measurement of the Sun-Earth distance, now called the astronomical unit (804,000,000 stadia). The measurement of the distance to the Moon (780,000 stadia). The measurement of the inclination of the ecliptic with an angle error 7'. He compiled a star catalogue containing 675 stars, which was not preserved. A map of the Nile's route as far as Khartoum. A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia. Only Hipparchus, Strabo, and Ptolemy were able to make more accurate maps in the classical and post-classical world.

Eratosthenes was known under the name β, because he supposedly proved himself to be the second in the world in many fields. He was also reputedly known for his haughty character. In 195 BC he became blind and a year later he starved himself to death.

The fragmentary collection of Hellenistic sky-myths called Catasterismi (Katasterismoi) was given an attribution to Eratosthenes, a name to conjure with, to add to its credibility.

Strabo on the Geography of Eratosthenes
From the description of Eratosthenes geography given by Strabo it would appear that he had access to accounts in his library which had measured the earth itself as far away as India with measuring lines in stadia of the Royal Road or Egyptian Atur. " it was particularly apparent from either either our previous discussion that a summary account placed forth Flow of any stream around a third book of his geographics by Eratosthenes of what was in his period repute India, that is, once Alexander invaded a united states, is a virtually all trusty; & a Indus River was a boundary between India & Ariana, which latter was located next to India on the west & was in the possession of the Persians at that instance; for late the Indians besides held great deal of Ariana, getting received it from the Macedonians. & a account from Eratosthenes is when follows: "...India...it has been measured with measuring lines, and there is a royal road of ten thousand stadia." "...Of the officials, some are market commissioners, others are city commissioners and others are in charge of the soldiers. Among these, the first keep the rivers improved and the land remeasured, as in Egypt, and inspect the closed canals from which the water is distributed into the conduits, in order that all may have an equal use of it. The same men also have charge of the hunters and are authorized to reward or punish those who deserve either. They also collect the taxes and superintend the crafts connected with the land -- those of wood-cutters, carpenters, workers in brass, and miners. And they make roads, and at every ten stadia place pillars showing the by-roads and the distances. "A entire length of a united states, at its minimum, is sixteen thousand stadia, equally taken from either the Register of Times' Journeying that is virtually all normally accepted, based on data from Eratosthenes; &, agreed using him"

Named after Eratosthenes
Sieve of Eratosthenes. Eratosthenes crater on the Moon. Eratosthenian period in the lunar geologic timescale.