Eratosthenes - Revision history

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2012-01-04T09:13:17Z

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Irlandos at 20:17, June 12, 2008

2008-06-12T20:17:03Z

Irlandos at 20:16, June 12, 2008

2008-06-12T20:16:44Z

Lazarus: New page: '''Eratosthenes of Cyrene''' (Greek language|Greek Ἐρατοσθένης 276 BCE - 194 BCE) was a Greek mathematician, poet, athlete, geographer and astronomer. His contemporaries nickna...

2008-06-12T11:53:23Z

New page: '''Eratosthenes of Cyrene''' (Greek language|Greek Ἐρατοσθένης 276 BCE - 194 BCE) was a Greek mathematician, poet, athlete, geographer and astronomer. His contemporaries nickna...

New page

'''Eratosthenes of Cyrene''' (Greek language|Greek Ἐρατοσθένης 276 BCE - 194 BCE) was a Greek mathematician, poet, athlete, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient Mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known person to have calculated the circumference of the Earth. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

==Life==
Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the [[Great Library of Alexandria]] and died in the capital of [[Ptolemaic Egypt]]. He never married.

Eratosthenes studied in Alexandria and claimed to have also studied for some years in [[Athens]]. In 236 BC he was appointed by [[Ptolemy III of Egypt|Ptolemy III Euergetes I]] as librarian of the [[Library of Alexandria|Alexandrian library]], succeeding the first librarian, [[Apollonius of Rhodes]], in that post[http://www.oxfordreference.com/views/ENTRY.html?entry=t111.e2478&srn=2&ssid=223186397#FIRSTHIT]. He made several important contributions to [[mathematics]] and [[science]], and was a good friend to [[Archimedes]]. Around 255 BC he invented{{Fact|date=January 2008}} the [http://en.wikipedia.org/wiki/Armillary_sphere armillary sphere], which was widely used until the invention of the orrery in the 18th century.

In 194 BC Eratosthenes became blind and, according to legends, a year later, he starved himself to death.

He is credited by [[Cleomedes]] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).

==Eratosthenes' measurement of the Earth's circumference==
Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 [[stadia]] (about 500 geographical or nautical miles). He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"<ref>traianus.rediris.es/topo01/surveying.pdf</ref> of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.<ref>There is a huge Eratosthenes-got-it-right literature based upon attacking the applicability of the standard 185m stadium to his experiment. Among advocates: F. Hultsch, ''Griechische und Römische Metrologie'', Berlin, 1882; E. Lehmann-Haupt, Stadion entry in ''Paulys Real-Encyclopädie'', Stuttgart, 1929; I. Fischer, ''Q. Jl. R. astr. Soc. 16.2'':152-167, 1975; Gulbekian (1987); Dutka (1993). The means employed include worrying various ratios of the stadium to the unstably defined "schoenus", or using a truncated passage from Pliny. (Gulbekian just computes the stadium from Eratosthenes's experiment instead of the reverse.) A disproportionality of literature exists because professional scholars of ancient science have generally regarded such speculation as special pleading and so have not bothered to write extensively on the issue. Skeptical works include E. Bunbury's classic ''History of Ancient Geography'', 1883; D. Dicks, ''Geographical Fragments of Hipparchus'', University of London, 1960; O. Neugebauer, ''History of Ancient Mathematical Astronomy'', Springer, 1975; J. Berggren and A. Jones, ''Ptolemy's Geography'', Princeton, 2000. Some difficulties with the several arguments for Eratosthenes's exact correctness are discussed by [[Dennis Rawlins|Rawlins]] in 1982b page 218 and in his [http://www.dioi.org/cot.htm#fpfw Contributions] and [http://www.dioi.org/gad.htm#rcgn Distillate].</ref>

Although Eratosthenes' method was well founded, the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is not precisely on the Tropic of Cancer, is not directly south of Alexandria, and the Sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. So the accuracy of Eratosthenes' size of the earth is surprising.

Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. His method was used by [[Posidonius]] about 150 years later.

==The mysterious astronomical distances==
Eusebius of Caesarea in his ''Preparatio Evangelica'' includes a brief chapter of three sentences on celestial distances ([http://www.tertullian.org/fathers/eusebius_pe_15_book15.htm Book XV], Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of [[stadia]] myriads 400 and 80,000") and the distance to the moon to be 780,000 [[stadia]]. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974-1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad.

This testimony of Eusebius is dismissed by the scholarly Dictionary of Scientific Biography. It is true that the distance Eusebius quotes for the moon is much too low (about 144,000 km) and Eratosthenes should have been able to do much better than this since he knew the size of the Earth and [[Aristarchus of Samos]] had already found the ratio of the Moon's distance to the size of the Earth. But if what Eusebius wrote was pure fiction, then it is difficult to explain the fact that, using the Greek, or Olympic, stadium of 185 metres, the figure of 804 million stadia that he quotes for the distance to the Sun comes to 149 million kilometres. The difference between this and the modern accepted value is less than 1%.<ref>Other than the distance to the moon, no celestial distance is unambiguously established as known in antiquity even to within a factor of two. As late as a century ago, the earth's distance to the sun (the A. U.) was known less accurately than 1%.</ref>

==Works==
* ''On the Measurement of the Earth'' (lost, summarized by [[Cleomedes]])
* ''Geographica'' (lost, criticized by Strabo)
* ''Arsinoe'' (a memoir of queen [[Arsinoe III of Egypt|Arsinoe]]; lost; quoted by [[Athenaeus]] in the ''[[Deipnosophistae]]'')
* A fragmentary collection of [[Hellenistic]] myths about the constellations, called ''[[Catasterismi]]'' (''Katasterismoi''), was attributed to Eratosthenes, perhaps to add to its credibility.

==Named after Eratosthenes==
* Sieve of Eratosthenes
* Eratosthenes crater on the [[Moon]]
* Eratosthenian period in the lunar geologic timescale
* Eratosthenes Seamount in the eastern Mediterranean Sea
* Jules Eratosthenes Brown (fictional character from the ''[[Back to the Future]]'' franchise)

==Further reading==
* Kathryn Lasky. ''The Librarian Who Measured the Earth''. New York: Little, Brown and Company, 1994. ISBN 0-316-51526-4. An illustrated biography for children focusing on the measurement of the earth. Kevin Hawkes, illustrator.

==External links==
* Bernhardy, Gottfried: "Eratosthenica" Berlin 1822 Reprinted Osnabruck 1968 (German text)
* [http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm Eratosthenes' sieve in Javascript]
* [http://www.math.utah.edu/history/eratosthenes.html Eratosthenes' sieve as a simple algorithm]
* [http://www.math.utah.edu/~pa/Eratosthenes.html About Eratosthenes' methods, including a Java applet]
* [http://www.algonet.se/~sirius/eaae/aol/market/collabor/erathost How to measure the earth with Eratosthenes' method]
* [http://galileoandeinstein.physics.virginia.edu/lectures/gkastr1.html How the Greeks estimated the distances to the moon and sun]
* [http://www.pbs.org/wnet/hawking/cosmostar/html/cstars_eratho.html Eratosthenes on PBS.org]
* [http://www.phys-astro.sonoma.edu/observatory/eratosthenes/ Inter-collegiate project for measuring the earth with Eratosthenes' method]
* [http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm Measuring the earth with Eratosthenes' method]
* [http://aleph0.clarku.edu/~djoyce/mathhist/greece.html List of ancient Greek mathematecians and contemporaries of Eratosthenes]
* [http://www.newadvent.org/cathen/01303a.htm New Advent Encyclopedia article on the Library of Alexandria]
* [http://www.christopherhenden.com/previously/primenumbers/ Eratosthenes' sieve explored and visualised in Flash]
* [http://www.quitebasic.com/prj/math/eratosthenes/ Eratosthenes' sieve in classic BASIC all-web based interactive programming environment]
* [http://www.mapmonde.org/eratos/index.php?lang=en Following in the footsteps of Eratosthenes] : project [http://fr.wikipedia.org/wiki/La_main_%C3%A0_la_p%C3%A2te].
{{Credit wikipedia}}
[[Category:276 BC births]]
[[Category:194 BC deaths]]
[[Category:Ancient Greek Astronomers]]
[[Category:Ancient Greek Geographers]]
[[Category:Ancient Greek mathematicians]]
[[Category:Cyrenean Greeks]]
[[Category:Hellenistic Egyptians]]
[[Category:Number theorists]]
[[Category:Geodesists]]
[[Category:Librarians of Alexandria]]
[[Category:Geometers]]

@@ Line 4: / Line 4: @@
 Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the [[Great Library of Alexandria]] and died in the capital of [[Ptolemaic Egypt]]. He never married.
-Eratosthenes studied in [[Alexandria]] and claimed to have also studied for some years in [[Athens]]. In [[236 BC]] he was appointed by [[Ptolemy III of Egypt|Ptolemy III Euergetes I]] as librarian of the [[Library of Alexandria|Alexandrian library]], succeeding the first librarian, [[Apollonius of Rhodes]], in that post[http://www.oxfordreference.com/views/ENTRY.html?entry=t111.e2478&srn=2&ssid=223186397#FIRSTHIT]. He made several important contributions to mathematics and science, and was a good friend to [[Archimedes]]. Around 255 BC he invented{{Fact|date=January  2008}} the [http://en.wikipedia.org/wiki/Armillary_sphere armillary sphere], which was widely used until the invention of the orrery in the 18th century.
+Eratosthenes studied in [[Alexandria]] and claimed to have also studied for some years in [[Athens]]. In [[236 BC]] he was appointed by [[Ptolemy III of Egypt|Ptolemy III Euergetes I]] as librarian of the [[Library of Alexandria|Alexandrian library]], succeeding the first librarian, [[Apollonius of Rhodes]], in that post[http://www.oxfordreference.com/views/ENTRY.html?entry=t111.e2478&srn=2&ssid=223186397#FIRSTHIT]. He made several important contributions to mathematics and science, and was a good friend to [[Archimedes]]. Around 255 BC he invented the [http://en.wikipedia.org/wiki/Armillary_sphere armillary sphere], which was widely used until the invention of the orrery in the 18th century.
 In [[194 BC]] Eratosthenes became blind and, according to legends, a year later, he  starved himself to death.

← Older revision		Revision as of 20:17, June 12, 2008
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−	'''Eratosthenes of Cyrene''' ([[Greek language]]\|Greek]] Ερατοσθένης [[276 BC]] - [[194 BC]]) was a [[Greeks\|Greek]] mathematician, poet, athlete, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient Mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known person to have calculated the circumference of the Earth. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.	+	'''Eratosthenes of Cyrene''' ([[Greek language\|Greek]] Ερατοσθένης [[276 BC]] - [[194 BC]]) was a [[Greeks\|Greek]] mathematician, poet, athlete, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient Mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known person to have calculated the circumference of the Earth. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

	==Life==		==Life==

@@ Line 56: / Line 56: @@
 [[Category:276 BC births]]
 [[Category:194 BC deaths]]
-[[Category:Ancient Greek Astronomers]]
+[[Category:Ancient Greek astronomers]]
-[[Category:Ancient Greek Geographers]]
+[[Category:Ancient Greek geographers]]
 [[Category:Ancient Greek mathematicians]]
 [[Category:Cyrenean Greeks]]

@@ Line 1: / Line 1: @@
-'''Eratosthenes of Cyrene''' (Greek language|Greek Ἐρατοσθένης 276 BCE - 194 BCE) was a Greek mathematician, poet, athlete, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient Mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known person to have calculated the circumference of the Earth. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
+'''Eratosthenes of Cyrene''' ([[Greek language]]|Greek]] Ερατοσθένης [[276 BC]] - [[194 BC]]) was a [[Greeks|Greek]] mathematician, poet, athlete, geographer and astronomer. His contemporaries nicknamed him "beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient Mediterranean region in many fields. He is noted for devising a system of latitude and longitude, and for being the first known person to have calculated the circumference of the Earth. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
 ==Life==
 Eratosthenes was born in Cyrene (in modern-day Libya). He was the chief librarian of the [[Great Library of Alexandria]] and died in the capital of [[Ptolemaic Egypt]]. He never married.
-Eratosthenes studied in Alexandria and claimed to have also studied for some years in [[Athens]]. In 236 BC he was appointed by [[Ptolemy III of Egypt|Ptolemy III Euergetes I]] as librarian of the [[Library of Alexandria|Alexandrian library]], succeeding the first librarian, [[Apollonius of Rhodes]], in that post[http://www.oxfordreference.com/views/ENTRY.html?entry=t111.e2478&srn=2&ssid=223186397#FIRSTHIT]. He made several important contributions to [[mathematics]] and [[science]], and was a good friend to [[Archimedes]]. Around 255 BC he invented{{Fact|date=January  2008}} the [http://en.wikipedia.org/wiki/Armillary_sphere armillary sphere], which was widely used until the invention of the orrery in the 18th century.
+Eratosthenes studied in [[Alexandria]] and claimed to have also studied for some years in [[Athens]]. In [[236 BC]] he was appointed by [[Ptolemy III of Egypt|Ptolemy III Euergetes I]] as librarian of the [[Library of Alexandria|Alexandrian library]], succeeding the first librarian, [[Apollonius of Rhodes]], in that post[http://www.oxfordreference.com/views/ENTRY.html?entry=t111.e2478&srn=2&ssid=223186397#FIRSTHIT]. He made several important contributions to mathematics and science, and was a good friend to [[Archimedes]]. Around 255 BC he invented{{Fact|date=January  2008}} the [http://en.wikipedia.org/wiki/Armillary_sphere armillary sphere], which was widely used until the invention of the orrery in the 18th century.
-In 194 BC Eratosthenes became blind and, according to legends, a year later, he  starved himself to death.
+In [[194 BC]] Eratosthenes became blind and, according to legends, a year later, he  starved himself to death.
-He is credited by [[Cleomedes]] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).
+He is credited by [[Cleomedes]] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's circumference around [[240 BC]], using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).
 ==Eratosthenes' measurement of the Earth's circumference==