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Encyclopedia > Eratosthenes

Eratosthenes of Cyrene (Greek Eρατοσθένης; 276 BC - 194 BC) 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 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. This article is about the ancient Athenian statesman of the fifth century BC. For the Greek scholar of the third century BC, see Eratosthenes. ... Image File history File links Eratosthenes. ... Image File history File links Eratosthenes. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... The poor poet A poet is a person who writes poetry. ... Look up Athlete in Wiktionary, the free dictionary. ... A geographer is a crazy psycho whose area of study is geocrap, the pseudoscientific study of Earths physical environment and human habitat and the study of boring students to death. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... Beta (upper case Î’, lower case β) is the second letter of the Greek alphabet. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... This article is about the geographical term. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... Man has always been interested in the Earth on which he lives. ... Ancient world maps cover depictions of the world from Classical times to the Age of Discovery and the emergence of modern Geography. ...

Contents

Life

Eratosthenes was born in Cyrene (in modern-day Libya). He worked at Alexandria and died in the capital of Ptolemaic Egypt. He was never married. He was reputed to have a haughty character. Cyrene, the ancient Greek city (in present-day Libya) was the oldest and most important of the five Greek cities in the region and gave eastern Libya the classical name Cyrenaica that it has retained to modern times. ... This article is about the city in Egypt. ... The Ptolemaic dynasty in Egypt began following Alexander the Greats conquest in 332 BC and ended with the death of Cleopatra VII and the Roman conquest in 30 BC. It was founded when Ptolemy I Soter declared himself Pharaoh of Egypt, creating a powerful Hellenistic state from southern Syria...


Eratosthenes studied in Alexandria and claimed to have done so for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Zenodotos, in that post. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere, which was widely used until the invention of the orrery in the 18th century. This article is about the capital of Greece. ... Ptolemy III Euergetes I, (Ptolemaeus III) (Evergetes, Euergetes) (reigned 246 BC-222 BC). ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... Zenodotus (Greek: ), Greek grammarian, literary critic, and scholar on Homer; first librarian of the Library of Alexandria; pupil of Philetas of Cos; a native of Ephesus. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Archimedes (disambiguation). ... Armillary sphere An armillary sphere (variations known as a spherical astrolabe, armilla, or armil) is a model of the celestial sphere, invented by the ancient Greek Eratosthenes in 255 BC. Its name comes from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking... A small orrery showing earth and the inner planets An orrery is a mechanical device that illustrates the relative positions and motions of the planets and moons in the solar system in heliocentric model. ... (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ...


In 194 BC Eratosthenes became blind and a year later he supposedly 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). Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... The circumference is the distance around a closed curve. ... The solar elevation angle is the elevation angle of the sun. ... Sol redirects here. ... Elephantine Island, showing the nilometer (lower left) and the Aswan Museum. ... Syene was the ancient Greek name for the Southern Egyptian town of Aswan. ... Egypt: Site of Aswan (bottom). ...


Eratosthenes' measurement of the earth's circumference

Eratosthenes knew that on the summer solstice at local noon in the town of 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 argued by those who suppose he got it right; but the common Attic stadion was about 185 m, which implies a circumference of 46620 km, i.e. 16.3% too large. Illumination of Earth by the sun on the northern hemisphere summer solstice The summer solstice is an astronomical term regarding the position of the sun in relation to the celestial equator. ... Syene was the ancient Greek name for the Southern Egyptian town of Aswan. ... For the novel by Henry Miller, see Tropic of Cancer (novel). ... Introduction Many systems of weights and measures have existed throughout history in different civilisations. ...


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 bust of Posidonius as an older man depicts his character as a Stoic philosopher. ...


The mysterious astronomical distances

Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (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. Eusebius of Caesarea Eusebius of Caesarea (c. ... Praeparatio evangelica (Preparation for the Gospel), commonly known by its Latin title, was a work by Eusebius which attempts to prove the excellence of Christianity over every pagan religion and philosophy. ... Introduction Many systems of weights and measures have existed throughout history in different civilisations. ... Introduction Many systems of weights and measures have existed throughout history in different civilisations. ...


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 Eratos should have been able to do much better than this since he knew the size of the Earth and Aristarchos 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 16%. The Dictionary of Scientific Biography is a reference work consisting of extensive biographies of scientists from antiquity to modern times, excluding scientists who were alive when the Dictionary was first put out. ... Statue of Aristarchus at Aristoteles University in Thessaloniki, Greece Aristarchus (310 BC - c. ...


Works

  • On the Measurement of the Earth (lost, summarized by Cleomedes)
  • Geographica (lost, criticized by Strabo)
  • Arsinoe (a memoir of queen 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.

Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... The Greek geographer Strabo in a 16th century engraving. ... Arsinoe III (246 BC or 245 BC - 204 BC) was Queen of Egypt (220 - 204 BC). ... Athenaeus (ca. ... The Deipnosophistes (deipnon “dinner” and sophistae, “the wise ones”) is variously translated as The Banquet of the Learned or Philosophers at Dinner or The Gastronomers is work of some 15 books (some complete and some surviving in summaries only) by the ancient Greek author Athenaeus of Naucratis in Egypt, written... The term Hellenistic (established by the German historian Johann Gustav Droysen) in the history of the ancient world is used to refer to the shift from a culture dominated by ethnic Greeks, however scattered geographically, to a culture dominated by Greek-speakers of whatever ethnicity, and from the political dominance... This article is about the star grouping. ... Catasterismi (Greek Katasterismoi, placings among the stars) is an Alexandrian prose retelling of the mythic origins of stars and constellations, as they were interpreted in Hellenistic culture. ...

Named after Eratosthenes

In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. ... Detail map of Mare Imbriums features. ... This article is about Earths moon. ... The Eratosthenian period in the lunar geologic timescale runs from 3,200 million years ago to 1,100 million years ago. ... The lunar geologic timescale (or perhaps more properly the selenologic timescale) divides the history of Earths Moon into six generally recognized geologic periods: Copernician Period : 1100 MY to present Eratosthenian Period : 3200 MY to 1100 MY Upper Imbrian Epoch : 3800 MY to 3200 MY Lower Imbrian Epoch : 3850 MY... The Eratosthenes Seamount is a seamount in the Eastern Mediterranean about 100 km south of Cyprus. ... Jules Eratosthenes Brown is a fictional character in the Back to the Future motion picture trilogy, played in Back to the Future Part III by Todd Cameron Brown and voiced in the animated series by Josh Keaton. ... This article is about the first film in the Back to the Future trilogy. ...

See also

Atlas Portal

Image File history File links Download high resolution version (1357x628, 23 KB) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Man has always been interested in the Earth on which he lives. ... For other uses, see Zhang Heng (disambiguation). ...

Further reading

  • Lasky, Kathryn. 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.
  • J J O'Connor and E F Robertson (January 1999). "Eratosthenes of Cyrene". MacTutor. School of Mathematics and Statistics University of St Andrews Scotland. 
  • E P Wolfer (1954). Eratosthenes von Kyrene als Mathematiker und Philosoph. Groningen-Djakarta. 
  • A V Dorofeeva (1988). "Eratosthenes (ca. 276-194 B.C.)" (in Russian). Mat. v Shkole (4): i. 
  • J Dutka (1993). "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55–66. 
  • B A El'natanov (1983). "A brief outline of the history of the development of the sieve of Eratosthenes" (in Russian). Istor.-Mat. Issled. 27: 238–259. 
  • D H Fowler (1983). "Eratosthenes' ratio for the obliquity of the ecliptic". Isis 74 (274): 556–562. 
  • B R Goldstein (1984). "Eratosthenes on the "measurement" of the earth". Historia Math. 11 (4): 411–416. 
  • E Gulbekian (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C". Arch. Hist. Exact Sci. 37 (4): 359–363. 
  • G Knaack (1907). "Eratosthenes". Pauly-Wissowa VI: 358–388. 
  • F Manna (1986). "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"" (in Italian). Atti Accad. Pontaniana (N.S.) 35: 37–44. 
  • A Muwaf and A N Philippou (1981). "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1–2): 174–147. 
  • D Rawlins (1982). "Eratosthenes' geodest unraveled : was there a high-accuracy Hellenistic astronomy". Isis 73: 259–265. 
  • D Rawlins (1982). "The Eratosthenes - Strabo Nile map. Is it the earliest surviving instance of spherical cartography? Did it supply the 5000 stades arc for Eratosthenes' experiment?". Arch. Hist. Exact Sci. 26 (3): 211–219. 
  • C M Taisbak (1984). "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus 27 (2): 165–167. 

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Eratosthenes (524 words)
Eratosthenes (276-194 BC) was a Greek scholar who was the first person to determine the circumference of the Earth.
Eratosthenes was the first to give what is essentially the correct answer, when he suggested that heavy rains sometimes fell in regions near the source of the river and that these would explain the flooding lower down the river.
Eratosthenes was born in 276 B.C. in the city of Cyrene which is in the modern-day country of Libya.
Eratosthenes (496 words)
Eratosthenes (276 BC - 194 BC) was a Greek mathematician, geographer and astronomer with (probably) Chaldean origins.
Eratosthenes knew that on the summer solstice at local noon in Syene, the Sun would appear at the zenith.
Eratosthenes was known under the name β, because he proved himself to be the second in the world in many fields and he was also supposedly known for his haughty character.
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