61. Links SQL: Physical Science/Astronomy/1. Fundamentals/(b) Greek Astronomy http//users.jagunet.com/~cjones6/aristotle_parallax_page/aristotle_parallax.html(Added Sat Oct 26 2002). eratosthenes of cyrene eratosthenes of cyrene (ca. http://www.mhhe.com/links/1258/1226/1388/1453/

HOME SEARCH Looking for something in particular? the entire directory only this category More search options Home Physical Science Astronomy ... 1. Fundamentals : (b) Greek Astronomy LINKS: Anaximander of Miletus Anaximander of Miletus (610-ca. 546 BC) conceived the idea that the stars were fixed on a crystalline sphere rotating around the Earth. Anaximander thought the Earth to be cylindrical with a diameter three times its height, and the center of the universe. http://scienceworld.wolfram.com/biography/Anaximander.html (Added: Sun Oct 27 2002) Anaximenes of Miletus Anaximenes was the first Greek to distinguish clearly between planets and stars. He believed the primary substance of the universe to be air, which could form the other elements of water, Earth, and fire by rarefaction and condensation. This page is part of Eric Weisstein's World of Scientific Biography. http://scienceworld.wolfram.com/biography/Anaximenes.html (Added: Sun Oct 27 2002) Aristarchus and the Size of the Moon The jump Aristarchus made from terrestrial measurements of scale to the celestial is truly remarkable. Without any measures of the sizes of or distances to any celestial objects, he was able to measure both for the Moon. http://www.hastings.edu/Courses/physics/sivron/astronomy/specials/aristarchus.html

62. Issue 19 - SpaceTides Historical Notes The Pleiades Star Cluster and ancient legends 6) Persons in theWorld of Astronomy eratosthenes of cyrene – measuring the Earth 7) Boyden http://www.geocities.com/assabfn/spacetides/issues/issue_19.htm

Newsletter # 19 - 23 August 2001 www.spacetides.cjb.net Internet Newsletter of ASSA Bloemfontein Centre, South Africa www.geocities.com/assabfn International Space Station Edition IN THIS WEEK'S ISSUE: 1) In Spaceflight this week: The International Space Station: It’s all about cooperation Space Shuttle Discovery returning to Earth 2) Sky Observation and Astronomy: Open Star Clusters – Enchanted viewing The Constellation of Libra 3) This week's Question: Many sunrises during each day 4) Interesting Space Facts: The ISS in Action 5) Historical Notes: The Pleiades Star Cluster and ancient legends 6) Persons in the World of Astronomy: Eratosthenes of Cyrene – measuring the Earth 7) Boyden Observatory: Famous presenter to visit Bloemfontein on 28 August 2001 8) Weblinks Ames Research Centre, The History Net, ExploreScience.com and more 1) IN SPACEFLIGHT THIS WEEK: The International Space Station (ISS) - the story in brief Image showing the configuration of the ISS in April after the huge robotic arm was installed. When the shuttle Endeavour undocked

63. GO.HRW.COM of St Andrews, Scotland, eratosthenes of cyrene This site providesinformation about Eratosthenes and his accomplishments. Dept. http://go.hrw.com/ndNSAPI.nd/gohrw_rls1/pKeywordResults?keyword=sc0 greek scient

64. IMSA Astrophysics Distance Ladder The actual size was calculated to good precision by eratosthenes of cyrene (284 192 BC), an ancient Greek and head of the famed library at Alexandria (Egypt http://www.imsa.edu/edu/astro/astrometry/ground1.html

65. Welcome To Turkey In Maps WORLD ACCORDING TO ERATOSTHENES, c. 194 BC A 19th century reconstructionof the world view of eratosthenes of cyrene (275194 BC). http://turkeyinmaps.com/Sayfa1.html

The Early Maps Mankind, from very early ages, have felt the need of making plans and maps to let each other know the whereabouts of locations of importance to them. Unfortunately, many of these early maps which were unique manuscripts, have not survived to our time. This is why most of the maps in this section are later reconstructions of the originals. I still preferred to include them in this section for they represent the cartographic knowledge of their times. I could not find maps of this period specific to Anatolia. However, the region is shown in most of the early maps being at the centre of the inhabited world Please also see the special sections on Ptolemaic and Medieval maps. Babylonian clay tablet world map, 600 B.C. CATAL HOYUK MAP, Turkey, c. 6,200 BC One of the earliest maps is the one discovered during an excavation in 1963 by James Mellaart in Ankara, Turkey at the archeological site at Catal Hoyuk (pronuonced Chatal Hoeyuek) in central Anatolia. This is a wall painting that is approximately nine feet long. It is believed that the map depicts the town plan of Catal Hoyuk itself. In the foreground is a town arising in graded terraces. Behind the town is an erupting volcano. This is possibly Hasan Dag. For more information please click on the map.

66. Title eratosthenes of cyrene Ca. 275 BCE to 200 BCE Originally from Cyrenein North Africa, Eratosthenes spent many years studying at http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/erattext.html

ERATOSTHENES OF CYRENE Ca. 275 BCE to 200 BCE Originally from Cyrene in North Africa, Eratosthenes spent many years studying at Plato 's Academy in Athens before coming to Alexandria where he spent the rest of his life. Eratosthenes was more than just a skilled mathematician. He was gifted in all areas that Greeks held in high esteem, including astronomy, philosophy, poetry, geography, history, and sports. In Alexandria, Eratosthenes became the head of the Great Library, which at this point was growing very quickly and contained hundreds of thousands of documents. Eratosthenes' major contribution to mathematics was his work with prime numbers. He developed an algorithm for finding primes which would soon come to be known as the Sieve of Eratosthenes . Please click on the link to view an animated applet illustrating the Sieve of Eratosthenes. This algorithm starts with a list of positive numbers starting with the number two because the number one is defined as not being a prime number. Since two is prime, we circle it and eliminate all of its multiples from the list. We move to the next number on the list which is not crossed out, circle it, and cross out all remaining multiples of that number. We keep repeating this process until we are left with a list of circled numbers, all of which are prime.

67. World InfoZone - Libya Facts century BC. eratosthenes of cyrene (276BC 197) was a famous Greekmathematician who worked on prime numbers and geometry. He made http://www.worldinfozone.com/facts.php?country=Libya

68. Home Introduction Romans Early Christianity Greek Mythology Other ScientistImportant year 305 BC Sex Male, Synonym(s) eratosthenes of cyrene.......Data on Persons. eratosthenes of cyrene Name Eratosthenes http://education.domaindlx.com/history/persns.asp?IntID=4012&Ename=Eratosthenes

69. The Alexandrian Library Tables. He was replaced by eratosthenes of cyrene in 235 BCE, a manwho was very knowledgeable in geography and chronology. Ptolemy http://www.richeast.org/htwm/Greeks/library/library.html

The Greeks The Greeks The Romans Other Civilizations Index Mare Nostrum The Alexandrian Library by V. Russell Establishment The Alexandrian Library played an important role throughout history. According to Little (35), it contained the largest collection of wisdom that ever existed. The earliest documentation of the library is in the Letter of Aristeas which describes the legend of seventy translators of the Hebrew Bible that had worked in Alexandria during the reign of Philadelphus (Fraser 320). It was in this city that the library was established. Alexandria was founded by Alexander the Great in 331 BCE. It is located on the northern part of Egypt where the Nile meets the Mediterranean Sea. Alexander's empire stretched from Egypt to Asia. After his death at the age of 32, his empire was divided among several rulers. Ptolemy, a Greek general, made himself pharaoh over all of Egypt. He also made Alexandria the capital of Egypt. Creation The library was created when Demetrius, a former ruler of Greece, suggested to Ptolemy that he should gather books in the style of Plato's philosopher kings on the world's people and on kingship and ruling. Demetrius is also believed to have helped to inspire the founding of the Museum of Alexandria, a temple dedicated to the Muses (Brudige). Most libraries back in the times of the Alexandrian Library were collections of manuscripts owned by private individuals. According to Bevan (125), after Plato's death, most of his library had been passed on to the Alexandrian Library. The fire that destroyed in the library in 48 BCE destroyed much information that may never be known again.

70. Rectangular Arrays The problem dates back at least to eratosthenes of cyrene (280 to 194 BCE), the acclaimedscholar and head of the Library at Alexandria in Egypt who wrote the http://www.recoveredscience.com/Primes1ebook01.htm

recoveredscience .com We offer surprises about in our e-book Prime Passages to Paradise by H. PeterAleff Site Contents PRIME PATTERNS Table of Contents Rectangular arrays Twin prime proof Prime facts Prime problems Polygonal numbers ... Reader responses Visit our other Sections: Constants Board Games Astronomy Medicine Store Stuff Home Page Search this site FAQ about e-books Download free e-books ... email us Footnotes : William Poundstone: "Labyrinths of Reason Paradox, Puzzles and the Frailty of Knowledge", Anchor Press, New York, 1988, in chapter on "NP-Completeness" on page 177. Sir Thomas Heath: "A History of Greek Mathematics", Clarendon Press, Oxford, 1921, edition consulted Dover, New York, 1981, Volume 2, page 104. Apollonius’ life dates are not known, but he was famous as an astronomer under Ptolemy Philopator (222 to 205 BCE). See Heath: "A History of Greek Mathematics", op. cit., Volume 2, page 126. Picture credit: Seven- circuit Labyrinth of Cretan type redrawn from Jeff Saward's Caerdroia Journal see our "useful Links" page.

71. Bible History Links - Ancient Greece - 2. General EAWC Ancient Greece Chronology Essays Images Internet Sites Texts Epidemicsand Military Battles eratosthenes of cyrene (ca. 284ca. http://www.bible-history.com/bhodb/links.cfm?cat=3&sub=246

72. Euclidswindow What, for example, could be more practical than measuring the size ofthe Earth? It was first done in 212 BC by eratosthenes of cyrene. http://scibooks.org/euclidswindow.html

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow, The Free Press, $26, 306 pages. The Chapel Hill News June 27, 2001 Einstein's debt to geometry By Phillip Manning; CHN Columnist Geometry is a high school subject that has few practical applications and is not important in modern science. At least that's what I thought before I read Leonard Mlodinow's captivating book "Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace" (The Free Press, $26). It turns out I was wrong on both counts. Geometry has important practical applications, and it played a starring role in one of the great scientific achievements of the 20th century. What, for example, could be more practical than measuring the size of the Earth? It was first done in 212 B.C. by Eratosthenes of Cyrene. He noticed that at noon of the summer solstice a stick stuck perfectly upright in the ground in his hometown cast no shadow. That meant that the sun's rays were parallel to the stick. If the earth is a sphere, Eratosthenes reasoned, then a stick in the ground a few miles away should cast a shadow. Eratosthenes then measured the angle of a shadow cast at noon in Alexandria. Employing perhaps the world's first graduate assistant (and treating him in a manner that all graduate assistants will understand), Eratosthenes had him walk between the two towns and measure the distance, a stroll that turned out to be 500 miles. Using the theorems of Euclid, the man who devised the geometry we study in high school, Eratosthenes calculated the circumference of the Earth. He came up with about 25,000 miles, very close to the correct value.

73. When Is A Triangle Not A Triangle In the third century BCE, the Greek polymath eratosthenes of cyrene calculatedthe circumference of the earth using gnomon (sundial) measurements and the http://www.cityu.edu.hk/ccs/Newsletter/newsletter5/Triangle.htm

When is a Triangle Not a Triangle? Lisa Raphals and celestial distances, including the distance to the ¡§ends of the earth¡¨ and the ¡§height of heaven.¡¨ They incorrectly assumed that the earth was flat, but correctly assumed that the sun was a finite, and measurable, distance from the earth. Their calculations were less accurate than Eratosthenes¡¦, but no less mathematically well reasoned. Similar Triangles in Greek Astronomy During the third century B.C.E., Greek mathematicians and astronomers developed hypotheses and calculations regarding the motion and sizes and distance of the sun, moon and earth. Aristarchus of Samos (310-230 B.C.E.) is best known as the first Greek exponent of a heliocentric theory, a view that his contemporaries rejected because it conflicted with the commonsense view that the earth did not move. In his one surviving work, he used assumptions and the properties of similar triangles to ¡§demonstrate¡¨ ratios between the diameters of the earth, sun and moon and their distances from each other. For example: ¡§The distance of the sun from the earth is greater than 18 times, but less than 20 times the distance of the moon from the earth.¡¨ The Greek text is a list of procedures for naming points and drawing lines and circles between them, with no visual representation. (Modern editions and translations typically add an illustrative diagram.) The Greek text has the look and feel of a proof by deduction from the properties of similar triangles, rather than calculation from actual measurements.

74. Eratosthenes--Biography eratosthenes. of cyrene (276194 Bc). http://www.albertson.edu/math/History/emacy/Classical/biography.htm

ACI Math Department Eratosthenes of Cyrene (276-194 B.c.) Eratosthenes historical setting discovery reference and links ... Math History Biographical Information Eratosthenes was born in what is now Shahhat, Libya in 276 BC. He learned from a variety of teachers, including Lysanias of Cyrene, Ariston of Chios, and Callimachus of Cyrene. These teachers gave him a wide background of study, from philosophy to poetry to mathematics to astronomy. His discoveries and contributions to mathematics show this diversity as well. After spending a few years studying in Athens, after which he traveled to Alexandria to tutor the son of Ptolemy III Euergetes. When his teacher Callimachus passed away, Eratosthenes took over his job as the librarian at Alexandria. This library was the best of the time, and his appointment to the job was a great honor for Eratosthenes. He held the position until his death in 194 BC. Although Eratosthenes showed great ingenuity and intelligence in his studies, he is not known as one of the elite mathematicians of his time. Much of this is due to the fact that he studied so many subjects that he did not finish many proofs or make significant breakthroughs. His work, however, formed the basis for many scholars who followed him and used his work to achieve greatness.

75. Sieve Of Eratosthenes Benchmark This method of finding prime numbers is named after its inventor, Eratosthenesof cyrene (now in Libya), who lived from 276 to 197 BC. http://www.bagley.org/~doug/shootout/bench/sieve/

Sieve of Eratosthenes Benchmark Back to the Language Shootout Back to Doug's Homepage [NEWS] [FAQ] ... [sort] Source Code CPU (sec) Mem (KB) Lines Code Log gcc log ghc log ... log Languages that compile to native code are in Bold Italics [Note: Values have been normalized to fall in the range of 0-10 for aesthetic reasons. Original value ranges are included on the X-axis. Click here for more detailed data and graphs. [Results last updated: Tue Sep 18 12:09:18 2001 CDT] About this test For this test, each program should be implemented in the same way The test programs are written to find the count of the primes from 2 up to 8192 and then print the count. Each program can take a single command line parameter to tell it how many times to find the count. For this test the number of iterations (N) is shown in the current graph above. Visit the detail page to see results for different values of N. The algorithm used is a naive implementation of the Sieve of Eratosthenes. The intention was to see how each language compares when using similar data structures and operations, (i.e. arrays, loops, loop counters, integer math ...). Each implementation should match as closely as possible the logic and data structures used in the C version The exceptions here are the purely functional languages: Erlang, Mercury, Haskell(GHC) and SML. Since they don't implement loops and arrays like the imperative languages shown here, the tests for these languages have been written with recursive implementations.

76. Eratosthenes school of philosophy. eratosthenes also studied under the poet andscholar Callimachus, also born in cyrene. eratosthenes went on http://www.grecoreport.com/eratosthenes.htm

Eratosthenes Eratosthenes, a Greek astronomer, mathematician, geographer, scientific writer and poet made a surprisingly accurate estimate of the earth's circumference. He was born [circa] 276 B.C., in the Greek colony of Cyrene, North Africa (now Shahhat, Libya). His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios, who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus, also born in Cyrene. Eratosthenes went on to study in Athens and later settled in Alexandria, Egypt, where he became the director of the Library of Alexandria. In the great Library of Alexandria,* he read that a deep vertical well near Syene (now Aswan), in southern Egypt, was entirely lit up by the sun at noon, once a year (June 21st) [the summer solstice. ed.]. Eratosthenes reasoned that, at this time, the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day, because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth by making two assumptionsthat the earth is round and that the sun's rays are essentially parallel. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria. Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. His result, 250,000 stadia (about 46,250 km) is quite close to modern measurements. [He later altered this figure to 252,000 stadia. ed.]. The formula Eratosthenes used is: D/d =A/a. Where d = distance between Syene and Alexandria, A = 360 degrees assumption of round earth, a = shadow angle of vertical stick, D = to be determined (circumference).

77. CollegeTermPapers - Mathematics - Eratosthenes - Free Term Papers, Book Reports, Can't find it here? Try MegaEssays.com eratosthenes By Chris Stewart eratostheneseratosthenes was born in cyrene which is now in Libya in North Africa. http://www.collegetermpapers.com/TermPapers/Mathematics/Eratosthenes.shtml

What Topic Is Your Essay Or Termpaper On ? Term Papers Can't find it here? Try MegaEssays.com Eratosthenes By: Chris Stewart Bibliography It is a report about Eratosthenes. Word Count: 691 Can't find it here? Try MegaEssays.com What Topic Is Your Essay Or Termpaper On ? DataBase Custom Term Papers Free Term Papers Free Research Papers Free Essays ... Free Book Reports Links Spring Break Vacations Term Paper Sites Top 100 Term Paper Sites Top 25 Essay Sites ... @ MegaEssays.com Free Essays Term Paper Sites Chuck III Net Essays BigNerds ... OPPapers Comments What would you like to see at College Term Papers ContactUs Can't Find it? Try one of these popular search engines Feedback Advertise on College Term Papers.com

78. Free-TermPapers.com - Eratosthenes We offer high quality and quick writing for only $12.95 per page! EratosthenesEratosthenes was born in cyrene which is now in Libya in North Africa. http://www.free-termpapers.com/tp/28/mdg14.shtml

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79. Inhoud 99 Kortom. We zijn op de goede weg. Maar natuurlijk moeten we met z'n allen nog.Maart 195 Blind tussen de boeken Over eratosthenes van cyrene Luc Devoldere. http://users.skynet.be/streven/Archief/inhoud1999.htm

Hieronder vindt u een overzicht per maand van de artikelen en forum- en podiumstukjes die verschenen in Streven in 1999. Van de artikelen vindt u telkens ook de korte inhoud. Per maand vindt u telkens één artikel dat u volledig kan raadplegen, u herkent het aan de onderlijnde titel. Voor een globaal overzicht per rubriek of alfabetisch per auteur en een algemeen overzicht van de boek- en filmrecensies en de besprekingen van tentoonstellingen, ga naar index 1999 . Voor de inhoud van andere jaargangen, ga terug naar archief Januari 4 De onbekende vader Cornelis Verhoeven Sperma afstaan is meer dan bloed geven: de gift zal voor een deel de identiteit van het kind bepalen. De donor zal echter voor het kind een onbekende vader blijven, omdat volgens de huidige wetgeving zijn anonimiteit bewaard blijft. Door de nieuwe medische technieken worden seks en procreatie losgekoppeld, en dat roept vragen op. Gaat het recht op kinderen voor op het recht van kinderen te weten wie hun biologische vader is? 14 Een nieuwe bijbelvertaling voor ons taalgebied Panc Beentjes Zes jaar geleden werd besloten een nieuwe interconfessionele bijbelvertaling voor het Nederlandse taalgebied te bezorgen. Aan het project werken tientallen deskundigen mee, volgens duidelijk afgesproken principes. Inmiddels zijn al een vijftal boeken van de nieuwe vertaling beschikbaar. Je hoeft er maar enkele passages van met oudere vertalingen te vergelijken om te merken hoe levendig en eigentijds de nieuwe vertaling is.

80. ChuckIII's College Resources - Mathematics - Eratosthenes - Free Term Papers, Bo eratosthenes By Chris Stewart Email dothestew@aol.com eratosthenes eratostheneswas born in cyrene which is now in Libya in North Africa. http://www.chuckiii.com/Reports/Mathematics/Eratosthenes.shtml

We are dedicated to helping students with their everyday College needs. If you have any questions or comments Please feel free to e-mail us @ feedback@ChuckIII.com Thanks to students like YOU! Please, Keep them coming and help us grow Eratosthenes By: Chris Stewart E-mail: dothestew@aol.com Bibliography About Eratosthenes Word Count: 691 Research Help HOME Custom Term Papers High Quality Term Papers Free Term Papers ... Citing Sources Pay Sites Research Assistance Search 80,000 Papers @ DirectEssays.com Search 86,000 Papers @ MegaEssays.com Search 95,000 Papers @ Example Essays.com Free Essay Sites Term Paper Sites College Term Papers Net Essays My Term Papers ... Planet Papers Links Spring Break Vacations Term Paper Sites College Links Top 100 Term Paper Sites ... Top 50 Essay Sites College Resources All Posters.com Dorm Check list Comments What would you like to see at ChuckIII's College Resources? Contact Us Info Advertising Info Jobs / Volunteers

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