41. Eratosthenes: The Measurement Of The Earth's Circumference eratosthenes of cyrene Michael Lahanas Measuring the Size of the Earth - D.Trapp, ie-Physics Eratosthenes’ Experiment The Circumference of the Earth http://www.juliantrubin.com/bigten/eratosthenes.html

jokes and science Scientific American Likes Our Site Following the Path of Discovery Top Site Home Fair Projects Jokes and Science Science Directory ... About Us Eratosthenes: The Measurement of the Earth's Circumference Web www.juliantrubin.com Home Ampère André-M. Archimedes Bell Alexander ... Weather Eratosthenes (276 BC-194 BC) Eratosthenes was a Greek mathematician, geographer and astronomer. He was born in Cyrene (now Libya) and died in Ptolemaic Alexandria. He is noted for devising a system of latitude and longitude and computing the size of the Earth. Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. 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. Circa 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth. Eratosthenes' other contributions include: The Sieve of Eratosthenes as a way of finding prime numbers.

42. Sieve Of Eratosthenes take the next unmarked integer as the next prime and mark every multiple ofthe prime. Note Invented by eratosthenes of cyrene (276 BC 194 BC). http://www.nist.gov/dads/HTML/sieve.html

sieve of Eratosthenes (algorithm) Definition: An algorithm to find all prime numbers up to a certain N. Begin with an (unmarked) array of integers from 2 to N. The first unmarked integer, 2, is the first prime. Mark every multiple of this prime. Repeatedly take the next unmarked integer as the next prime and mark every multiple of the prime. Note: Invented by Eratosthenes of Cyrene (276 BC - 194 BC). For example, here's a beginning array. Since 2 is unmarked, it is our first prime. We mark every second integer, that is, 4, 6, 8, 10, 12, etc. The next unmarked integer is 3, so it is prime, and we mark every third integer, i.e., 6, 9, 12, etc. Note that we mark 6, 12, 18, etc. again. Now 5 is the next prime, and we mark every fifth integer. The only new integer marked in range is 25. From here we find the primes 7, 11, 13, 17, 19, and 23. The naive implementation is not practical for large N since the memory is . More efficient implementations use a segmented sieve. Author: PEB Implementation various implementations (C, Perl, and Java)

43. Kosmosgenesis eratosthenes of cyrene. http//www.math.utah.edu/~alfeld/Eratosthenes.html.eratosthenes of cyrene (bc 276 BC, Cyrene, Libyadc 194, Alexandria, Egypt), http://groups.msn.com/kosmosgenesis/explorers1.msnw?action=get_message&mview=0&I

44. Consal ; Consal Communities - SPECIAL COLUMN References on eratosthenes of cyrene. Message. The references are provided by Dr.John J O Connor and Prof. Edmund F Robertson. Internet http://www.consal.org.sg/forums/forum.asp?F=111&M=1548

45. Eratosthenes eratosthenes of cyrene (bc 276 BC, Cyrene, Libyadc 194, Alexandria, Egypt),Greek scientific writer, astronomer, and poet, the first man known to have http://abyss.uoregon.edu/~js/glossary/eratosthenes.html

Eratosthenes After study in Alexandria and Athens, Eratosthenes settled in Alexandria about 255 BC and became director of the great library there. He worked out a calendar that included leap years, and he tried to fix the dates of literary and political events since the siege of Troy. His writings include a poem inspired by astronomy, as well as works on the theatre and on ethics. Eratosthenes was afflicted by blindness in his old age, and he is said to have committed suicide by voluntary starvation. Excerpt from the Encyclopedia Britannica without permission.

46. Eratosthenes eratosthenes of cyrene Born 276 BC in Cyrene, North Africa, now Liberia. He wasa highly regarded mathematician who worked in the Museum in Alexandria. http://alexandrias.tripod.com/eratosthenes.htm

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod Murderball Share This Page Report Abuse Edit your Site ... Don't forget to visit our discussion forum!!! Eratosthenes How Eratosthenes measured the diameter of Earth. (Taken from Cambridge Latin Course pg. 157) " At noon, when Eratosthenes had calculated that the sun was directly overhead in Syene, he measured the length of the shadow of an object in Alexandria. From this he could calculate the angle A between the sun's rays and the object. Since the sun's rays are parallel, by simple geometry angle B is the same size as angle A. Knowing angle B and the distance between Syene and Alexandria (which was north of Syene), he was able to calculate the circumference of the earth. " Eratosthenes of Cyrene Born: 276 BC in Cyrene, North Africa, now Liberia. He was a highly regarded mathematician who worked in the Museum in Alexandria. He was the director of the library of Alexandria for couple of decades. He was the first person to accurately calculate the diameter of Earth using only simple geometry. He also created "Sieve of Eratosthenes" a method of identifying prime number. Eratosthenes also measured the tilt of the Earths' axis by 23.5, which gave us the seasons. He was bind at an old age and died of voluntary starvation in 195 B.C. to scientists_of_alexandria@altavista.com

47. Bibliography Britannica Online. 1999. http//www.britannica.com/bcom/eb/article/0/0,5716,41048+1+40189,00.html. eratosthenes of cyrene. Discovering World History. 2000 http://alexandrias.tripod.com/bibliography.htm

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod 40 Yr Old Virgin Share This Page Report Abuse Edit your Site ... Don't forget to visit our discussion forum!!! Alfeld, Peter. Eratosthenes of Cyrene . 02-Jun-1998. http://www.math.utah.edu/~alfeld/Eratosthenes.html " Hero of Alexandria ." Funk and Wagnalls Online. http://www.funkandwagnalls.com/encyclopedia/low/articles/h/h011000819f.html "Ctesibius." Encarta Online Deluxe. 1999. "Eratosthenes." Encarta Online Deluxe. 1999 . " Ctesibius of Alexandria." Britannica Online. http://www.britannica.com/bcom/eb/article/0/0,5716,28547+1+28098,00.html "Hero of Alexandria." Britannica Online. http://www.britannica.com/bcom/eb/article/0/0,5716,41048+1+40189,00.html "Eratosthenes of Cyrene." Discovering World History. "Ctesibius of Alexandria" Discovering World History. "Hero of Alexandria" Discovering World History. Gillispie, Charles Coulston. Dictionary of scientific biography . New York: Scribner, 1980.

48. Erato - Columbia Encyclopedia® Article About Erato Eratosthenes crater eratosthenes of cyrene eratosthenes of cyrene eratosthenes of cyrene Eratosthenes Sieve Eratosthenes Sieve http://columbia.thefreedictionary.com/Erato

Domain='thefreedictionary.com' word='Erato' join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia Erato Also found in: Dictionary/thesaurus Acronyms Wikipedia Hutchinson 0.03 sec. Page tools Printer friendly Cite / link Email Feedback Erato : see Muses Muses, in Greek religion and mythology, patron goddesses of the arts, daughters of Zeus and Mnemosyne. Originally only three, they were later considered as nine. Calliope was the Muse of epic poetry and eloquence; Euterpe, of music or of lyric poetry; Erato, of the poetry of love; Polyhymnia (or Polymnia), of oratory or sacred poetry; Clio, of history; Melpomene, of tragedy; Thalia, of comedy; Terpsichore, of choral song and dance; Urania, of astronomy. Click the link for more information. Mentioned in References in classic literature Muses 75-103) These things, then, the Muses sang who dwell on Olympus, nine daughters begotten by great Zeus, Cleio and Euterpe, Thaleia, Melpomene and Terpsichore, and Erato and Polyhymnia and Urania and Calliope (3), who is the chiefest of them all, for she attends on worshipful princes: whomsoever of heaven-nourished princes the daughters of great Zeus honour, and behold him at his birth, they pour sweet dew upon his tongue, and from his lips flow gracious words.

49. February 2004 Web Sites eratosthenes of cyrene ( 6 - 12 ) - A versatile scholar, eratosthenes of cyrenelived approximately 275-195 BC. He was the first to estimate accurately http://members.shaw.ca/dbrear/February2004websites.html

February 2004 Web Sites The following Web sites looked interesting : From the magazine, Teaching Pre K - 8 February 2004 Topic : Hot Websites PBS KIds Democracy Project - the three main interactive areas of this site put students in a decision-making simulation that leads them to investigate the US government, the presidency and voting. The Science Spot - this site has everything you might need for the science curriculum. Cool Science for Curious Kids - investigating science is easy with this interactive site. Using Live Insects - Using Live Insects in Elementary Classrooms for Early Lessons in Life, funded by the National Institutes of Health Science Education Partnership Award, is a program dedicated to introducing health topics to children in kindergarten through third grade. The Amazing Human Body - is a resource that will engage students in scientific inquiry and enhance their knowledge of their body systems. Topic : Internet Internet 101 for students, learn all about the Internet, Email and the WWW. Email Tutorials - great source for Email tutorials.

50. 240s BC: Information From Answers.com In the year 240 bce Earth science eratosthenes of cyrene b. Cyrene (Shahhat,Libya), c. 276 bce , d. http://www.answers.com/topic/240s-bc

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping 240s BC In the year bce Earth science Eratosthenes of Cyrene [b. Cyrene (Shahhat, Libya), c. 276 bce , d. Alexandria, c. 194 bce ] calculates Earth's circumference, finding a value 15 percent higher than present estimates or even closer, depending on what one assumes about the actual length of the Greek measure called a stadium. See also bce Astronomy Eratosthenes gives the first correct explanation for the annual flood of the Nile, relating it to rains over lakes in East Africa that are the Nile's source. Mathematics Eratosthenes invents the sieve of Eratosthenes, a method that discovers all prime numbers (whole numbers with no whole-number factors other than one and themselves) up to a given prime factor. He also develops a mechanical device that can be used to double the cube. See also bce Mathematics Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); 240s BC Centuries 4th century BC 3rd century BC 2nd century BC ... 250s BC 240s BC 230s BC 220s BC 210s BC 200s BC ... 190s BC Years: 249 BC 248 BC 247 BC 246 BC ... 240 BC Events and trends This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see

51. Table Of Contents GEOGRAPHY AND CHRONOLOGY IN THE THIRD CENTURY eratosthenes of cyrene. ERATOSTHENES OFCYRENE. PREERATOSTHENIAN GEOGRAPHY. ERATOSTHENES GEOGRAPHIC WORKS http://web.doverpublications.com/cgi-bin/toc.pl/0486277402

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Coloring Books Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Psychology, Education Puzzles, Amusement, Recrea...... Science and Mathematics Shakespeare Shop Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Teacher's Store Travel and Adventure Women's Studies Clearance Center Hellenistic Science and Culture in the Last Three Centuries b.c. by George Sarton ISBN: 0486277402 Dover Publications Price: $13.95 click here to see this book Times Literary Supplement (London). 112 illus. Bibliography.

52. Observations On Educational Electronic Networks This is a replication of the eratosthenes of cyrene experiment of over 2000 years Al Rogers Project name eratosthenes of cyrene EXPERIMENT Purpose Use http://www.gsn.org/gsh/teach/articles/LRWS.html

Lists GSN Home Projects Registry CyberFair ... Contact Us [Electronically reprinted with permission from The Computing Teacher journal, published by the International Society for Technology in Education. This article appeared in 1989, volume 16.] Observations on educational electronic networks: The importance of appropriate activities for learning James A. Levin University of Illinois Al Rogers San Diego County Office of Education Michael L. Waugh University of Illinois Kathleen Smith Champaign School District The uses of long-distance computer networks are becoming increasingly attractive for educators, as the price of modems and communication decreases, and as communication software slowly becomes easier to use. Once we have purchased modems and interface cards and mastered complex communication programs, several questions remain to be answered: what are appropriate network-based activities? How can networks be most effectively used for education? Since this is a new frontier for education, these questions are by and large unanswered. However, in this paper we will describe several network-based activities, and by contrasting successful with less successful ones, try to sketch out some general guidelines of how to explore this new educational tool. An obvious but not-very-successful use of electronic networks.

53. Ancient Map Web List 112, Reconstruction of the World map, (eratosthenes of cyrene) 112B,Eratosthenes measurement of the earth, (eratosthenes of cyrene), modern (194 BC) http://www.henry-davis.com/MAPS/Ancient Web Pages/AncientL.html

Index of Cartographic Images illustrating maps from the Ancient Period: 6,200 B.C. to 400 A.D. Below are listed the cartographic images in my collection. Each of these items currently have links to the associated image and/or monograph web pages. If you see a map that you would like to view, simply click on that underlined number. If there are maps that you would like to see but do not currently have links to them, simply e-mail your request to jsiebold@cfl.rr.com and I will e-mail the page(s) directly to you ASAP. Time Chart of Ancient Cartography Slide # Title: Cartographer: Date: (redrawing) James Mellaart Modern (6200 B.C.) unknown 6200 B.C. unknown 6200 B.C. unknown 6200 B.C. Clay tablet from Ga-Sur unknown 2300 B.C. Clay tablet from Ga-Sur unknown 2,500 B.C. Clay tablet from Ga-Sur unknown (2,500 B.C.) Clay tablet from Ga-Sur unknown (2,500 B.C.) Mesopotamian City Plan, Nippur unknown 1500 BC Turin Papyrus unknown 1300 B.C. Turin Papyrus (interpretive drawing) unknown modern (1300 B.C.) Babylonian clay tablet, 600 B.C unknown 600 B.C.

54. Slide #112 Monograph AUTHOR eratosthenes of cyrene DESCRIPTION This slide shows a 19th centuryreconstruction of the world view of eratosthenes of cyrene (275194 BC). http://www.henry-davis.com/MAPS/Ancient Web Pages/112mono.html

Slide #112 TITLE: World according to Eratosthenes DATE: 194 B.C. AUTHOR: Eratosthenes of Cyrene DESCRIPTION: Slide #111 ). Geographic information that was gathered by Alexander the Great and his successors was the primary source used by Eratosthenes, a scholar with vision large enough to put this information into a logical framework. There can be no doubt that before the time of Eratosthenes the ideas of the learned world on the subject of geography had assumed a more regular and systematic form. And it is certain also that these had been embodied in the form of maps, which, however imperfect, were unquestionably very superior to anything that had preceded them. The first use of world maps by the Greeks had been introduced at a very early period by Anaximander (ca. 610-546 B.C. Slide #107 ), and maps of the world were not uncommon in the time of Herodotus (ca. 489-425 B.C. Slide #109 Slide #109 and Slide #108 Eratosthenes, head of the Library at Alexandria from 240 B.C. until his death, was known as beta to his contemporaries because they considered him second in all his varied academic pursuits. More critical of these accomplishments was Strabo (63 B.C.?- A.D.24, Slide #115 ) to whom we are indebted for much of our knowledge of geography in antiquity, including the work of Eratosthenes whose relevant works, neither of which survived, were

55. Eratosthenes, Measuring The Earth - Timeline Index eratosthenes of cyrene was a Greek scholar who lived and worked in Cyrene andAlexandria. Eratosthenes was director of the famous library in Alexandria, http://www.timelineindex.com/content/view/1135

Timeline Index Search About Create Link ... Which Timeline Site Information 275 BC 194 BC Scientists Back ... Eratosthenes, Measuring the Earth Categories Scientists Astronomy Discoveries Egypt ... Events Eratosthenes of Cyrene was a Greek scholar who lived and worked in Cyrene and Alexandria. Eratosthenes was director of the famous library in Alexandria, and is known for numerous important contributions to mathamatics, geography, and astronomy. In particular, he is remembered for a technique he introduced which enabled him to compute the first reliable determination of the true size of the earth. This technique is based on the observation by Eratosthenes that the sun is directly overhead at noon in Syene in southern Egypt on the first day of summer. (This is the time of the summer solstice.) While visiting Syene Eratosthenes apparently stopped at a well and noted that the noon sun reflected directly back from the water in the bottom of the well. Since Eratosthenes knew that the earth was a sphere, he correctly reasoned that if he could determine the altitude of the noon sun at some other location on the first day of summer, AND if he knew the distance between these two locations, he could compute the circumference of the earth as a simple ratio. Add Related Link More on this Website http://www.phys-astro.sonom ... ory/eratosthenes/

56. Astronomy eratosthenes of cyrene. Astronomy OnLine Eratosthenes Project - this project eratosthenes of cyrene - from Dr. Peter Alfeld of the University of Utah. http://www.cannylink.com/astronomy.htm

Web www.CannyLink.com Astromony Education Books Computers Homework ... X-Ray Astronomers Brahe, Tycho (1546-1601) Brahe Brahe, Tycho Noble Dane: Images of Tycho Brahe Tycho Brahe - biography of the astronomer from Rice University. Tycho Brahe Danish Astronomer Tychonides Bruce Medalists - brief biographies of astronomers awarded the Bruce Medal of the Astronomical Society of the Pacific since 1898. Copernicus, Nicolaus (1473-1543) Copernican Model: A Sun-Centered Solar System Copernican Revolution Copernican System Copernicus, Nicolaus - The Catholic Encyclopedia ... Copernicus, The Revolutions - dedication of the revolutions of the heavenly bodies. Monument to Copernicus - work in progress. Nicolaus Copernicus Scientists: Nicolas Copernicus Web Directory: Copernicus Links Deep Skies - general information about some astronomers and space travel related physics. Eratosthenes of Cyrene Astronomy On-Line: Eratosthenes Project - this project invites you to measure the circumference of the Earth, in a collaboration with other Astronomy On-Line groups. Eratosthenes of Cyrene - from Dr. Peter Alfeld of the University of Utah.

57. Sieve Of Eratosthenes eratosthenes of cyrene (276194 BC) was the first to estimate accurately thediameter of the earth. For several decades, he served as the director of the http://britton.disted.camosun.bc.ca/jberatosthenes.htm

Sieve of Eratosthenes A natural number is prime if it has exactly two positive divisors, 1 and itself. Otherwise it is composite . The number 1 is usually regarded as being neither prime nor composite. Eratosthenes of Cyrene (276-194 BC) was the first to estimate accurately the diameter of the earth. For several decades, he served as the director of the famous library in Alexandria. He was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. Eratosthenes devised a 'sieve' to identify prime numbers. A sieve is like a strainer that you drain spaghetti through when it is done cooking. The water drains out, leaving your spaghetti behind. The Sieve of Eratosthenes drains out composite numbers and leaves prime numbers behind. Make a list of all the integers less than or equal to n (and greater than one). Strike out the multiples of all primes less than or equal to the square root of n Then the numbers that are left are the primes. Note that if one divisor or factor of a number (other than a perfect square) is greater than its square root, then the other factor will be less than its square root. Hence all multiples of primes greater than the square root of n need not be considered.

58. The Mathematical Tourist discovered in the third century BC by eratosthenes of cyrene and goes by hisname. The sieve of Eratosthenes generates a list of prime numbers by the http://www.fortunecity.com/emachines/e11/86/tourist2b.html

web hosting domain names photo sharing Prime Pursuits Ivars Peterson PRIME PROPERTIES The study of prime numbers has long been a central part of number theory, a field traditionally pursued for its own sake and for the beauty of its results . Once thought to be the purest of pure mathematics, this ancient pastime now figures prominently in modern computer science. The security of modern cryptosystems depends very strongly on the twin questions of how easy it is to identify primes and how hard it is to factor a large, random number. Neither question has a clear answer yet. Divisible evenly only by themselves and the number 1, the primes stand at the center of number theory. Like chemical elements in chemistry or fundamental particles in physics, they are building blocks in the mathematics of whole numbers. All other whole numbers, known as composites, can be written as the product of smaller prime numbers. In fact, according to the fundamental theorem of arithmetic , each composite number has a unique set of prime factors. Hence, the composite number 20 can be broken down into the prime factors 2, 2, and 5. No other composite number has the same set of factors. The number 1 is considered to be neither prime nor composite.

59. MavicaNET - Ancient Greek Philosophy eratosthenes of cyrene, approximately 275195 BC The Sieve of Eratosthenes .eng. La Filosofia nell Antica Grecia Breve introduzione ai miti e alle http://www.mavicanet.com/lite/eng/2104.html

60. Ancient Greek Philosophy - MavicaNET eratosthenes of cyrene, approximately 275195 BC - English Eratosthenes ofCyrene (c.276-c.196 BC) - English http://www.mavicanet.com/directory/gle/2104.html

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