61. Rectangular Arrays The problem dates back at least to eratosthenes of cyrene (280 to 194 BCE), theacclaimed scholar and head of the Library at Alexandria in Egypt who wrote 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.

62. Eratosthenes Award The award is name for eratosthenes of cyrene, who lived in the second century BCin Alexandria, Egypt. Eratosthenes determined the size of the Earth from http://www.grad.ucalgary.ca/funding/internal_scholarships/lev_4/eratosthenes.htm

Home Prospective Students Current Students Faculty and Staff ... Contact Us Graduate Awards Eratosthenes This award was established on the occasion of the 25th anniversary of the Department of Geomatics Engineering. It was funded from research royalties obtained by Drs Klaus-Peter Schwartz and Naser El-Sheimy from the commercialization of KINGSOAD (INS/GPS Integration Software). The award is name for Eratosthenes of Cyrene, who lived in the second century BC in Alexandria, Egypt. Eratosthenes determined the size of the Earth from measurements on its surface, thus establishing geodesy as a subject of scientific study. Donor Klaus-Peter Schwartz and Naser El-Sheimy Program of Studies Geomatics Engineering Field of Studies History of Geomatics Engineering Number and Value One at $1,000 Duration One year Eligibility Year: Unrestricted Student Status: Full-time Program: Thesis-based Master's or doctoral program in the Department of Geomatics Engineering Faculty: Graduate Studies Citizenship: Unrestricted Where Tenable University of Calgary Apply Candidates should apply by letter to the Department of Geomatics Engineering. Applications must include a written statement of scholarly contribution to the history of Geomatics. This submission may take the form of a written report, draft of a paper, seminar report, or thesis outline.

63. Great Moments In Science - Cicadas In Their Prime the Greek scientific writer, poet and astronomer, eratosthenes of cyrene, To work the Sieve of Eratosthenes you write down all the numbers, http://www.abc.net.au/science/k2/moments/s421251.htm

ABC Home Radio Television News ... Play Cicadas In Their Prime Listen to Karl talk about Cicadas In Their Prime (You will need Real Audio which you can download for free 2,300 years ago, the Greek scientific writer, poet and astronomer, Eratosthenes of Cyrene, became the first person to calculate the circumference of the Earth. He also dabbled in a bit of maths, and invented the famous Sieve of Eratosthenes, which is an easy method for finding prime numbers. But now it seems that some recent research into cicadas gives us another way of finding prime numbers. Prime numbers are numbers that can be divided only by themselves and one. So 2, 3, 5, 7, 11, 13 and 17 are all prime numbers - but 18 is not a prime number, because you can divide it by both 2 and 9. To work the Sieve of Eratosthenes you write down all the numbers, and then simply strike out every second number that comes after 2, every third number following the number 3, and so forth. All the numbers that you have left will be prime numbers. It's called a Sieve because all the numbers that are not prime just "fall through". You also find prime numbers in the life cycles of cicadas. There are about 1,500 species of cicadas known. There are those that appear yearly in midsummer, and there are also the so-called "periodic" cicadas. They appear at prime number intervals - 7 years, 13 years and 17 years.

64. Welcome The Eratosthenes Project is named in honor of eratosthenes of cyrene (now knownas Libya, North Africa). Erastothenes (275195 BC) was a scholar, http://sunship.currentsky.com/

Welcome to the Sun Shadow Investigation Project. You are invited to take part in a science collaboration as a participant in a global Eratosthenes Project. The Eratosthenes Project is named in honor of Eratosthenes of Cyrene (now known as Libya, North Africa). Erastothenes (275-195 B.C.) was a scholar, and for many years was the Director of the Library of Alexandria. Eratosthenes made many contributions to Science and Mathematics but it was his accurate measurement of the Earth's circumference, using differences in the Sun's altitude and shadows between two different locations, that we seem to remember him mostly for. On the day of the 2005 September equinox, September 22 (2223 U.T.) (or during the week before or after), participating students from both the southern and northern hemispheres will measure the mid-day altitude of the Sun and take pictures of mid-day shadow at their location. This mid-day measurement will be used by the students to determine the circumference of the Earth, while the pictures will be sent to the SunShIP web site for a display of mid-day shadows from various latitudes. Check the FAQ page for more information about participating in the project, and also look at the Links page for lessons, activities and other resources relevant to the investigation of our Sun.

65. Alexandrian Scholarship 18 eratosthenes of cyrene, Stoic geographer and mathematician, succeeded him in235, and compiled his tetagmenos epi teis megaleis bibliothekeis , http://www.perseus.tufts.edu/GreekScience/Students/Ellen/Museum.html

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. The Library of Alexandria Ellen N. Brundige Look at the comments on this paper. Table of Contents The Legend of the Library Foundation Demetrius of Phaleron Precedents for the Museum ... Bibliography The Legend of the Library "And concerning the number of books, the establishment of libraries, and the collection in the Hall of the the Muses, why need I even speak, since they are all in men's memories?" Athenaeus The library of Alexandria is a legend. Not a myth, but a legend. The destruction of the library of the ancient world has been retold many times and attributed to just as many different factions and rulers, not for the purpose of chronicling that ediface of education, but as political slander. Much ink has been spilled, ancient and modern, over the 40,000 volumes housed in grain depots near the harbor, which were supposedly incinerated when Julius Caesar torched the fleet of Cleopatra's brother and rival monarch. So says Livy, apparently, in one of his lost books, which Seneca quotes. The figure of Hypatia , a fifth-century scholar and mathematician of Alexandria, being dragged from her chariot from an angry Pagan-hating mob of monks who flayed her alive then burned her upon the remnants of the old Library, has found her way into legend as well, thanks to a few contemporary sources which survived.

66. ERATOSTHENES ERATOSTHENES c.274 c.194 BC Greek Scholar. eratosthenes of cyrene studied inAlexandria and Athens. In Alexandria he was director of the great library. http://www.hyperhistory.com/online_n2/people_n2/persons2_n2/eratosthenes.html

ERATOSTHENES c.274 - c.194 BC Greek Scholar Eratosthenes of Cyrene studied in Alexandria and Athens. In Alexandria he was director of the great library. This scholar of natural history did his most outstanding work in mathematics and geography. Eratosthenes calculated the circumference of the earth correctly. This he did by observing the different angle's that the sun's rays fall in two cities 500 miles apart. He correctly assumed the Sun's distance to be so great that the rays are practically parallel when they reach the earth. www link : From the University of St. Andrews, Scotland School of Mathematics Biography

67. History Of Mathematics: Greece eratosthenes of cyrene (c. 276c. 195); Chrysippus (280-206); Conon of Samos (c.245); Apollonius of Perga (c. 260-c. 185); Nicomedes (c. 240? http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

68. History Of Mathematics: Chronology Of Mathematicians eratosthenes of cyrene (c. 276c. 195) *SB *MT; Chrysippus (280-206); Conon ofSamos (fl. c. 245) *SB; Apollonius of Perga (c. 260-c. http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

69. The Transit Of Venus And The Quest For The Solar Parallax The Greek astronomer, eratosthenes of cyrene (c276 195 BC), was able to deducethe Earth s radius by means of a strikingly simple set of observations. http://www.dsellers.demon.co.uk/venus/ven_ch1A.htm

T HE T RANSIT OF V ENUS The Quest for the Solar Parallax Now available as a full-length book: Order from Amazon! By David Sellers ( Leeds England Published by MagaVelda Press Almost every High School child knows that the Sun is 93 million miles (or 150 million Kilometres) away from the Earth. Despite the incredible immensity of this figure in comparison with everyday scales - or perhaps even because it is so hard to grasp - astronomical data of this kind is accepted on trust by most educated people. Very few pause to consider how it could be possible to measure such a distance - the 'Astronomical Unit' - and few are aware of the heroic efforts which attended early attempts at measuring it. Unfortunately, even most popular astronomy text books give insufficient information to allow one to see precisely how the task was accomplished. Sizing the Yardstick: the Diameter of the Earth In the history of astronomy, the quest for the Astronomical Unit (AU) has normally been regarded as the quest for a more fundamental quantity: namely, the 'Solar Parallax'. The solar parallax is not a distance at all. It is an angle: the angle subtended at the centre of the Sun by the Earth's radius (see Figure 1 ). If this angle is known and the radius of the Earth can be measured, then the distance to the Sun can be deduced by simple calculation. Clearly, the first piece of information which was needed in order to size the AU was the radius of the Earth.

70. WHKMLA : Era Of Discovery, Flat Earth Versus Round Globe Actually, eratosthenes of cyrene, head of the Great Library of Alexandria hadproven the FILES, eratosthenes of cyrene (276195 BC), from MacTutor; http://www.zum.de/whkmla/period/disc/flatearth.html

Flat Earth versus Round Globe The Bible (Genesis I.7) states that during creation, God separated the waters below the firmament from those above the firmament. This was interpreted as he earth being a flat disk, surrounded by the seas, and covered by the firmament (sky) in the shape of a half-globe, to the top of which the stars were fixed. This firmament again was thought to be covered by a stream of water (the waters above the firmament). Actually, Eratosthenes of Cyrene, head of the Great Library of Alexandria had proven the earth to be round. Knowing that on a certain day, at noon, an obelisk in Luxor (s. Egypt) would cast no shadow, at exactly the same time he measured the shadow of an obelisk in Alexandria. He knew the height of the obelisk and the distance between Alexandria and Luxor; the rest is trigonometry. Claudius Ptolemy's geography is also based on the concept of the earth being round, and sun, moon and the stars circling around the earth. During the Renaissance, Greek texts were rediscovered, among them Eratosthenes' calculation and Ptolemy's geography. Yet to openly state the earth to be round was generally perceived as contradicting the bible, which, in its entirety, was believed to be the word of God. A person who postulated the earth to be round was a case for the inquisition. Popular concept had it, that at the fringes of the earth people would fall down into the depth of hell. However, the campaigns of Alexander (to India), of Marco Polo and others (to China) were well-remembered and their travelogues not objected to by the Catholic church. The Viking discovery of Vinland (North America) was only remotely remembered; the church did not object to the concept that there were vast bodies of water and land out there yet to be discovered by christian Europeans.

71. IMSA Astrophysics: Distance Ladder was calculated to good precision by eratosthenes of cyrene (284 192 BC), So, how did Eratosthenes solve for the circumference of the earth from http://staff.imsa.edu/science/astro/astrometry/ground1.html

Distance and Size of the Moon Distance to the Sun Distance Ladder The Ground Floor: Circumference of the Earth Introduction Contrary to popular legend about people during Christopher Columbus' time believing the world is flat, the circumference of the spherical world was well known for over 1500 years prior to that time. 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). How did he do it? It all started when Eratosthenes read a story about a rather minor event that happened every year in Syene, a city located almost directly south of Alexandria, along the Nile River. Every year, on June 21st, the longest day of the year, at precisely noon, the sun's reflection could be seen in the water of the deepest wells. The author also noted that, at the same time, buildings and obelisks cast no shadows. Obviously the sun was directly overhead in Syene at that moment. Eratosthenes knew, also, that this phenomenon did not occur in Alexandria. This wouldn't make sense if the earth were flat. The ancient Greeks already knew that the sun was very far away, so far away that the rays of light striking the earth were essentially parallel. The sun could not be directly overhead in Syene and not be directly overhead in Alexandria if the world were flat. The only explanation for this difference was that the earth was round!

72. Singapore Science Centre ScienceNet Computer Science / IT eratosthenes of cyrene (c275c195 BC) was a Greek philosopher and mathematician.He also was the head of the great library at Alexandria. http://www.science.edu.sg/ssc/detailed.jsp?artid=540&type=6&root=1&parent=1&cat=

73. Euclidswindow It was first done in 212 BC by eratosthenes of cyrene. He noticed that at noonof the summer solstice a stick stuck perfectly upright in the ground in his http://www.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.

74. Eratosthenes And Archimedes 3) eratosthenes of cyrene (276194 BC). http//www.eranet.gr/eratosthenes/html/eoc.html. 3.What current country did Eratosthenes live? http://dal.lowell.smartedu.net/Giguere/skrekas/eras.html

Eratosthenes: 1) Eratosthenes Finds Diameter of Earth http://math.rice.edu/~ddonovan/Lessons/eratos.html 1a. Eratosthenes looked into a well and came up with the diameter and circumference of our planet. Where was he? 1b. How would email help do the same project much quicker? 2) Eratosthenes used geometry to estimate the circumference of the Earth http://astrosun.tn.cornell.edu/courses/astro201/eratosthenes.htm 2.What tilt of the Earth axis gives us the seasons? 3) Eratosthenes of Cyrene (276-194 BC) http://www.eranet.gr/eratosthenes/html/eoc.html 3.What current country did Eratosthenes live? 4) The Eratosthenes Project http://www.phys-astro.sonoma.edu/observatory/eratosthenes/ 5) Eratosthenes on pbs.org http://www.pbs.org/wnet/hawking/cosmostar/html/cstars_eratho.html 5. Who was Posidonius? 6) EratosthenesSieve http://mathworld.wolfram.com/EratosthenesSieve.html 6. This page shows an algorithm for making tables of what? Additional Information: Eratosthenes links http://www.knowdeep.org/eratosthenes/ B) From Wikipedia, the free encyclopedia, with sieve info. http://www.wikipedia.org/wiki/Eratosthenes

75. Bryn Mawr Classical Review 2003.05.14 Klaus Geus, Eratosthenes von Kyrene. Studien zur hellenistischen Kultur und at Alexandria between 246 and c.196 BC, eratosthenes of cyrene, came out. http://ccat.sas.upenn.edu/bmcr/2003/2003-05-14.html

Bryn Mawr Classical Review 2003.05.14 Klaus Geus, Word count: 2539 words At the time when the new library at Alexandria opened its gates, the first comprehensive monograph on the head librarian of the old library at Alexandria between 246 and c.196 BC, Eratosthenes of Cyrene, came out. This rich book is the somewhat revised version of Geus' Habilitationsschrift (post-doctoral thesis) at Bamberg University. Due to the universal interests of this Alexandrian scholar that comprised such diverse fields as philosophy, poetry, grammar, musical theory, history, chronography, mathematics, astronomy, and geography, nobody has tried to deal with life and the complete oeuvre of Eratosthenes in one book before. Geus' ambitious aim is to shape a full picture of this outstanding Hellenistic scholar and his "intellectual profile", including his significance for Hellenistic cultural history. He succeeds well and has produced a fine book, full of references, arguments and engaging details. The study of Eratosthenes is made difficult not only by the diversity of his interests, but also by the lack of a reliable edition of his fragments. The only collection that made an effort to include fragments from all fields, is the completely outdated Bernhardy of 1822 (repr. 1968). Other old editions give parts of the fragments: Berger the geographical, Strecker those on the old comedy, Powell the poetic, Jacoby the chronographical and some miscellaneous. The book contains 12 chapters, bibliography and two indices (that of passages includes references by fragment numbers to the diverse collections; the other one refers to names and subjects). Several line drawings illustrate difficult details. Chapters IV-XI deal with Eratosthenes' works according to his fields of interest. Each of these chapters is prefaced by the evidence, giving the references where possible pointing to the relevant collections of Eratosthenes' fragments supplemented by new fragments, mentioning those which have been dismissed, and the relevant literature.

76. When Is A Triangle Not A Triangle In the third century BCE, the Greek polymath eratosthenes of cyrene calculated the eratosthenes of cyrene (276–196 BCE), the sometime Librarian of 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.

77. Linux Cluster Workshop - Finding Prime Numbers The inventor of this algorithm is eratosthenes of cyrene (276 BC 194 BC).Basically, the algorithm begins with an unmarked array of integers from 2 to n. http://www.cs.hku.hk/linux-workshop/workshop01/prime.htm

Linux Cluster Workshop - Finding prime numbers Introduction Finding the number of prime numbers using Sieve of Eratosthenes in a cluster of machines Original author: Michael J. Quinn Some modifications have been made by CS Department, HKU to make it more stable Sieve of Eratosthenes - Definition It is an algorithm that finds all prime numbers up to a certain integer n. The inventor of this algorithm is Eratosthenes of Cyrene (276 BC - 194 BC). Basically, the algorithm begins with an unmarked array of integers from 2 to n. The first unmarked integer, 2, is the first prime number. All of its multiples, e.g. 4, 6, etc., up to n, are marked in the array. The following iterations start from the next unmarked integer, takes that integer as a prime number, and mark every multiples of that prime number. The algorithm ends when there is no more numbers that is unmarked. The find-prime.c program The program finds the number of prime numbers starting from 2 to a certain integer decided by the user based on Sieve of Eratosthenes. Instead of using one single machine to do so, the program splits the job and finds the result using a cluster of machines. The job is partitioned by giving each machine one region of the array of integers to mark. Its implementation is done by using MPI - the Message Passing Interface standard.

78. A161, Lecture 4 Measurement of Earth s circumference, by eratosthenes of cyrene in 3rd CenturyBC, a major accomplishment of Ancient Greek science. Heard that, in Syene, http://www-astronomy.mps.ohio-state.edu/~dhw/A161/lecture4.html

LECTURE 4: ANCIENT GREEK ASTRONOMY Reading for lectures 4, 5, and 6: Chapter 4-1 through 4-5. Key Questions: Why did ancient Greek philosophers believe in a spherical Earth? Why did most of these philosophers believe in a geocentric (Earth-centered) cosmos? What was the Aristotle/Eudoxus model of the cosmos? What were its strengths and weaknesses? How did Eratosthenes measure the size of the Earth? How did Aristarchus infer the distances and sizes of the Moon and the Sun? Why did Aristarchus advocate a heliocentric (Sun-centered) cosmos? Many ancient cultures carried out extensive astronomical observations, used them for calendar keeping, and incorporated them in religious rituals. As far as we know, only the ancient Greeks developed sophisticated models to explain what they saw. SPHERICAL EARTH Ancient Greek philosophers argued Earth was a sphere, on several grounds: Sphere a "perfect" shape. Ships disappear over horizon. Positions of constellation above horizon change as one goes north or south. Earth casts round shadow on Moon during a lunar eclipse.

79. Active Skim View Of: 7. The Golden Key, And An Improved Prime Number Theorem The Golden Key is, in fact, just a way that Leonhard Euler found to express thesieve of Eratosthenes in the language of analysis.34 eratosthenes of cyrene http://www.nap.edu/nap-cgi/skimit.cgi?isbn=0309085497&chap=99-117

80. Welcome To Turkey In Maps WORLD ACCORDING TO ERATOSTHENES, c. 194 BC. A 19th century reconstruction of theworld 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.

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