21. Ancient Greece Mathematics Timeline Birth of eratosthenes of cyrene (at?s? ? ?a?). About 270 BC Death ofEuclid. About 260250 BC. Archimedes of Syracuse contributed numerous http://www.mlahanas.de/Greeks/TLMathematics.htm

Mathematics Timeline : Ancient Greece Griechische Mathematik, Zeitlinie, Ereignisse Around 600 BC the Cretan poet Epimenides (Επιμενίδης o Κρης) is attributed to have invented the linguistic paradox with his phrase "Cretans are ever liars" - the Liar's Paradox. 2500 years later, the mathematician Kurt Gödel invents an adaptation of the Liar's Paradox that reveals serious axiomatic problems at the heart of modern mathematics. Thales of Miletus About 530 BC Pythagoras no common rational measure is discoverable About 480 BC Parmenides of Elea (Παρμενίδης ο Ελεάτης) founded the Eleatic School where he taught that 'all is one,' not an aggregation of units as Pythagoras had said, and that to arrive at a true statement, logical argument is necessary. Truth "is identical with the thought that recognizes it" (Lloyd 1963:327). Change or movement and non-being, he held, are impossibilities since everything is 'full' and 'nothing' is a contradiction which, as such, cannot exist. "Parmenides is said to have been the first to assert that the Earth is spherical in shape...; there was, however, an alternative tradition stating that it was Pythagoras" (Heath 1913:64). Corollary to Parmenides' rejection of the existence of 'nothing' is the Greek number system which, like the later Roman system, refused to use the Babylonian positional number system with its marker for 'nothing.' Making no clear distinction between nature and geometry, "mathematics, instead of being a science of possible relations, was to [the Greeks] the study of situations thought to subsist in nature" (Boyer 1949:25). Moreover, "almost everything in [Greek] philosophy became subordinated to the problem of change.... All temporal changes observed by the senses were mere permutations and combinations of 'eternal principles,' [and] the historical sequence of events (which formed part of the 'flux') lost all fundamental significance" (Toulmin and Goodfield 1965:40).

22. Greek Scientists of the great poet Callimachus was eratosthenes of cyrene (c.275192 BCE), Eratosthenes was nicknamed bêta or number two , because in no branch of http://www.livius.org/gi-gr/greeks/scientists.html

home index ancient Greece portrait gallery Greek scientists Authors Historians Philosophers Politicians Scientists We know almost nothing about Thales of Miletus . Later generations told many anecdotes about this wise man, but it is difficult to verify the reliability of these stories. What seems certain is that he predicted the solar eclipse of 28 May 585, which was remembered because the Lydian king Alyattes and the Median leader Cyaxares were fighting a battle on that day. Another reliable bit of information is that he did some geometrical research, which enabled him to measure the pyramids. However, his most important contribution to physics and philosophy is his attempt to give non-religious, rational explanations for physical phenomena. Behind the phenomena was not a catalogue of deities, but one single, original principle. Although his hypothesis that this principle was water is rather unfortunate, his idea to look for deeper causes was the true beginning of philosophy and science. One of the solutions to the problem postulated by Parmenides of Elea , was the hypothesis of Democritus of Abdera that matter was made up from atoms. There was no real evidence for this idea (which was not completely new), but is explained why change was possible. The atoms were always moving and clustering in various, temporary combinations. Therefore, things seemed to change, but 'not being' never changed into 'being'. (It was assumed that 'not being' was a vacuum, which means that it is in fact not a 'not being' because a vacuum exists in at least four dimensions.) The consequence of this idea is that we are allowed to use our senses, although Democritus warns us to be careful.

23. An Ancient Assessment Of Alexander The Great The Alexandrinian scientist eratosthenes of cyrene published his topographicalstudies in the third century BCE. They are now lost, but the geographer http://www.livius.org/aj-al/alexander/alexander_t33.html

home index ancient Persia ancient Greece ... Alexander An ancient assessment of Alexander the Great The Alexandrinian scientist Eratosthenes of Cyrene published his topographical studies in the third century BCE. They are now lost, but the geographer Strabo of Amasia quotes their conclusion in his Geography Alexander was responsible for a new opinion about civilization and barbarism. The translation was made by L. Jones. Eratosthenes ( Now, towards the end of his treatise -after withholding praise from those who divide the whole multitude of mankind into two groups, namely Greeks and Barbarians, and also from those who advised Alexander to treat the Greeks as friend but the Barbarians as enemies- Eratosthenes goes on to say that it would be better to make such divisions according to good and bad qualities; for not only are many of the Greeks bad, but many of the Barbarians are refined - Indians and Arians for example, and, further, Romans and Carthaginians , who carry on their governments so admirably. And this, Eratosthenes says, is the reason why Alexander, disregarding his advisers, welcomed as many as he could of the men of fair repute an did them favors. home index ancient Persia ancient Greece ... Alexander

24. TMTh:: ERATOSTHENES OF CYRENE eratosthenes of cyrene (fl. 276 194 BC). Life One of the greatest of the ancientGreek sages and the first great geographer of the ancient world, http://www.tmth.edu.gr/en/aet/2/43.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS ASTRONOMER, GEOGRAPHER ERATOSTHENES OF CYRENE (fl. 276 - 194 BC) Life One of the greatest of the ancient Greek sages and the first great geographer of the ancient world, Eratosthenes is considered the founder of physical and mathematical geography. He studied in Athens with Ariston of Chios and Archesilaus, then moved to Alexandria, where he spent most of the rest of his life. Ptolemy III Euergetes appointed him director of the famous Library of Alexandria. It was Eratosothenes who coined the term "philologist". Archimedes, his senior by 11 years, held him in very high esteem, and dedicated two of his works to him: "On the Method of Mechanical Theorems" and "The Cattle Problem". He is cited by Stobaeus. One of the moon's craters has been named "Eratosthenes" in his honour. Work His principal works are: "Proof of the sphericity of the earth": In this work Eratosthenes employed a method still used in modern astronomy, which was based on four assumptions: A) At Syene (now Aswan, in Upper Egypt), which is in the Tropic of Cancer, the sun's rays fall vertically at noon at the summer solstice.

25. Eratosthenes Of Cyrene eratosthenes of cyrene. bc 276 BC, Cyrene, Libya dc 194, Alexandria, Egypt.Greek scientific writer, astronomer, and poet, the first man known to have http://www.omhros.gr/Kat/History/Greek/Sc/Eratosthenes.htm

Eratosthenes Of Cyrene b. c. 276 BC, Cyrene, Libya d. c. 194, Alexandria, Egypt Greek scientific writer, astronomer, and poet, the first man known to have calculated the Earth's circumference. At Syene (now Aswan), some 800 km (500 miles) southeast of Alexandria in Egypt, the Sun's rays fall vertically at noon at the summer solstice. Eratosthenes noted that at Alexandria, at the same date and time, sunlight fell at an angle of about 7 from the vertical. He correctly assumed the Sun's distance to be very great; its rays therefore are practically parallel when they reach the Earth. Given estimates of the distance between the two cities, he was able to calculate the circumference of the Earth. The exact length of the units (stadia) he used is doubtful, and the accuracy of his result is therefore uncertain; it may have varied by 0.5 to 17 percent from the value accepted by modern astronomers. He also measured the degree of obliquity of the ecliptic (in effect, the tilt of the Earth's axis) with great accuracy and compiled a star catalog. His mathematical work is known principally from the writings of Pappus of Alexandria. 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.

26. Science: Mathematics: Mathematicians: Eratosthenes Of Cyrene - Open Site Science Mathematics Mathematicians eratosthenes of cyrene Open Site. http://open-site.org/Science/Mathematics/Mathematicians/Eratosthenes_of_Cyrene/

Open Site The Open Encyclopedia Project home submit content become an editor the entire directory only in Mathematicians/Eratosthenes_of_Cyrene Top Science Mathematics Mathematicians : Eratosthenes of Cyrene Section Index Biography Influences Achievements and Awards Publications of Importance Inventions or Contributions to Knowledge Other Areas of Interest Internet Links of Significance Biography Eratosthenes was born 276 BC in Cyrene, North Africa, which is now Shahhat in Libya. He died in 194 BC in Alexandria, Egypt. It is he became blind in old age and further that he died as a result of self imposed starvation. Influences Lysanias of Cyrene Ariston of Chios ( educted by Zeno, the founder of the Stoic school of philosophy) Callimachus of Cyrene Achievements and Awards Publications of Importance Platonicus None in existence On means None in existence On the measurement of the Earth None in existence Hermes a poem Inventions or Contributions to Knowledge Mathematics Measurement of the circumference of the Earth.Details of his calculations appear in works by Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.

27. Eratosthenes eratosthenes of cyrene. A postulate of spherical astronomy is that the Earth isa small point in relation to the heavenly bodies. http://share2.esd105.wednet.edu/jmcald/Aristarchus/eratosthenes.html

Eratosthenes of Cyrene A postulate of spherical astronomy is that the Earth is a small point in relation to the heavenly bodies. From this Eratosthenes reasoned the Sun's rays strike the Earth parallel over its entire surface. Working in Syene and Alexandria, which Eratosthenes assumed were on the same meridian, he estimated the distance between the cities to be about 5,000 stades (a stade is believed to be about 559 feet - approximately one-tenth of a mile). At summer solstice, at noon, the Sun cast no shadow in Syene, but in Alexandria a shadow was visible. Using a gnomon (a vertical stick), Eratosthenes measured the shadow's angle to be about one-fiftieth of a circle. Using this result, r = 39,788.7 stades = 22,241,883.3 feet = 4,212.5 miles (The actual radius of the Earth is 3,963.21 miles) Using the work of Aristarchus with that of Eratosthenes we find: The radius of the Moon is, (The actual radius of the Moon is 1,080 miles) Since the radius of the Sun is, miles (The actual radius of the Sun is approximately 433,200 miles) Home History Half-Moon Solar Eclipse ... Apparent Diameter

28. Malaspina.com - Eratosthenes Of Cyrene (ca. 276-ca. 196 BC) Research bibliography, books and links to 1000 other interdisciplinary entriescompiled by Russell McNeil. http://www.mala.bc.ca/~mcneil/eratos1.htm

Eratosthenes of Cyrene (ca. 276-ca. 196 BC) [MacTutor] Great Books Biography [Malaspina] Amazon Search Form] Library of Congress Online Citations [LC] Library of Congress Offline Citations [MGB] COPAC UK Online Citations [COPAC] Free Online Practice Exams [Grad Links] Canadian Book Orders! Chapters-Indigo Save on Textbooks! [Study Abroad] Used Books Search Form Alibris Dummies Books Amazon Books from Amazon Amazon EBay! Ebay Books from Amazon UK Amazon UK Books from Chapters Canada [Orders through Chapters The librarian who measured the earth Amazon Eratosthenes of Cyrene Amazon The Sieve of Eratosthenes [MacTutor, St. Andrews] Additional Biography [University of Virginia] More on the sieve of Eratosthenes [Jim Carlson] Map of the World according the Eratosthenes of Cyrene Top of Page

29. Eratosthenes “Eratosthenes Who Was eratosthenes of cyrene”. http//www.eranet.gr/eratosthenes/html/eoc.html O Conner, JJ and Robertson, EF “Eratosthenes ofCyrene”. http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/eros.html

Eratosthenes Eratosthenes was an important mathematical figure of ancient Greece. Among his accomplishments was the accurate measurement of the earth's circumference. He also wrote works on mathematics, geography, philosophy, and astronomy. Although many of his works have been lost, historians have uncovered a substantial amount of information about important events in his life and his accomplishments. Q: Where were you born and where did you grow up? A: I was born in Cyrene, Greece (which is present-day Libya, in South Africa), in 276 B.C. Both of my parents were Greek and there, on the coast of Africa, I grew up. Q: Did you have any nicknames growing up? A: I did have one; my friends called me Beta, which is the second letter of the Greek alphabet. They teased with me, saying I fell just short of first place (which was occupied by Archimedes). Later on in my life, I received the nickname Pentathlos. It's funny, because literally this word refers to an athlete that participated in 5 sporting events, but eventually was used to describe someone who was well-rounded, or good at several different things. Q: What was your childhood like?

30. Eratosthenes Of Cyrene (ca. 284-ca. 192 BC) -- From Eric Weisstein's World Of Sc eratosthenes of cyreneDRAFT. eratosthenes of cyrene. History of Computing People A B C D E F G H I J K L M N O P Q R S T U http://www.astro.virginia.edu/~eww6n/bios/Eratosthenes.html

Branch of Science Astronomers Branch of Science Geographers ... Greek Eratosthenes of Cyrene (ca. 284-ca. 192 BC) Consummate Greek scholar whose status as second best in each field earned him the nickname "Beta." He served as librarian at the great library in Alexandria, and wrote works of mathematics, geography, philosophy, and astronomy. He also wrote a poem called Hermes which described the fundamentals of astronomy in verse! Although most of Eratosthenes' writings are lost, many are preserved through the writings of commentators. Among Eratosthenes' accomplishments was the accurate measurement the diameter of the Earth by observing that, on the day of the summer solstice the Sun zenith in Alexandria, which he assumed was due north of Syene (Dunham 1990). Unfortunately, since the original work On the Measurement of the Earth was lost, the details of Eratosthenes' procedure are not known. Eratosthenes also determined the obliquity of the ecliptic prepared a star map containing 675 stars suggested that a leap day be added every fourth year, tried to construct an accurately-dated history, and developed the " sieve of Eratosthenes " method of finding

31. Eratosthenes Of Cyrene (c.276-c.194 B.C.) eratosthenes of cyrene (c.276c.196 BC) He compared the midsummer’s noonshadow in deep wells in Cyrene (now Aswan on the Nile in Egypt) and Alexandria. http://www.daviddarling.info/encyclopedia/E/Eratosthenes.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Eratosthenes of Cyrene (c.276-c.196 B.C.) ancient philosophy, related to the possibility of extraterrestrial life GREEK ASTRONOMY BACK TO TOP var site="s13space1234"

32. Eratosthenes eratosthenes of cyrene (276 BC. Cyrene, North Africa Alexandria, Egypt, 194 BC.)One of Eratosthenes teachers was Ariston of Chios, who studied under http://www.mathsisgoodforyou.com/people/eratosthenes.htm

Eratosthenes home courses topics theorems ... timeline Eratosthenes of Cyrene (276 BC. Cyrene, North Africa - Alexandria, Egypt, 194 BC.) One of Eratosthenes' teachers was Ariston of Chios, who studied under Zeno, who himself was a founder of the Stoic school of Philosophy. His other teaher, Callimachus became the librarian of the Alexandrian library - one of the greatest libraries that ever were, which holdings included hundreds of thousands of papyri and vellum scrolls. Eratosthenes went to Alexandria with Callimachus and when Callimachus died in about 240BC, Eratosthenes became a new librarian. He was a third librarian of this famous library. Eratosthenes will always be remembered for his ingenuity in measuring the circumference of Earth. He gave a surprisingly accurate measurement - and this obviously involved his insight that Earth was a sphere. The details of the measurement were given in his book On the measurement of the Earth which is now lost. Other writers have, however, written on it, so we know that this measurement came from Eratosthenes. Another great achievement of Eratosthenes was his invention of the calendar that included leap years. Once he did this, he tried to make a comprehensive history of all major events which happened to his time since the siege of Troy.

33. Encyclopedia Of Astronomy And Astrophysics » Eratosthenes Of Cyrene (c. 276†eratosthenes of cyrene (c. 276–c. 196 BC). DOI 10.1888/0333750888/3607; PublishedNovember 2000. Icon Full text (PDF, 19K) http://eaa.iop.org/index.cfm?action=summary&doc=eaa/3607@eaa-xml

34. Who Was Who In Roman Times: Data On Persons: Eratosthenes Of Cyrene Index to Romans, Greek mythology, Early Christianity and images thereof. http://www.romansonline.com/persns.asp?IntID=4012&Ename=Eratosthenes of Cyrene

35. Data On Eratosthenes Of Cyrene(4012) Function Scientist Quotes Data on eratosthenes of cyrene(4012). Function Scientist Quotes regardingeratosthenes of cyrene No image available Important year 305 BC http://www.romansonline.com/FR_Prs_Menu.asp?IntID=4012&Ename=Eratosthenes of Cyr

36. PSIgate - Physical Sciences Information Gateway Search/Browse Results eratosthenes of cyrene Born 276 BC in Cyrene, North Africa (now Shahhat, Eratosthenes eratosthenes of cyrene (bc 276 BC, Cyrene, Libyadc 194, http://www.psigate.ac.uk/roads/cgi-bin/search_webcatalogue.pl?term1=Eratosthenes

37. Eratosthenes--References eratosthenes of cyrene. University of Utah. eratosthenes of cyrene. O Connor,JJ, and Robertson, EF Cited January 25, 2002. The picture on the left and http://www.albertson.edu/math/History/emacy/Classical/references.htm

ACI Math Department Eratosthenes of Cyrene (276-194 b.c.) Eratosthenes biography historical setting discovery ... Math History References and Interesting Links Eratosthenes of Cyrene. University of Utah. Cited January 25, 2002. http://www.math.utah.edu/~alfeld/Eratosthenes.html Encyclopedia.com. Electric Library. Cited January 25, 2002 http://www.encyclopedia.com/articles/04184.html This link has a diagram showing the manner in which Eratosthenes measured the circumference of the earth. http://astrosun.tn.cornell.edu/courses/astro201/eratosthenes.html Follow this link for an experiment for high school geometry students. This site gives detailed instructions in how to proceed with a cooperative effort among school. Use of satellite uplinks is recommended in order to share results in real time. http://math.rice.edu/~ddonovan/Lessons/eratos.html Eratosthenes of Cyrene. O'Connor, JJ, and Robertson, E. F. Cited January 25, 2002. The picture on the left and throughout this site comes from this article. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html

38. PowerBasic Crypto Archives News eratosthenes of cyrene Links http//wwwgap.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html Back to The Archives. http://www.pbcrypto.com/greatminds/eratosthenes.php

Eratosthenes of Cyrene Links: http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html Back to The Archives

39. PowerBasic Crypto Archives - The Sieve Of Eratosthenes NAME The Sieve of Eratosthenes CREATOR eratosthenes of cyrene 276 196 BC PBAUTHOR Frank Ferrell DESCRIPTION Search for prime numbers using the Sieve http://www.pbcrypto.com/view.php?algorithm=dos-eratosthenes

40. Math History - Pre-historic And Ancient Times About 235BC, eratosthenes of cyrene estimates the Earth s circumference with About 230BC, eratosthenes of cyrene develops his sieve method for finding http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MpreAndAncient.

Math History Timeline Pre-historic and Ancient Times 1,000,000 B.C. - 500 A.D. Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... 20th Century ... non-Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... External Resources About 30000BC Palaeolithic peoples in central Europe and France record numbers on bones. About 25000BC Early geometric designs used. About 4000BC Babylonian and Egyptian calendars in use. About 3400BC The first symbols for numbers, simple straight lines, are used in Egypt. About 3000BC Babylonians begin to use a sexagesimal number system for recording financial transactions. It is a place-value system without a zero place value. About 3000BC Hieroglyphic numerals in use in Egypt. About 3000BC The abacus is developed in the Middle East and in areas around the Mediterranean. A somewhat different type of abacus is used in China. About 1950BC Babylonians solve quadratic equations.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 2     21-40 of 93    Back | 1  | 2  | 3  | 4  | 5  | Next 20