21. ThinkQuest Library Of Entries ¥±. The greek mathematics Demonstrative Geometry. ßCharacteristicof greek mathematics In the 600 BC Mathematics was focused http://library.thinkquest.org/22584/temh2200.htm

Welcome to the ThinkQuest Internet Challenge of Entries The web site you have requested, Mathematics History , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Mathematics History click here Back to the Previous Page The Site you have Requested ... Mathematics History click here to view this site A ThinkQuest Internet Challenge 1998 Entry Click image for the Site Languages : Site Desciption An extensive history of mathematics is at your fingertips, from Babylonian cuneiforms to advances in Egyptian geometry, from Mayan numbers to contemporary theories of axiomatical mathematics. You will find it all here. Biographical information about a number of important mathematicians is included at this excellent site. Students Hyun-jin Jae-yun Hwang(Seoul Yo Sang) Korea, South Kyung-sun Jae-yun Hwang(Seoul Yo Sang) Korea, South So-young Jae-yun Hwang(Seoul Yo Sang) Korea, South

22. Basic Ideas In Greek Mathematics Basic Ideas in greek mathematics. Michael Fowler. University of Virginia. http://landau1.phys.virginia.edu/classes/109/lectures/greek_math.htm

Basic Ideas in Greek Mathematics Michael Fowler University of Virginia Index of Lectures and Overview of the Course Link to Previous Lecture Closing in on the Square Root of 2 In our earlier discussion of the irrationality of the square root of 2, we presented a list of squares of the first 17 integers, and remarked that there were several "near misses" to solutions of the equation m n . Specifically, 3 + 1. These results were also noted by the Greeks, and set down in tabular form as follows: After staring at this pattern of numbers for a while, the pattern emerges: 3 + 2 = 5 and 7 + 5 = 12, so the number in the right-hand column, after the first row, is the sum of the two numbers in the row above. Furthermore, 2 + 5 = 7 and 5 + 12 = 17, so the number in the left-hand column is the sum of the number to its right and the number immediately above that one. The question is: does this pattern continue? To find out, we use it to find the next pair. The right hand number should be 17 + 12 = 29, the left-hand 29 + 12 = 41. Now 41 = 1681, and 29

23. A History Of Greek Mathematics, Vol. 2 Click to enlage A History of greek mathematics, Vol. 2 Sir Thomas Heath. Our Price,$14.95. Availability In Stock. (Usually ships in 24 to 48 hours). Format Book. http://store.doverpublications.com/0486240746.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Astronomy Biology and Medicine Bridge and Other Card Game...... Chemistry Chess Children Consumer Catalogs Cookbooks, Nutrition Crafts Detective Stories, Science...... Dover Phoenix Editions Earth Science Engineering Ethnic Interest Features Science Gift Certificates Gift Ideas Giftpack History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Mathematics Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Physics Psychology Puzzles, Amusement, Recrea...... Reference Specialty Stores Sports, Out-of-door Activi...... Science and Mathematics Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies By Subject Science and Mathematics General Science A History of Greek Mathematics, Vol. 2 Sir Thomas Heath Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Volume 2 of an authoritative coverage of essentials of mathematics, every important innovation, every important figure—Euclid, Apollonius, others. Total in set: 262 illustrations.

24. A History Of Greek Mathematics, Vol. 1 Click to enlage A History of greek mathematics, Vol. 1 Sir Thomas Heath. Our Price,$14.95. Availability In Stock. (Usually ships in 24 to 48 hours). Format Book. http://store.doverpublications.com/0486240738.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Astronomy Biology and Medicine Bridge and Other Card Game...... Chemistry Chess Children Consumer Catalogs Cookbooks, Nutrition Crafts Detective Stories, Science...... Dover Phoenix Editions Earth Science Engineering Ethnic Interest Features Science Gift Certificates Gift Ideas Giftpack History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Mathematics Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Physics Psychology Puzzles, Amusement, Recrea...... Reference Specialty Stores Sports, Out-of-door Activi...... Science and Mathematics Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies By Subject Science and Mathematics General Science A History of Greek Mathematics, Vol. 1 Sir Thomas Heath Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Volume 1 of an authoritative coverage of essentials of mathematics, every important innovation, every important figure—Euclid, Apollonius, others. Total in set: 262 illustrations.

25. Math Lair - Ancient Greek Mathematics History Click Here! Ancient greek mathematics History. View a note on thesetimelines. 600 BC Thales introduces deductive geometry. It was http://www.stormloader.com/ajy/greek.html

Ancient Greek Mathematics History View a note on these timelines 600 B.C. Thales introduces deductive geometry. It was developed over the years by Pythagoras and the Pythagoreans, Plato, Aristotle, Euclid, and others. 540 B.C. Pythagoras does geometrical work. 450 B.C. Zeno of Elea (489 B.C. - 430? B.C.) formulates Zeno's paradox 380 B.C. Plato, whose ideas were influenced by the Pythagoreans, is writing philosophy. 340 B.C. Aristotle is writing philosophy. 300 B.C. Euclid compiles, organizes and systematizes geometric ideas which had been discovered and proven into thirteen books, called The Elements 240 B.C. Eratosthenes determines that the Earth is spherical and computes its diameter. 225 B.C. Archimedes (287 B.C. - 212 B.C.) does work on circles, spheres, areas, infinite series, and other things. 225 B.C. Appolonius works on conic sections If you're using , you can view a graphical timeline of famous mathematicians . If you're not, a text version may be more to your liking. After this point, see Greco-Roman mathematical history The main number system used by the Greeks during this period was the Attic system.

26. KLUWER Academic Publishers | The Beginnings Of Greek Mathematics Books » The Beginnings of greek mathematics. The Beginnings of GreekMathematics. Kluwer Academic Publishers is pleased to make this http://www.wkap.nl/prod/b/90-277-0819-3

Title Authors Affiliation ISBN ISSN advanced search search tips Books The Beginnings of Greek Mathematics The Beginnings of Greek Mathematics Kluwer Academic Publishers is pleased to make this title available as a special Printing on Demand (PoD) edition. PoD books will be sent to you within 6-9 weeks of receipt of your order. Firm orders only!: returns cannot be accepted as PoD books are only printed on request. Add to cart by translated by A.M. Ungar Book Series: SYNTHESE HISTORICAL LIBRARY Volume 17 D. Reidel Publishing Company Hardbound, ISBN 90-277-0819-3 November 1978, 358 pp. Printing on Demand EUR 192.50 / USD 243.00 / GBP 146.75 Home Help section About Us Contact Us ... Search

27. The Golden Age Of Greek Mathematics THE GOLDEN AGE OF greek mathematics. The Death of Alexander the Gratled to internal strife but by 306BC control of the Egyptian http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/gagm.htm

THE GOLDEN AGE OF GREEK MATHEMATICS The Death of Alexander the Grat led to internal strife but by 306BC control of the Egyptian portion of the empire was in the hands of Ptolemy 1. He established a school at Alexandria and Euclid became a teacher there. 5 works of Euclid have survived ' Elements ', 'Data', 'Division of Figures', Phaenomena' and 'Optics'. Euclid was a good teacher - no new discovery is attributed to him, he just wrote 'Elements' as a textbook. University students were being presented with a textbook ('Elements') which gave them the fundamentals of elementary mathematics (geometry and algebra). 'Elements' is divided into 13 books of which the first half dozen were at elementary plane geometry next 3 on numbers, book X on incommensurables and the last 3 on solid geometry. Euclid's 'Elements' - Book 1 The book opens with a list of 23 definitions. Definitions do not really define because they use words which are no better known than the word being defined. eg. The Euclidean definition of a plane angle as "the inclination to one another of 2 lines in a plane which meet one another and do not lie in a straight line" is not very good because inclination has not being previously defined and is not better known than the word "angle". Following the definitions Euclid listed 5 postulates and 5 common notions (axioms).

28. Read This: The Shaping Of Deduction In Greek Mathematics Read This! The MAA Online book review column review of The Shapingof Deduction in greek mathematics, by Reviel Netz. Read This! http://www.maa.org/reviews/netz.html

Read This! The MAA Online book review column The Shaping of Deduction in Greek Mathematics A study in cognitive history by Reviel Netz Reviewed by Christian Marinus Taisbak Reviel Netz has written an stimulating book about diagrams and mathematics, telling us facts that we all know, but hardly ever thought of. Thus he sets himself in the best of company, for isn't that what Euclid did from the very first proposition in the Elements? "The diagram is the metonym of mathematics" is RN's main claim. To understand what he means by that, think of two typical situations in the circus of conferences: if a philosopher or historian gives a talk, he will read aloud for half an hour, facing his audience without moving from his chair. If a mathematician gives a talk, he will dance around the platform talking to the blackboard while writing figures and letters on it, most of the time ignoring his audience and concentrating on his written deductions as they emerge out of sheer necessity. Years ago David Fowler (of Plato's Academy ) coined a motto: "Greek mathematics is to draw a figure and tell a story about it." RN has widened and deepened this into "Deductive mathematics grew out of the Greeks drawing lettered diagrams and telling stories by means of them, not only about them." The diagram and the argument live in such a close symbiosis that one cannot be understood without the other. The diagram is the metonym of mathematics.

29. Nardia Symonds : Greek Mathematics Nardia Symonds gives a survey of the history of greek mathematics as part of theassessment for the Honours Pure Mathematics subject 'History of Mathematics http://www.maths.adelaide.edu.au/pure/pscott/history/nardia/symonds1.htm

History of Greek Mathematics Thales Pythagoras Zeno Euclid ... Archimedes Timeline All dates are BCE INDEX Links to related sites

30. Nardia Symonds : Greek Mathematics Pythagoras gained an interest in mathematics, astronomy and travelling,from Thales. However most of what he was taught was by Anazimander http://www.maths.adelaide.edu.au/pure/pscott/history/nardia/symonds3.htm

Thales Pythagoras Zeno Euclid Eratosthenes Archimedes Pythagoras of Samos 500 BC Pythagoras gained an interest in mathematics, astronomy and travelling, from Thales. However most of what he was taught was by Anazimander, Thales pupil, whose ideas left an impression on Pythagoras. There is not much that is known about the actual work of Pythagoras and the secrecy of his community makes it difficult to distinguish between his work and the work of the community. The work of the Pythagoreans was great and their contributions to mathematics, outstanding. They were interested in the principles of mathematics, concepts and abstract ideas of proof, rather than solving physical problems. The Pythagoreans believed all relations could be reduced to numbers. From this they classified numbers; some of their classfications include: female (even), male (odd), triangular, square, prime, composite or perfect. Today, Pythagoras is remembered for his famous geometry theorem. It is believed that, although the Babylonians knew of this theorem 1000 years earlier, Pythagoras was the first to prove it. Next page Greek Mathematics home page

31. About "Basic Ideas In Greek Mathematics" Basic Ideas in greek mathematics. Library Home Full Table of Contents Suggest a Link Library Help Visit this site http//galileoandeinstein http://mathforum.org/library/view/41703.html

Basic Ideas in Greek Mathematics Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://galileoandeinstein.physics.virginia.edu/lectures/greek_math.htm Author: Michael Fowler; University of Virginia Description: Lecture notes from a course entitled "Galileo and Einstein." Nailing down the square root of 2. Zeno's paradoxes: Achilles and the tortoise. Proving an arrow can never move - analyzing motion, the beginning of calculus. How Archimedes calculated Pi to impressive accuracy, squared the circle, and did an integral to find the area of a sphere. Levels: High School (9-12) College Languages: English Resource Types: Course Notes Math Topics: Imaginary/Complex Numbers Pi Euclidean Plane Geometry History and Biography ... Search http://mathforum.org/ webmaster@mathforum.org

32. [HM] Is Greek Mathematics The *real* Thing? a topic from HistoriaMatematica Discussion Group HM Is greek mathematics the*real* thing? post a message on this topic post a message on a new topic http://mathforum.org/epigone/historia_matematica/fringblingshu/

a topic from Historia-Matematica Discussion Group [HM] Is Greek mathematics the *real* thing? post a message on this topic post a message on a new topic 2 Nov 1998 [HM] Is Greek mathematics the *real* thing? , by Julio Gonzalez Cabillon 2 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by barnabas hughes 2 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Glen Van Brummelen 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Gordon Fisher 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by George Gheverghese Joseph 6 Nov 1998 [HM] Is Greek mathematics the *real* thing? , by Moshe' Machover 6 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Jeremy Smith 9 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by kermit@polaris.net 9 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Jeremy Smith 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Daryn Lehoux 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing? , by Roger Cooke 3 Nov 1998 Re: [HM] Is Greek mathematics the *real* thing?

33. C. 4th Greek Mathematics Day 17 4th century greek mathematics. Summary. Development 190. R. Netz,The Shaping of Deduction in greek mathematics, 272311. On to Day 18. http://it.stlawu.edu/~dmelvill/323/Day17.html

Day 17: 4th century Greek mathematics Summary Development of mathematics in the 4th century up to Alexander. Who developed mathematics? How many mathematicians were there? Where did they live? How did they communicate? What topics interested them? We will pay particular attention to Theaetetus and Eudoxus. In the readings, look especially at the ideas of ratio and proportion. Reading B.L. van der Waerden, Science Awakening R. Netz, The Shaping of Deduction in Greek Mathematics On to Day 18 Up to Ancient and Classical Mathematics Last modified: 21 October 2001 Duncan J. Melville Comments to dmelville@stlawu.edu

34. Exam 2: Greek And Hellenistic Mathematics Discuss the role of computation in greek mathematics. Discuss the idea of definitionsin greek mathematics. Discuss the role of patronage in greek mathematics. http://it.stlawu.edu/~dmelvill/323/Day26.html

Day 26: Exam 2 Coverage This second exam will cover the material since the first exam. That is, Greek and Hellenistic mathematics. Some of the topics you should be familiar with are: geography of the Mediterranean littoral: Miletus, Samos, Athens, Alexandria, Syracuse, Pergamum; dates at which various centers flourished: Plato's Academy, Alexandria; location, date, sources and significance of the contributions of: Plato, Eudoxus, Theaetetus, Euclid, Archimedes, Apollonius; Greek numerical systems; 'fractions'; Greek arithmetic and the abacus; arithmetical tables; Pythagorean number theory; incommensurability: side and diagonal arguments; classification of 'irrationals'; numbers and magnitudes; ratio and proportion; axiomatic presentation of mathematics; Platonic mathematical philosophy: the nature of forms; the Platonic curriculum: use and purpose of mathematics; actual usage and purpose of mathematics in the classical world; Netz's analysis of classical mathematics and mathematicians; sources and transmission in the classical world: how mathematicians learned and corresponded;

35. ¥±. The Greek Mathematics : Demonstrative Geometry ?. The greek mathematics Demonstrative Geometry. Characteristicof greek mathematics In greek mathematics after Euclid. One http://seoul-gchs.seoul.kr/~contest/tq/mathematics/temh2200.htm

HOME Back Graphic Version ¥±. The Greek Mathematics : Demonstrative Geometry ¢º Characteristic of Greek Mathematics ¢º Pythagorean Mathematics ¢º The Three Famous Problems ¢º Greek Mathematics After Euclid ¡ßCharacteristic of Greek Mathematics In the 600 B.C. Mathematics was focused as a study and a science in the ancient Greek as a matter of course in China, India and Babylonia and to learn Geometry in Egypt. Thales, Pythagoras and Plato in Greek studied in Egypt and joined with Egypt culture Greek produced achivements at mathematics formed a term of now civilization accepting the Egypt culture. That is "Elements" of Euclid, "The Theory of conic sections " of Apollonius, "Arithmetica" of Diophantus and many reserch achivements of Archimedes. Many scholar represented as Aristotle. Plato focused only philosophy and mathematics. The story, Plato wrote "NO one knows Geometry, No admission" at the enterance to a hall, is famous. Euclid is known affected by Aristotle and plato. His "Elements" is the first arranged and systematized book logically and had been used as a textbook toward the end of the 1800's in Europe.

36. Greece - Greek Math Resources on ancient greek mathematics, calculations, geometry,and on Zeno, Archimedes, and Roman numerals. http://ancienthistory.about.com/cs/greekmath/

zfp=-1 var z336=0; About History Ancient/Classical History Search in this topic on About on the Web in Products Web Hosting in partnership with Ancient/Classical History with N.S. Gill Your Guide to one of hundreds of sites Home Articles Forums ... Help zmhp('style="color:#fff"') This Week's Articles tod('tih'); Today in History Daily Quiz tod('pod'); Picture of the Day Special Subscription Offers Subscribe Now Choose One: Subscribe Customer Service Subjects A to Z COLOSSEUM Cleopatra Pictures WEAPONS WARFARE ... All articles on this topic Stay up-to-date! Subscribe to our newsletter. Advertising Free Credit Report Free Psychics Advertisement Greece - Greek Math Resources on ancient Greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. Archimedes Basic information on Archimedes, the Greek mathematician of Syracuse. Euclid An Alexandrian mathematician and teacher, Euclid is most famous for his geometry with its logical deductions, axioms and postulates. Proclus Diadochus Proclus Diadochus was the head of the Academy and a follower of Neoplatonism known for his Commentary on Euclid's Geometry. Greece: Astronomy Information on the Greeks' calculations of time, the constellations, measurement, geometry, and the solar system.

37. Resources For Greek Mathematics Resources and Notes for greek mathematics. Powerpoint demonstrationof squaring a triangle; Squaring the circle; Doubling the cube; http://www2.sunysuffolk.edu/wrightj/MA28/Greek/

Resources and Notes for Greek Mathematics Powerpoint demonstration of squaring a triangle Squaring the circle Doubling the cube Trisecting an angle ... Chronology of the Greek period: 650 BC - 500 AD Resources and Notes for Geometry Impossible Constructions About Basic Geometry Basic Constructions Determining Triangle Similarity ... Unproven Fundamentals of Geometry Resources and Notes for Archimedes Biography Archimedes Home page Palimpsest Class Page ... Wright Page LastM = document.lastModified; document.write(" Last Modified " + LastM + "");

38. GREEK   MATHEMATICS greek mathematics. SCAVENGER HUNT. Use complete paragraphs so that your answerstell the story of ancient Greek contributions to the history of mathematics. http://www.fort-mill.k12.sc.us/fmhs/fosterc/greek_mathematics.htm

GREEK MATHEMATICS SCAVENGER HUNT INTRODUCTION The Geometry we study is called Euclidean Geometry because Arabic and Latin translations of Euclid's 13 volume work, The Elements , are among the oldest known records of the formal study of mathematics. Because little original work of ancient Greek mathematicians still exist, we cannot be sure how much of mathematics in The Elements can be credited to Euclid. At the very least, Euclid arranged, perfected and provided rigorous proof for mathematics originated by his predecessors. Euclid and his followers were among the first mathematicians to recognize the importance of rigorous proof. They were not content to accept a rule just because it was true in a particular case. A few rules, called postulates, were accepted as true because they were obvious truths which could not be disproved. Other rules, called theorems, were proved using postulates and previously proved theorems. Thus the study of mathematics moved from discovery (inductive reasoning) to demonstration that those discoveries must be true (deductive reasoning.) By studying the history of Greek mathematics and Greek mathematicians, you will learn the basis for your study of Euclidean Geometry this semester. Later this will serve as a contrast to two non-Euclidean geometries, Elliptic and Hyperbolic.

39. Greek Mathematics The mathematics we use today, and its content, are for the most partGreek. The There are many famous Greek names in mathematics. One http://atschool.eduweb.co.uk/sirrobhitch.suffolk/Portland State University Greek

GREEK MATHEMATICIANS The ancient Greeks were very interested in scientific thought. They were not satisfied with just knowing the facts; they wanted to know the why and how. It should be no surprise that the Greeks were extremely successful in the area of mathematics. The mathematics we use today, and its content, are for the most part Greek. The Greeks laid down the first principles, and invented methods for solving problems. Though most people don't realize it, mathematics is a Greek science - regardless of what modern day analysis might bring. When people look back on Greek genius, they may naturally call to mind masterpieces in Greek literature and art . But the Greeks, with their insatiable desire to know the true meaning of everything and give a rational explanation of it, were irresistibly drawn to the sciences, exact reasoning in general, and logic. There are many famous Greek names in mathematics. One of which is Aristotle , who said he could conceive of nothing more beautiful than the objects of mathematics. Plato , delighted in geometry and the wonders of numbers, inscribed, "let no one destitute of geometry enter my doors" over the entrance to his academy.

40. Greek Mathematics James J. Woeppel 3Sep-02 greek mathematics James J. Woeppel http://portfolio.iu.edu/jwoeppel/M110/Greekmath.htm

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