21. Greek Mathematics The greek mathematicians defined arithmetic differently than we do today.The word encompassed not only logistic, or what we commonly associate as http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.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. Chris Weinkopf Greek Mathematics April 19, 1995 Look at the comments on this paper. Table of Contents The Divisions The Pure and the Physical Order, Purpose, and Method Greek mathematics was premised on inductive reasoning. Whereas ancient historians sough to deduce facts from observations, the mathematicians sought to explore and discover truths working from a factual foundation. Theoretical mathematics also provided ancient philosophers with the tools of logic, which were thus employed in the pursuit of practical ends. The classical interpretation of mathematics, as well as the subdivision of the discipline into specific categories, demonstrates the Greeks' approach to the subject. The Divisions A fragment of Archytus , a Pythagorean friend and contemporary of Plato, explains the Quadrivivium , the four fields into which the Pythagoreans divided mathematics: arithmetic, geometry, sphaeric (astronomy), and music. Plato classified mathematics into the same categories, but included as a separate division stereometry three-dimensional geometry between geometry and sphaeric. (The Pythagoreans considered stereometry as subfield of geometry).

22. Alexandrian Scholarship was one of the last of the greek mathematicians and concentrated on large set down many of the geometric principles of earlier greek mathematicians, 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.

23. History Of Greek Mathematicians :: Term Papers, Essays - Free Summary Of Researc A short history of the great greek mathematicians. Amongst those discussed arePythagoras, Zeno, Euclid, Hippocrates, and Thales. http://www.academon.com/lib/paper/443.html

Home Sell Buy FAQs ... Contact Us Welcome to AcaDemon We have thousands of high-quality term papers, research papers, essays, book reports and dissertations on every topic. At AcaDemon, you can download those term papers to help you write yours! You can be sure that the term paper, essay, book report or research paper, you download are top-quality, competitively priced and high-level work. Papers on "History of Greek Mathematicians" and similar term paper topics: Paper #000443 :: History of Greek Mathematicians - Buy and instantly download this paper now A short history of the great Greek mathematicians. Amongst those discussed are Pythagoras, Zeno, Euclid, Hippocrates, and Thales. 742 words, 4 sources, $ 28.95 USD Paper Summary: A short history of the great Greek mathematicians. Amongst those discussed are Pythagoras, Zeno, Euclid, Hippocrates, and Thales. This essay is a brief overview of their major contributions to modern mathematics. Keywords: greek hippocrates mathematicians mathematics pythagoras thales zeno Paper #017364 :: Greek Myth as History ( 3,150 words, 10 sources, $ 111.95 USD )

24. Mathematics In Greek Art :: Term Papers, Essays - Free Summary Of Research Paper In addition to the philosophers, ancient greek mathematicians laid the foundations The greek mathematicians were themselves influenced by the Egyptians, http://www.academon.com/lib/paper/54204.html

Home Sell Buy FAQs ... Contact Us Welcome to AcaDemon We have thousands of high-quality term papers, research papers, essays, book reports and dissertations on every topic. At AcaDemon, you can download those term papers to help you write yours! You can be sure that the term paper, essay, book report or research paper, you download are top-quality, competitively priced and high-level work. Papers on "Mathematics in Greek Art" and similar term paper topics: Paper #054204 :: Mathematics in Greek Art - Buy and instantly download this paper now A discussion on the reflections of Greek mathematics in ancient Greek art. 1,691 words, 10 sources, MLA, $ 56.95 USD Paper Summary: This paper examines how the contributions of the Greek civilization to the world are undeniable and how, in addition to being the home of many philosophers such as Plato, Aristotle, Socrates, and others, Greece has also made contributions to the world of mathematics and assisted in laying its foundations. It explores how the influence of Pythagoras (572-501 BC), Plato (430-349 BC), and the Alexandrine School (300 BC-500 AD) are significant for the development of Greek mathematics. In particular, it looks at how the mathematical thinking which was developed by the Greeks can be noticed in works of art from the ancient Greek period. From the Paper: "The contributions of the Greeks to the modern world and especially the western civilization are considerable. Greece was the home of many renowned philosophers including Plato, Aristotle and Socrates amongst others. These philosophers laid the foundations of modern philosophy and western thought. In addition to the philosophers, ancient Greek mathematicians laid the foundations of mathematics, geometry, trigonometry and logic. The Greek mathematicians were themselves influenced by the Egyptians, who had been using geometry empirically to find the boundaries of their land which had been covered by water as a result of the frequent floods in the Nile. Unfortunately, the Egyptians were not interested in measuring the height of the pyramids that they had constructed in memory of their Pharos."

25. Timeline Of Greek Mathematicians Mathematician Thales Pythagoras Parmenides Zeno Plato Theatetus XenocratesAristotle Euclid Archimedes Eratosthenes Apollonius. http://www.stormloader.com/ajy/grk_timeline.html

Mathematician Thales Pythagoras Parmenides Zeno Plato Theatetus Xenocrates Aristotle Euclid Archimedes Eratosthenes Apollonius

26. Math Lair - Greek Mathematicians greek mathematicians and Philosophers. Some of these dates are necessarilyapproximate. Thales 634548; Pythagoras 580-500; Parmenides 515-450 http://www.stormloader.com/ajy/greekdates.html

Greek Mathematicians and Philosophers Some of these dates are necessarily approximate. Thales Pythagoras Parmenides Zeno Socrates Plato Theatetus Xenocrates Aristotle Euclid Archimedes Conon Eratosthenes Apollonius Last updated May 21, 2001. URL: http://www.stormloader.com/ajy/greekdates.html For questions or comments email James Yolkowski Math Lair home page

27. The Shaping Of Deduction In Greek Mathematics - Cambridge University Press The aim of this book is to explain the shape of Greek mathematical thinking. The historical setting; Appendix the main greek mathematicians cited in http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521541204

28. Read This: The Shaping Of Deduction In Greek Mathematics There are differences, though greek mathematicians were not illiterate oral By the end of chapter 4 we have finally found the Greek mathematician http://www.maa.org/reviews/netz.html

Search MAA Online MAA Home 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. Read This: The Mathematics Of Plato's Academy The early greek mathematicians worked with several different concepts of ratio , He argues that the greek mathematicians would understand, say, http://www.maa.org/reviews/mpa.html

Search MAA Online MAA Home Read This! The MAA Online book review column The Mathematics Of Plato's Academy: A New Reconstruction (Second Edition) by David Fowler Reviewed by Fernando Q. Gouvêa Most mathematicians who know anything about the history of their subject know the standard story about Greek mathematics. David Fowler describes that story like this: The early Pythagoreans based their mathematics on commensurable magnitudes (or on rational numbers, or on common fractions m/n), but their discovery of the phenomenon of incommensurability (or the irrationality of the square root of 2) showed that this was inadequate. This provoked problems in the foundation of mathematics that were not resolved before the discovery of the proportion theory that we find in Book V of Euclid's Elements (p. 356). As he points out, we have all heard, and some of us have told, that story. It may be somewhat surprising, then, to discover that many, if not most, historians of ancient mathematics disbelieve some or all of this story. In The Mathematics of Plato's Academy , David Fowler gives a convincing account of the reasons for rejecting the standard story, and offers a very interesting alternative reconstruction of the history of early Greek mathematics.

30. Read About Category:Ancient Greek Mathematicians At WorldVillage Encyclopedia. R CategoryAncient greek mathematicians. Everything you wanted to know aboutCategoryAncient greek mathematicians but had no clue how to find it. http://encyclopedia.worldvillage.com/s/b/Category:Ancient_Greek_mathematicians

Culture Geography History Life ... WorldVillage Category:Ancient Greek mathematicians From Wikipedia, the free encyclopedia. Mathematicians from Europe by nationality Austrian Azerbaijani Belgian British ... Ukrainian Other continents: Africa Americas Asia and Oceania This category is for Ancient Greek mathematicians . Mathematicians can also be browsed by field and by period . The root category for mathematicians is here Mathematicians of the Greek World Ancient Greek Byzantine Modern Greek Those mathematicians associated with Greek civilization have been subcategorised by period. Articles in category "Ancient Greek mathematicians" There are 7 articles in this category. A Archimedes Aristotle D Democritus Diophantus E Eratosthenes H Hypatia of Alexandria P Pappus of Alexandria Retrieved from " http://en.wikipedia.org/s/b/Category:Ancient_Greek_mathematicians Categories Ancient mathematicians Mathematicians by nationality ... Greek mathematicians This document is licensed under the GNU Free Documentation License (GFDL), which means that you can copy and modify it as long as the entire work (including additions) remains under this license.

31. Aristotle And Greek Mathematics: A Supplement To Aristotle And Mathematics greek mathematicians wisely avoided nonuniform magnitudes which could not bereduced to uniform magnitudes. The reason for this has partly to do with the http://plato.stanford.edu/entries/aristotle-mathematics/supplement4.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and Greek Mathematics This supplement provides some general indications of Aristotle's awareness and participation in mathematical activities of his time. Greek mathematics in Aristotle's Works Here are twenty-five of his favorite propositions (the list is not exhaustive). Where a proposition occurs in Euclid's Elements , the number is given, * indicates that we can reconstruct from what Aristotle says a proof different from that found in Euclid). Where the attribution is in doubt, I cite the scholar who endorses it. In many cases, the theorem is inferred from the context. In a given circle equal chords form equal angles with the circumference of the circle ( Prior Analytics i.24; not at all Euclidean in conception) The angles at the base of an isosceles triangle are equal ( Prior Analytics i.24; Eucl. i.5*). The angles about a point are two right angles ( Metaphysics ix 9; Eucl. follows from i def. 10). If two straight-lines are parallel and a straight-line intersects them, the interior angle is equal to the exterior angle (

32. Annotated Bibliography On Analysis -- §2: Ancient Conceptions Of Analysis: A Su MIT Press); Netz, Reviel, 2000, ‘Why did greek mathematicians Publish their Analyses? 1941, Greek Mathematical Works, Vol. II, Loeb Classical Library, http://plato.stanford.edu/entries/analysis/bib2.html

Stanford Encyclopedia of Philosophy Supplement to Analysis Citation Information Annotated Bibliography on Analysis This bibliography is intended as a reference guide to the key works that deal, in whole or in part, with analysis and related topics such as analyticity and definition. Cross-references are by name(s) of author(s) or editor(s) and either year of publication or abbreviation as indicated immediately after their name(s). Notes in square brackets at the end of an entry indicate the relevant part(s) of the work and/or its significance to the topic of analysis. This section of the bibliography corresponds to Section 2 of the main entry, and is divided into subsections which correspond to the subsections of the supplementary document on Ancient Conceptions of Analysis . Where works include important material under more than one heading, they are cited under each heading; but duplication has been kept to a minimum. Cross-references to other (sub)sections are provided in curly brackets. 2.1 General

33. About "How Do We Know About Greek Mathematicians?" How do we know about greek mathematicians? ways to gain information aboutthe ancient greek mathematicians, with references and other related web sites. http://mathforum.org/library/view/12307.html

How do we know about Greek mathematicians? Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www-history.mcs.st-and.ac.uk/history/HistTopics/Greek_sources_2.html Author: MacTutor Math History Archives Description: Linked essay examining how the dates of Diocles given in the MacTutor archive have been determined, and other ways to gain information about the ancient Greek mathematicians, with references and other related web sites. Levels: Middle School (6-8) High School (9-12) College Languages: English Resource Types: Articles Bibliographies Math Topics: History and Biography Home The Math Library Quick Reference ... Help http://mathforum.org/

34. Math Forum - Ask Dr. Math It took some time for the greek mathematicians to recover from this shock. The Greek mathematician Eudoxus apparently came up with the resolution that http://mathforum.org/library/drmath/view/52602.html

Associated Topics Dr. Math Home Search Dr. Math Do Pyramids Really Exist? Date: 02/27/2002 at 15:27:01 From: Joeli Subject: Do Pyramids really exist? Hi, I was just wondering if certain shapes can really exist. For example, if the base of an isosceles triangle is 4, and the height is 5, then using the Pythagorean theorem the sides are equal to the square root of 21. How can this triangle exist (except in theory) if you can never measure or draw the square root of 21? I have yet to find a triangle that does not involve square roots. Is there one? What about pi? Do circles, cylinders, cones not exist because you can't measure a distance of pi? Thanks. Joeli http://www-groups.dcs.st-and.ac.uk/~history/Indexes/E.html Euclid's presentation of Eudoxus' approach of the incommensurability problem is found in Book V of his Elements: Euclid's Elements (David Joyce) http://aleph0.clarku.edu/~djoyce/java/elements/bookV/bookV.html By the way, there are triangles whose sides are commensurable. You can just pick any 3 integers and make a triangle with these sides. Moreover, there are right triangles whose sides are commensurable: the 3-4-5 right triangle is most well known. See Pythagorean triples from the Dr. Math FAQ: these are sets of integers that are the sides of right triangles. http://mathforum.org/dr.math/faq/faq.pythag.triples.html

35. Term Papers (model), Term Papers (model) And More Term Papers (model) Mathematic The Importance of Mathematics in Early Greek Culture A 12 page comprehensivestudy of early greek mathematicians and their cultural significance. http://www.termpapers-on-file.com/term-papers/mathmatics.htm

MATHEMATICIANS Back to Main Categories Back to Main Categories ... Categories NOW! ALL PAPERS ON FILE ARE ONLY $8.95/PAGE!!! MORE EXAMPLE TERM PAPERS ON MATHEMATICS A 15 page paper that provides an overview of the history and development of the abacus. The report essentially compares the Chinese, Roman, Greek, Russian and Indian counting methods utilizing similar instruments. Bibliography lists 6 sources. Abacus.doc Benefits Of Computer-Taught Math Over Standard Textbook Practices A 10 page study that provides support for the hypothesis that computer taught math provides significant beneficial outcomes for learners in terms of test scores. Bibliography lists 10 sources. Mtcomp.wps Differential Equations An 18 page research paper on every available aspect of differential equations including Laplace Transforms and much more. A number of graphical illustrations are provided and the bibliography lists more than 8 sources. Diffequa.wps Linear Algebra A 15 page research paper on various concepts in linear algebra. The writer details multivariables, vectors, determinants, gaussian elimination, and other elements of linear algebra. Bibliography lists 6 sources. Linalgeb.wps

36. ARCHIMEDES: The Greatest Mathematician Of Antiquity Archimedes was a Greek mathematician, physicist and inventor, But Archimedeswas different from earlier greek mathematicians like Euclid in that he was http://uzweb.uz.ac.zw/science/maths/zimaths/33/archimed.htm

ARCHIMEDES: the greatest mathematician of antiquity Archimedes was a Greek mathematician, physicist and inventor, who made profoundly original contributions in mathematics, founded all by himself the fields of statics, hydrostatics and mathematical physics, and invented mechanical devices useful in war and peace. The achievements of Archimedes probably make him the foremost scientist before Newton. Life and Mayor Discoveries Archimedes was born about 287 B.C. in Syracuse, Sicily, a Greek colony. His father, Pheidias, was an astronomer. Archimedes studied at Alexandria, then the center of the scientific world, as a student of followers of Euclid. During his stay in Alexandria he invented a ``screw'' for raising water from the Nile to irrigate fields. The design of the Archimedes screw is based on two geometrical forms, the helix and the cylinder. After his return to Syracuse, he devoted himself mainly to science. Plutarch, the Roman historian, wrote that oftenhis intense concentration on mathematics ``made him forget his food and neglect his person to that degree that, when he was carried by absolute violence to bathe or have his body annointed, he used to trace geometrical diagrams in the ashes of the fire, and diagrams in the oil on his body, being in a state of entire preoccupation, and, in the truest sense, divine possession with his love and delight in science''.

37. Bryn Mawr Classical Review 2004.10.25 Where The Shaping of Deduction was primarily about greek mathematicians use oflanguage, That is, when a Greek mathematician, Diocles for example, http://ccat.sas.upenn.edu/bmcr/2004/2004-10-25.html

Bryn Mawr Classical Review 2004.10.25 Reviel Netz, The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations . Cambridge: Cambridge University Press, 2004. Pp. 198. ISBN 0-521-82996-8. $70.00. Reviewed by Anne Mahoney, Tufts University (anne.mahoney@tufts.edu) Word count: 1987 words In this book, Netz argues that the history of mathematics should consist not only of a catalog of which mathematicians worked on what problems when, but also of an analysis of how they conceived of the problems they were solving. He observes that many modern textbooks, sourcebooks, and even more scholarly works on the history of mathematics obscure the line of development when they almost automatically translate earlier works into modern notation. The example he develops throughout is a problem studied by Archimedes: how do you cut a sphere, with a plane going through one of the latitude lines, so that the volume of the bigger part has a certain given ratio to the volume of the smaller part? For Archimedes, this is essentially a geometric problem, to be solved by manipulating geometric objects and their ratios lines, rectangles, similar triangles, and so on. But for Omar Khayyam, the 11th-12th century mathematician perhaps better known for

38. Mathematical Masterpieces: Teaching With Original Sources After Babylonian and ancient greek mathematicians systematically solved quadraticequations, progress passed to the medieval Arab world. http://math.nmsu.edu/~history/masterpieces/masterpieces.html

Next: References Mathematical Masterpieces: Teaching with Original Sources Mathematics, New Mexico State University, Las Cruces, NM 88003 Vita Mathematica: Historical Research and Integration with Teaching R. Calinger (ed.), MAA, Washington, 1996, pp. 257260] Our upper-level university honors course, entitled Great Theorems: The Art of Mathematics To achieve our aims we have selected mathematical masterpieces meeting the following criteria. First, sources must be original in the sense that new mathematics is captured in the words and notation of the inventor. Thus we assemble original works or English translations. When English translations are not available, we and our students read certain works in their original French, German, or Latin. In the case of ancient sources, we must often depend upon restored originals and probe the process of restoration. Texts selected also encompass a breadth of mathematical subjects from antiquity to the twentieth century, and include the work of men and women and of Western and non-Western mathematicians. Finally, our selection provides a broad view of mathematics building upon our students' background, and aims, in some cases, to reveal the development over time of strands of mathematical thought. At present the masterpieces are selected from the following. ARCHIMEDES: The Greek method of exhaustion for computing areas and volumes, pioneered by Eudoxus, reached its pinnacle in the work of Archimedes during the third century BC. A beautiful illustration of this method is Archimedes's determination of the area inside a spiral. [

39. Template greek mathematicians came up with many of today s theorems. The Greekmathematicians made contributions in Algebra, calculus, and mainly geometry. http://www.heidelberg.edu/~ddemeio/webquest.html

History of Mathematics WebQuest A WebQuest for 10th Grade (Mathematics) Designed by Darren DeMeio ddemeio@heidelberg.edu Introduction Task Process Evaluation ... Other Resources Introduction Greek mathematicians came up with many of today's theorems. There were very many of these mathematicians that cme up with these theorems. The Greek mathematicians made contributions in Algebra, calculus, and mainly geometry. Introduction Task Process Evaluation ... Other Resources The Task You and a partner will need to answer the questions below to find a mathematician to research more. The questions will introduce you and your partner to some of the Greek mathematicians but not all of them. You and your partner will need to know the history of the mathematician you chose and their accomplishments to write a research paper. 1. What are the sections of math that Euclid's "Elements" covers? 2. Give an example of Plato's Theory of Forms. 3. What group of people were pretty sure the Pythagorean Theorem was true two thousand years before Pytahgoras proved it to be true all the time? 4. What theory came out of Euclid's "Optics"?

40. Greek Mathematics Index How do we know about greek mathematicians? Greek number systems. Various listsof greek mathematicians. Full list Mathematicans/Philosophers http://gw.capetown.gov.za/wcms/eDocuments/Index_of_Ancient_Greek_mathematics_151

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... Greek number systems Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa Franco of Liège James Gregory Lambert Leonardo Lindemann ... Societies, honours, etc

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