61. About "Basic Ideas In Greek Mathematics" The Math Forum Internet Mathematics Library. Basic Ideas in greek mathematics. _ Library Home Full Table of Contents 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 ... Help http://mathforum.org/

62. About "Greek Mathematics And Its Modern Heirs" The Math Forum Internet Mathematics Library. greek mathematics and its Modern Heirs. _ http://mathforum.org/library/view/4535.html

Greek Mathematics and its Modern Heirs Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html Author: SunSITE's Vatican Exhibit; Library of Congress Description: Classical roots of the scientific revolution. An essay on the history of Greek Math, with sample math problems. Covers Euclid's Elements and Optics, Archimedes' Works, Piero della Francesca's De quinque corporibus regularibus, and links to Ptolemy's Geography and Greek Astronomy. Levels: Middle School (6-8) High School (9-12) College Languages: English Resource Types: Articles Books Math Topics: Basic Algebra Higher-Dimensional Geometry Euclidean Plane Geometry History and Biography ... Help http://mathforum.org/

63. Ancient Greek Mathematics Welcome. Ancient greek mathematics evolved from a much older civilization, the Egyptian culture. Pythagoras Ancient Greek mathematicians studied the http://www.delfossedesigns.com/website/Moore/HTML/math.html

A ncient Greek Mathematics evolved from a much older civilization, the Egyptian culture. Pythagoras Ancient Greek mathematicians studied the relationships they found among measurements of figures. This branch of mathematics became known as geometry Measurement The basic unit of measurement in ancient Greece was a finger. A finger was roughly equal to three-quarters of an inch (about the width of a man's fingernail). INTEGRATION OF MATH AND LANGUAGE ARTS STATE GOAL 8:CAS A. List as many was as you can that people use geometry in everyday life. Measure Your desks and other objects in hands and feet. Measure various classroom objects using your own fingers as units of measure. Compare and discuss why measurements might be different. Determine how many fingers are in a foot, yard, mile etc Look up the definitions of the following geometric terms: point, plane, line, angle, cylinder, cube, and sphere. ART MATH SCIENCE SOCIAL STUDIES LIBRARY CONTACT US ... ENTRANCE

64. Lecture 3 Hippocrates Quadrature Of Lunes The distinguishing feature of greek mathematics is that it is concerned with We use the term greek mathematics to denote mathematics written in the http://www.maths.uwa.edu.au/~schultz/3M3/L3Hippocrates.html

Lecture 3 Hippocrates Quadrature of Lunes Greek mathematics The distinguishing feature of Greek mathematics is that it is concerned with logical development, not problem solving. We use the term Greek Mathematics to denote mathematics written in the Greek language between about -600 (Thales) and about 250 (Diophantos). The mathematicians were not necessarily ethnically Greek nor living in the region we now call Greece. In fact the major developments occurred in the Greek colonies now known as Turkey, Egypt and Italy. The Greeks did not have a sophisticated number system. The integers were expressed by concatenating the letters a-k for 19, and l-u for1090 etc. Special letters were invented for larger numbers. Later, Archimedes in the "Sand Reckoner", (in which he calculated the number of grains of sand needed to fill the Universe) developed an exponential system for arbitrarily large numbers. The Greeks used a decimal system for common purposes and a sexigesimal system for scientific purposes, for example astronomy. Concatenations of unit fractions were used for rationals, although later Diophantos developed special symbols for rationals. In Greek mathematics the numbers were 2,3,4,.. The unity 1 was not a number, but the unit in which the numbers were measured. There were no negative numbers or zero. Geometrical quantities such as line segments, angles, areas and volumes were called

65. PHILOSOPHY OF SCIENCE Basic Ideas in greek mathematics with section on Zeno Infinity A Platonic Realms MiniText Numbers A Platonic Realms Mini-Text http://www.anselm.edu/homepage/dbanach/ph31a.htm

Greek Science and The Golden Section Ancient Science and Mathematics Selections from Julia E. Diggins String, Straightedge, and Shadow Viking Press, New York 1965. (Illustrations by Corydon Bell) Now back in print! Purchase at http://wholespiritpress.com/string.htm Chapters 8, 9: Thales Chapters 11, 12: Pythagoras and his Theorem ... Homage to Pythagoras One of the most comprehensive sets of resources on Pythagoras on the net Selection from Burnet's Early Greek Philosophy on Pythagoras from the site above. A collection of ancient quotes and sources on Pythagoras from the same site, originally from Arthur Fairbanks, ed. and trans. The First Philosophers of Greece, 1898. Harmony and Proportion Plato and Pythagoras on Music; Alberti and Palladio on architectural space. Pythagoras on Proportion in Music From the above site, MathGYM Pythagoreans activity pages. The Pythagorean Theorem essay Activity Prove the theorem graphically. Another applet that proves the theorm graphically from U. of British Columbia 43 proofs of the Theorem from the Cut the Kot site by Alex Bogomolny Here is an applet that demonstrates the method used in the Diggins book from this site.

66. Vignettes Of Ancient Mathematics mostly in ancient greek mathematics, but other related examples will be included. This will not be a history of greek mathematics but will contain http://www.calstatela.edu/faculty/hmendel/Ancient Mathematics/VignettesAncientMa

Vignettes of Ancient Mathematics by Henry Mendell, Cal. State U., L.A. General Contents Philosophical Texts Mathematical Authors Special Topics Textual Notes The purpose of this site is to illustrate various mathematical techniques and strategies, mostly in ancient Greek mathematics, but other related examples will be included. This will not be a history of Greek mathematics but will contain examples designed to bring out a few interesting features. For the perspective of evidence, the techniques included will be of four sorts: Texts with explanatory diagrams. The diagrams will be 'modern' in the sense that they will walk the reader through the proof. Paraphrases or summaries with explanatory diagrams. Here the argument does occur in our sources, but a simpler paraphrase was used to facilitate understanding. For example, the mathematician may have needed the elaborate original text to explain matters easily understood by a series of well constructed diagrams. Simple illustrations of techniques: these illustrations are simpler than the examples which occur in ancient texts and so are useful for learning the techniques. Reconstructions of arguments which are lost, but which seem plausible. Some of these are standard in the modern literature; others express the personal tastes of the author.

67. Quantum Books: Manual Of Greek Mathematics Manual of greek mathematics. Author Heath, Sir Thomas L. ISBN 0486432319 Pub Date Dec 1, 2003 Publisher Dover Publications Shipping Weight 1.60 pounds http://www.quantumbooks.com/Merchant2/merchant.mvc?Screen=PROD&Store_Code=qb&Pro

68. ANCIENT GREEK MATHEMATICS If you are interested in learning more about greek mathematics, you can browse this greek mathematics has made an astonishing impact on our world. http://www.angelfire.com/me/Huffamoose/

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "angelfire.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Angelfire Star Wars Share This Page Report Abuse Edit your Site ... Next ANCIENT GREEK MATHEMATICS Space provided by Angelfire Communications. Best viewed at 640 X 480 (256 colors). If you are interested in learning more about Greek mathematics, you can browse this website or chat (below) with others about the influence of Greek mathematics on western civilization. For those who have little knowledge about this subject, ask yourself: "How will I ever use these postulates and theorems, and who has come up with all of these interesting ideas? Where did all of this come from?".... If you guessed Ancient Greece, you're right! While Alexander the Great was out on his conquests, mathematicians like Euclid and Aristotle were coming up with new ideas which would benefit western civilization 2300 years later. If you look at the Parthenon (bottom of page) from a distance away, it looks perfectly rectangular. But in fact, the floor, walls, and columns are actually bowed. The ancient Greek architects who calculated the measurements that would be used in the construction of the Parthenon, used mathematics to come up with their designs. Buildings, like the Parthenon, have influenced many modern buildings like the Philadelphia Art Museum. Greek mathematics has made an astonishing impact on our world. By scrolling down this page, you will be able to see the influence that Ancient Greek mathematics has had on Western Civilization.... Your journey begins here.

69. A Manual Of Greek Mathematics From Bestprices.com Books A Manual A Manual of greek mathematics only $20.85, get the A Manual of greek mathematics book from BestPrices.com! http://www.bestprices.com/cgi-bin/vlink/0486432319BT.html

70. A Short History Of Greek Mathematics From Bestprices.com Books A A Short History of greek mathematics only $41.76, get the A Short History of greek mathematics book from BestPrices.com! http://www.bestprices.com/cgi-bin/vlink/0486495892BT.html

71. Bryn Mawr Classical Review 2004.10.25 Although greek mathematics is an ancestor of modern mathematics, In short, Hellenistic greek mathematics, whose practice may be summed up by the aura, 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

72. Expression Calculator Mathematics The spirit of greek mathematics is typified in one of its most lasting When the Hellenic civilization declined, greek mathematics (and the rest of Greek http://excalc.vestris.com/docs/math.html

Software Documentation Chapter 3. Expression Calculator Mathematics Table of Contents Mathematics Algebra Trigonometry Calculus and Analysis ... Functions Mathematics Mathematics is the science of relationships between numbers, between spatial configurations, and abstract structures. The main divisions of pure mathematics include geometry, arithmetic, algebra, calculus, and trigonometry. Mechanics, statistics, numerical analysis, computing, the mathematical theories of astronomy, electricity, optics, thermodynamics, and atomic studies come under the heading of applied mathematics. Prehistoric humans probably learned to count at least up to ten on their fingers. The ancient Egyptians (3rd millennium BC), Sumerians (2000-1500 BC), and Chinese (1500 BC) had systems for writing down numbers and could perform calculations using various types of abacus. They used some fractions. Mathematicians in ancient Egypt could solve simple problems which involved finding a quantity that satisfied a given linear relationship. Sumerian mathematicians knew how to solve problems that involved quadratic equations. The fact that, in a right-angled triangle, the square of the longest side is equal to the sum of the squares of the other two sides (Pythagoras' theorem) was known in various forms in these cultures and also in Vedic India (1500 BC). The first theoretical mathematician is held to be Thales of Miletus (c. 580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognized science among the Greeks. Pythagoras began to insist that mathematical statements must be proved using a logical chain of reasoning starting from acceptable assumptions. Undoubtedly the impetus for this demand for logical proof came from the discovery by this group of the surprising fact that the square root of 2 is a number which cannot be expressed as the ratio of two whole numbers. The use of logical reasoning, the methods of which were summarized by Aristotle, enabled Greek mathematicians to make general statements instead of merely solving individual problems as earlier mathematicians had done.

73. MSN Encarta - Mathematics The new element in greek mathematics was the invention of an abstract mathematics founded on a logical structure of definitions, axioms (propositions http://encarta.msn.com/encyclopedia_761578291_5/Mathematics.html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Upgrade your Encarta Experience Spend less time searching and more time learning. Learn more Tasks Find in this article Print Preview Related Items Math Homework Help Mathematics more... Further Reading Editors' picks for Mathematics Search for books and more related to Mathematics Encarta Search Search Encarta about Mathematics Editors' Picks Great books about your topic, Mathematics ... Click here Advertisement document.write(' Page 5 of 12 Mathematics Encyclopedia Article Multimedia 45 items Article Outline Introduction Mathematics: The Language of Science Branches of Mathematics History of Mathematics A Mathematics in Antiquity The Babylonians of ancient Mesopotamia and the ancient Egyptians left the earliest records of organized mathematics. Arithmetic dominated their mathematics. In geometry, measurement and calculation were emphasized, with no trace of concepts such as axioms or proofs. A Babylonia Our knowledge of Babylonia comes from well-preserved clay tablets on which people wrote with wedge-shaped marks known as cuneiform . The earliest tablets date from about 3000 bc . Much of the mathematics on the tablets involved commerce. The Babylonians used arithmetic and simple algebra to exchange money and merchandise, compute simple and compound interest, calculate taxes, and allocate shares of a harvest to the state, temple, and farmer. The building of canals, granaries, and other public works also required using arithmetic and geometry. Calendar reckoning, used to determine the times for planting and for religious events, was another important application of mathematics.

74. History News Network It was a dense and learned tome on ancient greek mathematics that he was about to In fifthcentury Athens, greek mathematics was all about numbers, http://hnn.us/roundup/archives/14/2004/05/

@import url("/css/style.css"); HNN History News Network Because the Past is the Present, and the Future too. Donations Archives ... FAQs Search HNN: Breaking News Departments HNN Articles Hot Topics Books Features ... Russell Kirk: The Historian of Conservatism Wednesday, May 26, 2004 David Fowler: Obituary of the British Historian of Mathematics Steve Russ, Eleanor Robson, Rona Epstein, and David Epstein in the London Independent (May 24, 2004): AS THE first Manager of the Mathematics Research Centre at Warwick University, from 1967, David Fowler played an important part in establishing, through the research symposia organised at the centre, the outstanding international reputation that Warwick now enjoys in many branches of mathematics. As a distinguished scholar of the history of mathematics he has left a wonderful legacy in the form of a series of papers and books presenting, in rich detail, a far-reaching, original and inventive re-interpretation of early Greek mathematics.... Not so long ago, a mathematician was sent a book to review. It was a dense and learned tome on ancient Greek mathematics that he was about to return when he noticed the price. Intrigued that a book could be both so incomprehensible and so expensive, he took it home out of sheer curiosity and ended up becoming a historian of Greek mathematics himself. The year was 1975, the book Wilbur Knorr's The Evolution of the Euclidean Elements, and the mathematician David Fowler. This was the story he liked to tell of his origins as a historian, although ironically the whole of his subsequent career was spent in refuting the accepted story of the origins of Greek mathematics and arguing, very engagingly and persuasively, for another one.

75. Mathematical Quotations A In Ivor Thomas greek mathematics in JR Newman (ed. On The Heavens , in T. L. Heath Manual of greek mathematics, Oxford Oxford University Press, http://math.furman.edu/~mwoodard/ascquota.html

Mathematical Quotations A Back to MQS Home Page Forward to "B" Quotations Abel, Niels H. (1802 - 1829) If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words,the most important parts of mathematics stand without a foundation. In G. F. Simmons, Calculus Gems , New York: Mcgraw Hill, Inc., 1992, p. 188. [A reply to a question about how he got his expertise:] By studying the masters and not their pupils. [About Gauss' mathematical writing style] He is like the fox, who effaces his tracks in the sand with his tail. In G. F. Simmons, Calculus Gems , New York: Mcgraw Hill, Inc., 1992, p. 177. Adams, Douglas (1952 - 2001) Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants. The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.

76. Other Topics In Greek Mathematics Other Topics in greek mathematics. _. Commensurability. Choose One of the Following, Commensurate Lines Measured by http://math.furman.edu/~jpoole/mth15hp/othertopicsgk/othertopicsgk.htm

Other Topics in Greek Mathematics Commensurability Choose One of the Following: Commensurate Lines Measured by the Greatest Common Measure A Geometric Proof Assuming all Lines are Commensurable Back to Mth 15 Home Page

77. Jekyll.comm - Article "Leopardi And The Ancient Greek Mathematics" In the case of the ancient greek mathematics this “lyrical” mistrust can be defined as a “conspiracy of silence”, for Leopardi does not mention ancient http://jekyll.comm.sissa.it/articoli/art02_01_eng.htm

Leopardi and the ancient Greek mathematics Annalisa Reggi Member of the editorial staff of Settesere , cooperativa Bachilega “I consider Leopardi’s poetry and pessimism to be the best expression of what a scientist’s credo should be”. This quotation is from Bertrand Russell, no less. With these very emblematic words, the greatest man of letters, the supreme icon of the Italian Parnasse, the author of such collections of poems as Canti (Poems) and Operette Morali (The Moral Essays) and philosophical thoughts as Zibaldone (Miscellany) has been associated to the world of science. This relationship, very intense and to a certain extent new, was greatly emphasised on the occasion of the poet’s birth bicentenary. During the celebration in 1996, an exhibition with the name of Giacomo and Science was organized in his birthplace to underline the close connection between the poet and the scientific culture of his epoch. This point has also been stressed recently: “Leopardi must be acknowledged as a man of extraordinary learning, since he blended literature and philosophy with interests of quintessentially scientific nature”. He developed this passion for science from a very young age, as an analysis of the Italian poet’s bibliography reveals. He was only 14 when, together with his brother Carlo, he published

78. "Mathematics On Stamps" Webring 3, Mathematics in the 17th Century, 3, greek mathematics I. 4, Computing on Stamps, 4, greek mathematics II. 15 (1993), 1, greek mathematics III http://www.oliver-faulhaber.de/mathstamps.htm

"Mathematics on Stamps" Webring Ring Links: [ List Sites Join Statistics Questions Internal Links: [ Collectors Literature Wilson's column Dealers ... Links COLLECTORS If you want to be added to this list, just send me an eMail Name Country Homepage Wantlist List of Doubles Manfred Börgens Germany Yes Tuvi Etzion Israel Oliver Faulhaber Germany Yes Yes Yes Norbert Gengler Luxembourg Gunnar Gjone Norway (currently US) Bert Jagers Netherlands Yes Thomas Jahre Germany Yes Jeff Miller USA Yes John Oberman Israel Yes Arnauld Pascal France David Stone England Yes Yes Magnus Waller Sweden Yes LITERATURE If you know any book which you find missing here, just send me an eMail Boyer: Philately and Mathematics , Scripta Mathematica 15/1949. van Dijk: Mathematelie Gjone, Gunnar: Mathematikhistorie i miniatyr Larsen: Mathematics and Philately , American Mathematical Monthly 60/1953. Larsen: Mathematics on Stamps , Mathematics Teacher Nov. 1955. Schaaf: Mathematics in the Classroom , Mathematics Teacher Jan. 1974. Schaaf, William L.: Mathematics and Science. An Adventure in Postage Stamps Schreiber: Die Mathematik und ihre Geschichte im Spiegel der Philatelie , 101 p., 1980, BSB B.G. Teubner Verlagsgesellschaft. Small book with 16 color pages, gives mainly a brief history of mathematics (from a kind of "east" point of view, since it was published in the former German Democratic Republic). One of its highlights is a complete list of all "mathematical" stamps issued so far.

79. Plato And Mathematics the stock example or how not to do rigorous greek mathematics. to know a great deal more about the nature and the influences of greek mathematics, http://community.middlebury.edu/~harris/Philosophy/Plato.html

PLATO Mathematician or Mystic ? Plato believed at first that Mathematics would be the key to Thought, but in the Meno he abandons hope in the context of a few sentences, which we have constantly misread. This paper examine that crux. No reader of Plato can fail to recognize the important role which mathematics plays in his writing, as would indeed be expected for an author about whom the ancient tradition maintains that he had hung over the entry to his school the words "Let No One Un-versed in Geometry Enter". Presumably it was the level of ability to work with abstract concepts that Plato was interested in primarily, but if the student really had never studied Greek geometric materials there would be many passages in the lectures which would be scarcely intelligible to him. Modern readers, versed in a much higher level of mathematical abstraction which our society can offer, have sometimes felt that Plato's famous "mathematical examples'" were illustrations rather than central to his arguments, and some of Plato's mathematical excursuses have remained obscure to the present time. When Euclid put together his masterful compendium in the 3 rd C. B.C. he was obviously drawing on a legacy of accumulated mathematical research which went back well into the 5th C. B.C. and possibly even further. Activity can be pushed back well into the 5th C. B.C. in view of the quite reasonable ancient assignment of the Pythagorean Theorem of Euclid I 47 to the master himself; this would naturally involve understanding of squares and irrational numbers. And i4 should be noted that well back into that century Iktinos, the architect of the Parthenon was not only considering but actually using in his work the square root of the diagonal of a 1:2 rectangle in the form which later became famous as the Golden Mean, more specifically in the ratio l.6l8 : l

80. Buy Open University Learning Resources - (MA290) Topics In The History Of Mathem Print, Topics in the History of Mathematics Mathematics in the Greek World and Quartis in sixteenth-century Italy • The recovery of greek mathematics http://www.ouw.co.uk/bin/ouwsdll.dll?COURSEMA290_Classical_Studies

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