81. ABC Geometry - Words To Help You Think About Space, Shape, Measurement And The L euclid s axiomatic foundations for geometry contained several definitions, some postulates and a few common notions. http://www.mdx.ac.uk/www/study/glonumge.htm

The ABC Study Guide, University education in plain English alphabetically indexed. Click here to go to the main index ABC Geometry Words to help you think about space, shape, measurement and the laws of thought. Geometry: The ancient Egyptians and Mesopotamians developed methods of measuring objects and calculating relations that they used to build monuments like the pyramids The Greeks called this geometry, which means earth- measurement. About , a Greek called Euclid , who lived in Egypt, developed proofs of the geometric rules that the Egyptians had devised. Euclid's proofs started from axioms and reasoned logically from them to conclusions. This has been seen by some philosophers as a model for what science (or part of Science) should be. Hobbes argued for a Social Science based on Euclidian methods. Poincare used Euclidian and other geometries to argue that science is based on imagination. The 3,4,5 rule Take three straight lines Make one 3 units long, make another 4 units long, make the other 5 units long.

82. No Match For Euclid's Geometry Sorry, the term euclid s geometry is not in the dictionary. Check the spelling and try removing suffixes like ing and -s . http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Euclid's geometry

83. EAGER - European Algebraic Geometry Research Training Network http://www-euclid.mathematik.uni-kl.de/

Your browser does not support frames! Click here for the EAGER welcome page. Click here for the EAGER menu.

84. American Prospect Online - ViewPrint made acquaintance as boy or girl with the proud edifice of euclid s geometry thus begins was akin to the axiom of parallels in euclid s geometry. http://www.prospect.org/web/view-print.ww?id=5092

85. The Origins Of Geometry Thus, almost from its inception, euclidean geometry had something of the character of dogma. euclid based his geometry on five fundamental assumptions http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node4.html

!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.0//EN"> Next: Spherical Geometry Up: Neutral and Non-Euclidean Geometries Previous: List of Tables The Origins of Geometry In the beginning geometry was a collection of rules for computing lengths, areas, and volumes. Many were crude approximations derived by trial and error. This body of knowledge, developed and used in construction, navigation, and surveying by the Babylonians and Egyptians, was passed to the Greeks. The Greek historian Herodotus (5th century B C .) credits the Egyptians with having originated the subject, but there is much evidence that the Babylonians, the Hindu civilization, and the Chinese knew much of what was passed along to the Egyptians. The Babylonians of 2,000 to 1,600 B C knew much about navigation and astronomy, which required a knowledge of geometry . They also considered the circumference of the circle to be three times the diameter. Of course, this would make a small problem. This value for carried along to later times. The Roman architect Vitruvius took . Prior to this it seems that the Chinese mathematicians had taken the same value for . This value for was sanctified by the ancient Jewish civilization and sanctioned in the scriptures. In

86. Gresham College | Lecture Archive as in euclid s geometry, you would get forever further away, should be further tests of whether space conforms to euclid s geometry rather than to http://www.gresham.ac.uk/event.asp?PageId=39&EventId=183

87. Citebase - The Equation Of Causality Ob jects of euclid s geometry are a part of a system of homogeneous entities. euclid s geometry is only a limited case of this generalized geometry. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:physics/9912007

88. MATH 360: Foundations Of Geometry Chapter 1, euclid s geometry , pages 19 in Wolfe, and Chapter 1 in Meschkowski. Introductory and historical materials. 23. http://people.hws.edu/mitchell/math360s05.html

Math 360: Foundations of Geometry Offered: Spring 2005 Instructor: Kevin J. Mitchell Office: Lansing 305 Phone: (315)781-3619 Fax: (315)781-3860 E-mail: mitchell@hws.edu Information Available: About the course Outline of Weekly Readings Assessment Office Hours ... Additional Sources on Reserve About the Course This course is about geometry and, in particular, the discovery (creation) of non-Euclidean geometry about 200 years ago. At the same time, the course serves as an example of how the discipline of mathematics works, illuminating the roles of axioms, definitions, logic, and proof. In this sense, the course is about the process of doing mathematics. The course provides a rare opportunity to see how and why mathematicians struggled with key ideas-sometimes getting things wrong, other times having great insights (though occasionally they did not recognize this fact). History is important to this subject; this course should convince you that mathematics is a very human endeavor. The course focuses on Euclid's Parallel Axiom: "For any line l and any point P not on l, there is a unique line through P parallel to l." In particular, could this axiom be deduced as a consequence of the earlier and more intuitive axioms that Euclid had laid out for his geometry? Mathematicians struggled with this question for 2000 years before successfully answering it. The answer had a profound philosophical effect on all later mathematics, as we will see.

89. Zoe Woodworth euclid s geometry was a mental abstraction that could be used to rationally define spaces. The idea that straight lines could be combined in different ways http://www.andrew.cmu.edu/course/60-105/finals/Woodworth_Z/'woodworth_z.html

The Artwork of Revolutionary Reason, and of Fearsome Faith: An Examination of the Transition from the Classical to the Christian Era Pre-Industrial Visual Cultures Final Paper The rise of rational doubt among ancient Greek philosophers lay the groundwork for a dramatic reconceptualization of time and space in the Classical Era. In this paper, I will expose some basic characteristics of the artwork which came out of this era. I will then examine the subsequent rise of Christianity, and how this radical change in the belief system affected the artwork which we see, in turn, from this era. Rational doubt sharply separated the Greek system of beliefs from other systems based on religious notions. The effect it had in Classical society was to sweep away convoluted magical explanations and replace them with the mechanism of logic. In societies which preceded Greece such as the ancient Egyptians, Hindus, and aborigines it was generally held that time was cyclical, and meandered back and forth between reality and myth. Furthermore, in these cultures there was typically no distinction made between the "in here" space of human imagination and the "out there" space of reality. In fact, the mixing of the inner space of dream, trance, and myth with the real space of everyday existence was a characteristic of nearly every cultural system of beliefs worldwide before the Greeks. However, using their newly-crafted mechanism of logic, philosophers of Greek Civilization made deep inquiry into the concepts of time and space. Their conclusions had a profound effect on art. According to Leonard Shlain, author of

90. P13 of euclid s geometry and its more recent descendants. Also included are complete Contents euclid s geometry. Hilbert s Axioms.- geometry over Fields. http://www.yurinsha.com/321/p13.htm

Hindry, M., Universite de Paris, France Silverman, J.H., Brown University, Providence, RI, USA Diophantine Geometry An Introduction 2000. Approx. 520 pp. 8 figs. This an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In the part of the book, the reader will find numerous exercises. Contents: The Geometry of Curves and Abelian Varieties.- Height Functions.- Rational Points on Abelian Varieties.- Diophantine Approximation and Integral Points on Curves.- Rational Points on Curves of Genus Greater Than 2.- Further Results and Open Problems. Series : Graduate Texts in Mathematics.VOL. 201 Book category: Graduate Textbook Publication language: English Publication date: April 2000 Stahl, A., University of Bonn, Germany Physics with Tau Leptons 2000. VIII, 316 pp. 236 figs. The book reviews the current status of tau physics. It addresses the properties of the tau lepton and summarizes

91. ROBUST STRIATIONS euclid s geometry had been the most profound argument for the concept of The theory argues that these fundamental forms of euclid s geometry, http://www.reiser-umemoto.com/books/tokyobay/david/david.htm

ROBUST STRIATIONS David Ruy At the Emerging Complexities conference at Columbia University, Professor Noriaki Kamiya delivered a paper, 'Integral Isotopies, Genotopies and Isodualities of the Theory of Numbers,' that was a bewildering presence from the standpoint of architectural theory. The difficult language and the difficult concepts presented in the paper, emblematic of modern mathematics in its undiluted state demonstrates if nothing else, that architecture's professed intimacy with geometry may not be so intimate after all. It has been argued, at times apologetically, that the geometry known to architecture is sufficient to architecture; that architecture's instruments have little bearing on the more important problem, architecture's cultural content and intentions. This certainly underestimates the degree to which the instruments assumed by architecture ultimately condition the conceptual limits of spatiality by reducing possibilities. This, of course, would not be a problem if it were the case that there is one and only one true space. However, it is this very notion that is challenged by the shifts that have occurred in the mathematics of the past two centuries, and it is worthwhile to more closely examine the math itself. Much is attributed to or blamed on Euclidean geometry when the spatiality of architecture is questioned. However, the particulars of what Euclid actually stated is seldom discussed. The concept of infinite extension can certainly be found in Euclid. However, neither the universality of spatial conditions nor anything remotely like the idea can be found. Homogeneity of space is implied, but never directly stated. The properties of figures are proposed, but never asserted as necessary. There is never any interpretation nor are there any statements at all regarding the nature of space and spatiality made by Euclid. In Euclid's original text, the character and bias of space is always a consequence of geometry's propositions taken collectively. In fact, the question of geometric space's relationship to actual space is something that has never been comfortable for mathematicians or physicists.

92. Euclid --  Encyclopædia Britannica euclid the most prominent mathematician of GrecoRoman antiquity, best known for his treatise on geometry, the e ty = i Elements /e . http://www.britannica.com/eb/article-9033178

Home Browse Newsletters Store ... Subscribe Already a member? Log in Content Related to this Topic This Article's Table of Contents Introduction Life Sources and contents of the Elements Renditions of the Elements Other writings ... Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Euclid Page 1 of 8 flourished c. BC , Alexandria, Egypt Greek Eukleides the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements Euclid... (75 of 1972 words) var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: "Euclid."

93. Geometry: Euclid And Beyond (Hartshorne)-Springer Geometry Book This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of euclid s Elements http://www.springeronline.com/sgw/cda/frontpage/0,10735,4-102-22-2013290-0,00.ht

94. Cynthia Lanius' Lessons: The History Of Geometry euclid gave five postulates. The fifth postulate reads Given a line and a point not Research a mathematician who has made a contribution to geometry. http://math.rice.edu/~lanius/Geom/his.html

Cynthia Lanius Thanks to PBS for permission to use the Pyramid photo. History of Geometry Egyptians c. 2000 - 500 B.C. Ancient Egyptians demonstrated a practical knowledge of geometry through surveying and construction projects. The Nile River overflowed its banks every year, and the river banks would have to be re-surveyed. See a PBS Nova unit on those big pointy buildings. In the Rhind Papyrus, pi is approximated. Babylonians c. 2000 - 500 B.C. Ancient clay tablets reveal that the Babylonians knew the Pythagorean relationships. One clay tablet reads 4 is the length and 5 the diagonal. What is the breadth? Its size is not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? 3 times 3 is 9. 3 is the breadth. Greeks c. 750-250 B.C. Ancient Greeks practiced centuries of experimental geometry like Egypt and Babylonia had, and they absorbed the experimental geometry of both of those cultures. Then they created the first formal mathematics of any kind by organizing geometry with rules of logic. Euclid's (400BC) important geometry book The Elements formed the basis for most of the geometry studied in schools ever since.

95. American Mathematical Monthly, The: Geometry: Euclid And Beyond Full text of the article, geometry euclid and Beyond from American Mathematical Monthly, The, a publication in the field of Reference Education, http://www.findarticles.com/p/articles/mi_qa3742/is_200301/ai_n9200362

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Home Advanced Search IN free articles only all articles this publication Automotive Sports FindArticles American Mathematical Monthly, The Jan 2003 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Geometry: Euclid and Beyond American Mathematical Monthly, The Jan 2003 by Pambuccian, Victor Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. REVIEWS Edited by Gerald B. Folland Mathematics Department, University of Washington, Seattle, WA 98195-4350 Geometry: Euclid and Beyond. By Robin Hartshorne. Springer, New York, 2000, xii + 526 pp., ISBN 0-387-48650-2, $49.95. Reviewed by Victor Pambuccian The twentieth century has been not only the century of "Euclid must go!" but also the one in which the axiomatics of the many geometries that the nineteenth century had brought to the fore was carried out with remarkable success. These axiomatic accomplishments have been largely forgotten. Few would associate the axiomatic foundations of geometry with the names of Emil Artin, Karl Menger, Kurt Reidemeister, Max Dehn, Alfred Tarski, Reinhold Baer, Wilhelm Klingenberg, and Bartel Leenert van der Waerden, who are better known for their contributions to other fields that later became mainstream.

96. Abstract: Axiomatic Systems And The Hilbert-Frege Controversy Thus, euclid s geometry is transformed into an euclidean model divided into five groups of axioms. Each group pertains to a particular relation, http://www.societies.stir.ac.uk/sppa/proceedings/papers/jhudry38056abstract.html

The Scottish Postgraduate Philosophy Association [Home] [Events] [News] ... Abstracts > Axiomatic systems and the Hilbert-Frege controversy Axiomatic systems and the Hilbert-Frege controversy Jean-Louis Hudry, University of Edinburgh (10 Mar 2004) First SPPA Seminar Day , University of Edinburgh In his 'Grundlagen der Geometrie' (1899), Hilbert provides us with an account of Euclid's geometry, defined as a system of axioms and no longer as a collection of definitions, postulates and common notions. Thus, Euclid's geometry is transformed into an Euclidean model divided into five groups of axioms. Each group pertains to a particular relation, such as a relation of betweenness for the Axioms of Order or a relation of completeness for the Axioms of Continuity. Frege rejects the Euclidean model and claims that it is composed of pseudo-axioms and pseudo definitions that do not refer to proper geometric objects. He appeals to the notion of thought or sense, to which a truth condition is applied, and an axiom is true only if it asserts something that is already laid down by a true thought. In other words, an axiom cannot be a definition, since a merely assertive proposition does not define a concept; only a thought does. As well, Frege accuses Hilbert of confusing first-level concepts with second level ones, and of neglecting the fact that only first-level concepts, under which objects fall, can be laid down by real definitions and asserted by real axioms. If points, lines and planes are first-level concepts about geometric objects, then they do not belong to a second-level system of things, meaning that they are not interchangeable with 'love, law, chimney sweep' or 'table, chair, mug'.

97. The Cornell Library Historical Mathematics Monographs Document name Greek geometry from Thales to euclid. Go to. page NA Title page, page 186 Text. View as. 100%, 75%, 50%, pdf, text, thumbnails http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=03200004&se

98. Journal Of Differential Geometry, Volume 69, No. 3 Project euclid. update profile The Journal of Differential geometry is devoted to the publication of research papers in differential geometry and http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.jdg

99. Geometry Although in the time of euclid, geometry was modelled on a flat plane, in the past century mathematicians have turned to the study of curved spaces like the http://comet.lehman.cuny.edu/sormani/explore/geometry.html

Explore Geometry! Geometry is one of the oldest forms of mathematics, used in every ancient culture from Egyptians and Greeks to Mayas and Azteks. Today it is an active field applied to the study of the universe, crystals, and many other objects of interest. Although in the time of Euclid, geometry was modelled on a flat plane, in the past century mathematicians have turned to the study of curved spaces like the surface of the earth and more exotic spaces like the grid of streets navigated by a taxi driver. Here we introduce these concepts at the level of a high school or junior high school student. We have links to lesson plans for teachers that introduce spherical, hyperbolic and taxicab geometry. These plans were written by my masters students, many of whom teach at nearby high schools. We also have a page about metric spaces . Although such a space can be explained to a high school student, the study of metric spaces is one of the most advanced fields of mathematics. We would like to recommend Jeff Week's Geometry Games Webpage Here is a webpage for undergraduate math majors describing Perelman's work and the Poincare Conjecture.

100. Math 300 Guidelines For Papers euclid s geometry (Elements xiii.10) Archimedes Measurement of the Circle Nicole Oresme s Questions concerning euclid s geometry, Question 10 http://cerebro.cs.xu.edu/math/math300/02s/papers.html

Math 300 Great Moments in Mathematics Spring 2002 Guidelines for papers You will prepare two research papers for this course: a biographical paper, due February 21 , that relates the mathematical career of a noted historical figure born before 1700; and a paper due April 18 that performs a critical reading of an original source of importance in the history of mathematics. Your biographical paper should conform to the following guidelines, listed in order of importance, and will be evaluated against them: The paper should present a comprehensively researched discussion of the life history of your chosen mathematician; this person's significant mathematical accomplishments must be thoroughly discussed. (35%) It should be presented in a clear and coherent writing style , using correct spelling, proper pronunciation and good grammar. (25%) It should contain a bibliography with at least three sources including at least three print-published (not Web) sources, it should make appropriate use of direct quotations , and should include in-text citations (as either footnotes or endnotes). (25%)

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 5     81-100 of 109    Back | 1  | 2  | 3  | 4  | 5  | 6  | Next 20