1. KEGP KANT ON euclid geometry IN PERSPECTIVE. http://www.hkbu.edu.hk/~ppp/srp/arts/KEGP.html

KANT ON EUCLID: GEOMETRY IN PERSPECTIVE by Stephen Palmquist stevepq@hkbu.edu.hk I. The Perspectival Aim of the first Critique There is a common assumption among philosophers, shared even by many Kant-scholars, that Kant had a naive faith in the absolute valid­ity of Euclidean geometry, Aristotelian logic, and Newtonian physics, and that his primary goal in the Critique of Pure Reason was to pro­vide a rational foundation upon which these classical scientific theories could be based. This, it might be thought, is the essence of his attempt to solve the problem which, as he says in a footnote to the second edition Preface, "still remains a scandal to philosophy and to human reason in general"namely, "that the existence of things outside us...must be accepted merely on faith , and that if anyone thinks good to doubt their existence, we are unable to counter his doubts by any satisfactory proof" [K2:xxxix]. This assumption, in turn, is frequently used to deny the validity of some or all of Kant's philosophical projector at least its relevance to modern philosophi­cal understandings of scientific knowledge. Swinburne, for instance, asserts that an acceptance of the views expressed in Kant's first Critique "would rule out in advance most of the great achievements of science since his day."

2. Geometry: Euclid Geometry, Euclid Mathematician: WSM Explains Metaphysical Found Geometry, Euclid, Physics The Wave Structure of Matter (WSM) explains the Metaphysical Foundations of Euclid s Geometry. Matter http://www.spaceandmotion.com/Physics-Geometry-Euclid.htm

The Content and Anchor Links for the top part of this page are currently being upgraded (to be completed by May 2004) Search WSM Group Top of Page Geometry Euclid Geometry, Euclid Mathematician The Spherical Wave Structure of Matter (WSM) Explains the Metaphysical Foundations of Euclid's Geometry and Albert Einstein's Non-Euclidean Geometry Geometry - Euclid Geometry, Euclid Mathematician. WSM explains Metaphysical Foundations Euclid's Geometry Philosophy-Physics-Metaphysics@SpaceandMotion.com From the latest results of the theory of relativity it is probable that our three dimensional space is also approximately spherical , that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry but approximately by spherical geometry. (Albert Einstein, 1954) Geometry - Euclid Geometry, Euclid Mathematician. WSM explains Metaphysical Foundations Euclid's Geometry Philosophy-Physics-Metaphysics@SpaceandMotion.com (by Philosopher of Science Geoff Haselhurst David Hume , 1737) And though the philosopher may live remote from business, the genius of philosophy, if carefully cultivated by several, must gradually diffuse itself throughout the whole society, and bestow a similar correctness on every art and calling.

3. Biography Of Riemann What is Riemann Geometry? Riemann Geometry, or Elliptical Geometry, is one of the first types of noneuclid geometry. While in euclid geometry, there are. http://www.andrews.edu/~calkins/math/biograph/bioriema.htm

Back to the Table of Contents Biographies of Mathematicians - Riemann Riemann's Life Georg Friedrich Bernhard Riemann was born on September 17, 1826 in Breselenz, Germany to Georg Friedrich Bernhard Riemann and Charlotte Ebell. He grew up in the home of a pastor during a time of poverty. Along with his four siblings, he fought hunger and malnutrition. But despite all these problems, his family was close. Riemann's Most Famous Achievements Georg Friedrich Bernhard Riemann began his career by working on the theory of functions, but he is best remembered for his development of non-Euclidean geometry. This is used today in physics and in the relativity theory. He completed all of the following studies: developed the subjects of partial equations, complex variable theory, differential geometry, analytic number theory, and laid down the foundations for modern topography. The Riemann Hypothesis The Riemann Hypothesis states that the nontrivial roots of the Riemann zeta function (which is explained later in the web page) defined on the complex plane C all have real part 1/2. The line Re(z) equaling 1/2 is called the critical line. Or if you want the Riemann Hypothesis in plain English, all of the complex zeroes of the zeta function have real part 1/2. No one has solved has solved the hypothesis because it is terribly difficult and confusing. However, there are many ideas. One of the better ideas for proving the hypothesis was put forth by Polya and Hilbert. However the reasoning of solving the hypothesis is quite confusing.

4. MathsNet Resources: Geometry Books Starting with euclid geometry has flowed out over the centuries describing the universe and, Mlodinow argues, making modern civilization possible. http://www.mathsnet.net/resource/geometry.html

Euclid Born: about 325 BC Died: about 265 BC in Alexandria, Egypt The Thirteen Books of The Elements, Vol I and II Dover. Translated by Sir Thomas L. Heath Buy at Robert Lawlor sacred geometry explores geometry using illustrations from science and art, such as Islamic tiles, atomic structure, architectural proportions and fine art. Nine workbooks lead you through geometric constructions using only a pencil, compass, straight-edge and graph paper. Includes the Vesica Piscis, Golden Section, Squaring the Circle, Geometry and Music, the Platonic Solids and more. Interspersed with philosophy about the meanings and symbolism of sacred geometry. Buy at Roger B. Nelson Proofs without Words Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics. Buy at Proofs without Words II

5. Metting René THOM Moreover, I believe that it was in third grade, we had elementary euclid geometry ; my teacher was not particularly brilliant , but he had managed to arouse my http://perso.wanadoo.fr/jacques.nimier/meeting_rene_thom.htm

Field medal award ( Nobel prize for mathmatics) ) How the motivation of a discipline fits the personality (Translation by Michel DURAND) Subtitles and bold types are of my own responsibility.The bold types indicate that what I mean as an emotional aspect, according to my point of view ,therefore belonging to the category of the " cognitive-emotional " interactions A nostalgia of the triangles era - N: .. Do you remember your early attempts in researches? - T: Yes, I translated all known theorems in geometry R3 to geometry R4 That was, if I dare to say, my first attempt to do something a little bit original; but it was for me a way to succeed in the understanding of how was made, let us say a system of two plans in R4 Etc. and I believe that I attained a very good intuition in that time, and I could already see a space in four dimensions when I was ten, or eleven years old. - N: And so , have you other remembrances of that period?

6. Descartes And The Galilean Scientific Revolution a geometric object. It allows the algebriecal expression of euclid geometry and it allows to geometrize Algebra. It allows the visualization http://www.ensc.sfu.ca/people/grad/brassard/personal/THESIS/node24.html

Next: Leibniz's Perceptual Monads Up: STRUCTURALISM Previous: Aristotle Descartes and the Galilean Scientific Revolution The Galilean scientific revolution that took place in the Renaissance Europe. It is borne of the naturalistic spirit of the late middle ages that culminated with the rejection of the scholastic philosophy. The scholatic philosopy is a High middle age formulation of the Aristotelian philosophy and it was central to the Catholic church's view of the world. Copernicus's model of the planets following circular trajectories around the sun, Galileo's support of this theory by the observation of the planets and their satellites with the telescope, Galileo's experiments with falling bodies contradicting Aristotle's physics, and many more ground breaking discoveries, have shaken the physics of Aristotle, showed the mathematical (Platonic) nature of the world, and have renewed the status of experience as the arbitrator of truth. This scientific revolution was also putting in question the meaning of human life, the religious and political orders and in this new world. Then flourished different philosophical positions having in common the core values of experimental sciences and to retain of only one aspect of the physics of Aristotle: the first cause. And among these new philosophical positions, Descartes' philosophy became dominant.

7. Geometry: Euclid drop becket@jollyroger.com a line. Euclid geometry. DR. euclid geometry Discussion Deck. Euclid Discussion Deck Euclid Other http://westerncanon.com/cgibin/lecture/Euclidhall/cas/44.html

geometry: Euclid Discussion Deck If ye would like to moderate the Euclid Discussion Deck, please drop becket@jollyroger.com //Required //var site = '681666'; //var mnum = '139010'; //Not Required var max_words = 3; var max_links_per_word = 4; var link_color = '0107A1'; var boxbg_color = 'FFFAEA'; var boxtitle_color = 'black'; var boxdesc_color = 'black'; var boxurl_color = 'red'; DR. ELLIOT'S NORTH AMERICAN GREAT BOOKS TOURCOMING TO A BOOK STORE NEAR YOU WRITER S WORD.COM: Open Source CMS][ ... The World's Largest Literary Cafe: Carolinanavy.com Posted by ME on November 02, 19102 at 21:25:15: i hate geometry Follow Ups: Post a Followup Name: E-Mail: Subject: Comments: : i hate geometry Optional Link URL: Link Title: Optional Image URL: Follow Ups Post Followup Euclid Discussion Deck The Jolly Roger ... The World's Largest Literary Cafe : Carolinanavy.com ] Carolinanavy.com Nantuckets.com BusinessPhilosophy.com Classicals.com ... SEARCH Euclid geometry: Discussion Deck Euclid Discussion Deck If ye would like to moderate the Euclid Discussion Deck, please drop becket@jollyroger.com

8. Euclid's Elements, Introduction This dynamically illustrated edition of euclid s Elements includes 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

Introduction New: Jaume Domenech Larraz has translated the Elements into Catalan at http://www.euclides.org/ Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages. I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive. The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. I still have a lot to write in the guide sections and that will keep me busy for quite a while. This edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate the diagrams. If you enable Java on your browser, then you'll be able to dynamically change the diagrams. In order to see how, please read

9. Introduction To The Works Of Euclid Covers the life of euclid and a discussion of euclidean geometry. http://www.obkb.com/dcljr/euclid.html

An Introduction to the Works of Euclid with an Emphasis on the Elements (first posted to the web in 1995) jump to: outline of paper text of paper suggestions for further study bibliography ... anchor here Outline of paper Introduction I. The Life of Euclid II. The Works of Euclid Other than the Elements ... Bibliography About this paper This is a paper I wrote in college for a History of Science course (although I've taken the liberty of modifying it slightly from time to time since I put it online). I know it's not publishable or anything, but it's still one of my favorite papers because it was so difficult to do. (I wrote it on a computer with about 12K of free RAM and only a cassette tape drive for storage!) In fact, the whole History of Science course was quite an experience. Students wishing to use this paper for their own reports on Euclid should know how to avoid plagiarism and how to cite online sources . In addition, I urge students to seek out the original printed sources yes, that means going to the library and not rely merely on what I say in this paper. (I'm always surprised by the number of junior high and high school students who e-mail me saying they can't find any information about Euclid!) Note that is used to denote square roots and all Greek letters used as symbols ( alpha beta , ...) are spelled out. Superscripts are implemented by using the appropriate HTML tags and may not display properly in some browsers. In this case, hopefully the meaning will be clear from the context.

10. Euclid's Geometry euclid's geometry. Constructions. Write a 510 page paper on the problem of contructing the regular polygons. It was proved by C.F. Gauss that a regular polygon with n sides can be constructed if and http://www.math.uga.edu/~cantarel/teaching/math170/projects/node1.html

Next: Spherical and Non-Euclidean Geometry Up: Math 170 Possible Final Previous: Math 170 Possible Final Euclid's Geometry Constructions. Write a 5-10 page paper on the problem of contructing the regular polygons. It was proved by C.F. Gauss that a regular polygon with n sides can be constructed if and only if where and the are primes in the form for some integer j . Explain this theorem. A good lead is Coxeter An Introduction to Geometry Constructions. Since is prime, a regular 17-gon is constructible. Get a BIG sheet of paper, and construct the regular 17-gon. A good lead is Palacios Velez, Oscar Luis A chord approach for an alternative ruler and compass construction of the 17-side regular polygon. Geom Dedicata 52 (1994), no. 3, 209 - 213. Non-circular Curves. Design and build a device which automatically draws a conchoid or a quadratrix. Napoleon's Theorem. We have seen that the construction of equilateral triangles on each side of a given triangles gives an equilateral triangle when the centers of these triangles are connected. Prove it. Hint: Draw circles around the equilateral triangles. Incommensurables. One great crisis in Pythagorean mathematics came about when it was proved that the diagonal of a square of side one is not an even multiple of some fraction of the length of the length of the side in modern language, when it was proved that the square root of 2 was irrational. Write a paper explaining the proof that

11. EAGER - European Algebraic Geometry Research Training Network European algebraic geometry research training network. http://euclid.mathematik.uni-kl.de/

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

12. Mathlab.com Home of Handson geometry euclid's Elements, the most significant scientific text of euclid applet can draw lines and circles. Lines and circles are the fundamental building blocks of the euclidean geometry http://www.mathlab.com/

E uclid's Elements, the most significant scientific text of all time has been the main source of inspiration for the creation of this web site. In his Elements, Euclid laid the foundations of mathematics based solely on physical tools, straightedge and drawing compass. This site offers virtual straightedge and compass , through a Java applet named after Euclid. U sing virtual straightedge and compass our Euclid applet can draw lines and circles . Lines and circles are the fundamental building blocks of the Euclidean geometry. The Euclidean geometry is a tradition that was pioneered by the Greek mathematicians of antiquity over two millennia ago. We hope to keep that tradition alive. C lick here to open our help page in a new window called "Help." The help page shows you how to use our Euclid applet, and it contains a few propositions from Euclid's Elements. L et's start the Euclid applet in a new window called "Euclid," if you have not already done so. (WARNING: If you start Euclid again you will lose all the previous drawings.) We recommend that you open our help page before you start Euclid, especially if this is your first visit to our web site. I f you have any comment or question, please send it to

13. EAGER:List Of Conferences A list maintained by the EAGER node at Kaiserslautern, Germany. http://www-euclid.mathematik.uni-kl.de/conferences/

Conferences in algebraic geometry and related fields This list of announcements and links to upcoming activitiesis compiled by submission .If you know of an activity that should be added to this list,please contact its organizer or Kristian Ranestad the administrator of this page Conferences here include also schools, workshops and specialmonths/years. Past conferences Current conferences Upcoming conferences Upcoming conferences to Noncommutative Algebra and Algebraic Geometry at University of Warwick Organizers: Colin Ingalls, Miles Reid Additional information at http://www.maths.warwick.ac.uk/~ingalls/participants.html Further remarks: The program includes talks by Professors Bridgeland, Buchweitz, Chan, Coffee, Craw, Hacking, Ishii, Kulkarni, Kuznetsov, Lunch, McKay, Rogalski, Sheiham, Smith, Stafford, Van den Bergh, Yekutieli. to Algebraic Geometry at Paris Organizers: A. Beauville, F. Han, L. Koelblen, C. Sorger, C. Voisin Additional information at http://www.institut.math.jussieu.fr/~koelblen/ga2004/ Further remarks: Conference in honour of Joseph Le Potier and Christian Peskine Confirmed speakers: M. Brion, J.-P. Demailly, O. Debarre, D. Eisenbud, G. Ellingsrud, W. Fulton, L. Gruson, A. Hirschowitz, K. Hulek, D. Huybrechts, R. Lazarsfeld, K. O'Grady, R. Piene, M. Popa, S. Popescu, K. Ranestad, S.-A. Strømme, F. Zak

14. Euclid's Elements euclid's elements This World Wide Web (WWW) site, for teachers, students and others interested in geometry, was created by David E. Joyce of Clark University to rekindle interest in euclid's http://rdre1.inktomi.com/click?u=http://aleph0.clarku.edu/~djoyce/java/elements/

15. The Geometry Applet This geometry applet is being used to illustrate euclid s Elements. Above you see an icosahedron, that is, a regular 20sided solid http://aleph0.clarku.edu/~djoyce/java/Geometry/Geometry.html

The Geometry Applet version 2.2 *** If you can read this, you're only seeing an image, not the real java applet! *** I began writing this applet in Feb. 1996. The current verion is 2.2 which fixes a couple of bugs in 2.0 and has a new construction to find harmonic conjugate points. Version 2.0 (May, 1997) does three-dimensional constructions whereas the earlier version 1.3 only did plane constructions. Version 2.0 also has many minor improvements. It takes a while to test everything. Please send a note if you find any bugs. They'll be fixed as soon as possible. (Note that arcs and sectors on slanted planes cannot yet be illustrated.) Also, there may be still later versions than 2.2 with more functionality. This geometry applet is being used to illustrate Euclid's Elements . Above you see an icosahedron, that is, a regular 20-sided solid, constructed according to Euclid's construction in proposition XIII.16 Another example using this Geometry Applet illustrates the Euler line of a triangle Here's how you can manipulate the figure that appears above. If you click on a point in the figure, you can usually move it in some way. A free point , usually colored red, can be freely dragged about, and as they move, the rest of the diagram (except the other free points) will adjust appropriately. A sliding point

16. History Of Mathematics - Table Of Contents Topics include background in Babylonian, euclid, Al'Khwarizmi, pi, and trigonometry. Also has recreations and java chat. http://members.aol.com/bbyars1/contents.html

And Insights into the History of Mathematics Table of Contents Prologue The First Mathematicians The Most Famous Teacher Pi: It Will Blow Your Mind ... Comments and Notices

17. Euclid's Geometry History And Practice euclid's geometry History and Practice A series of interdisciplinary lessons on euclid's Elements, researched and written by a Classicist and hosted by the Math Forum. The material is organized http://rdre1.inktomi.com/click?u=http://mathforum.org/geometry/wwweuclid/&y=

18. Euclid's Geometry: History And Practice euclid S geometry History and Practice. This series of interdisciplinary lessons on euclid s Elements was researched and written http://mathforum.org/geometry/wwweuclid/

EUCLID'S GEOMETRY: History and Practice This series of interdisciplinary lessons on Euclid's Elements was researched and written by Alex Pearson, a Classicist at The Episcopal Academy in Merion, Pennsylvania. The material is organized into class work, short historical articles, assignments, essay questions, and a quiz. For the Greek text and a full translation of The Elements, see the Perseus Project at Tufts University. Introduction "Why do we have to learn this?" A discussion of how geometry has seemed indispensable to some people for over two millennia. Unit 1 Definitions, axioms and Theorem One. On a given finite straight line construct an equilateral triangle. Upon a given point place a straight line equal to a given straight line. Unit 2 Theorem Two and an introduction to history. Upon a given point place a straight line equal to a given straight line. Historical articles essay questions. Unit 3 Group discussions on the Elements; history and propositions; preparation for the Unit 4 Quiz. Unit 4 Quiz: Complete Euclid's Fifth Theorem and identify the definitions, common notions, postulates and prior theorems by number. Prove two of the historical propositions using at least two different pages from my

19. Euclid's Elements, Table Of Contents Using the geometry Applet. About the text. euclid. A quick trip through the Elements. References to euclid's Elements on the Web http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

Table of Contents Prematter Introduction Using the Geometry Applet About the text Euclid ... A quick trip through the Elements References to Euclid's Elements on the Web Subject index Book I The fundamentals of geometry: theories of triangles, parallels, and area. Definitions Postulates Common Notions Propositions ... Book II Geometric algebra. Definitions Propositions Book III Theory of circles. Definitions Propositions Book IV Constructions for inscribed and circumscribed figures. Definitions Propositions Book V Theory of abstract proportions. Definitions Propositions Book VI Similar figures and proportions in geometry. Definitions Propositions Book VII Fundamentals of number theory. Definitions Propositions Book VIII Continued proportions in number theory. Propositions Book IX Number theory. Propositions Book X Classification of incommensurables. Definitions I Propositions 1-47 Definitions II Propositions 48-84 ... Book XI Solid geometry. Definitions Propositions Book XII Measurement of figures. Propositions Book XIII Regular solids. Propositions (June, 1997.)

20. Euclid's Geometry: Euclid's Biography someone who had begun to read geometry with euclid, when he had learnt the first theorem, asked euclid, what shall I get by learning these things? euclid http://mathforum.org/geometry/wwweuclid/bio.htm

3. Euclid's biography Heath, History p. 354: Proclus (410-485, an Athenian philosopher, head of the Platonic school) on Eucl. I, p. 68-20: Not much younger than these is Euclid, who put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first, makes mention of Euclid; and further they say that Ptolemy once asked him if there was in geometry any shorter way that that of the Elements, and he replied that there was no royal road to geometry. He is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, the latter having been contemporaries, as Eratosthenes somewhere says. (Plato died 347 B.C.; Archimedes lived 287-212 B.C.) Heath, History p. 357: Latin author, Stobaeus (5th Century A.D.): someone who had begun to read geometry with Euclid, when he had learnt the first theorem, asked Euclid, "what shall I get by learning these things?" Euclid called his slave and said, "Give him threepence, since he must make gain out of what he learns." Sarton, p. 19: Athenian philosopher, Proclus (410 A.D. - 485): Ptolemy I, king of Egypt, asked Euclid "if there was in geometry any shorter way than that of the

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