21. 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 by Alex Pearson, 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

22. 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 Midwest Algebra, Geometry and their Interactions Conference (MAGIC05) at University of Notre Dame, Indiana, USA Organizers: Alberto Corso, Juan Migliore and Claudia Polini Additional information at http://www.nd.edu/~magic05/ Further remarks: The conference continues the tradition of commutative algebra and algebraic geometry meetings in the Midwest, among which we single out MAGC97 at the University of Notre Dame in 1997, BACH2 at the University of Kentucky in 2003 and the Lipman-Fest at Purdue University in 2004. This year though the meeting will also have an applied component. Please check the conference website for the list of speakers. The conference will be preceded by a public lecture delivered by Professor Bernd Sturmfels, on October 7, 2005. to Complex algebraic geometry at CIRM Luminy Organizers: S. Druel, N. Perrin

23. 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? 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

24. 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

25. The Geometry Applet geometry so that the postulate euclid s Fourteenth Book and is there a noneuclidean geometry? 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

26. Euclid euclid was the fundamental text in the study of geometry, although only the first six books were usually required. Although books were the basis for http://special.lib.gla.ac.uk/exhibns/month/june2001.html

Special Collections Library Home Special Collections Catalogues Main Library ... Course Material Book of the Month June 2001 Euclid's Geometry France: c. 1480 Sp Coll MS Gen. 1115 This month's book has been chosen as one of the items to be displayed on Friday 15 June in the exhibition Information Services through the Ages organized by the Library Special Collections Department and the University Archive Services as part of the Information Services Open Day. It is a fifteenth century manuscript of Euclid's Elements in Latin with other texts mainly on geometry. front flyleaf: early pressmarks Glasgow University was founded in 1451. Although we do not know for sure, this manuscript was possibly used in early teaching at the University. Certainly, it is a typical example of the kind of textbook that would have been used as part of the medieval curriculum. While there is no record of how the manuscript was acquired by the Library, it does bear early University press marks on the front flyleaf: Ff.3. n.5, and another earlier Glasgow mark, now crossed out and obscured, but possibly beginning with a 'G'. folio 8r: beginning of Euclid's elements The main item in the manuscript (folios 8-172v) is a copy of Euclid's Elements , translated out of Arabic into Latin by the English scholastic philosopher Adelard of Bath. Its colophon states that it was finished being written out on 4 December 1480. This manuscript copy therefore predates the first printed edition, produced in Venice by Erhard Ratdolt in 1482, by just two years.

27. Euclid's Geometry euclid s geometry. euclid s geometry. Constructions. Write a 510 page paper on the problem of contructing the regular polygons. http://ada.math.uga.edu/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

28. Zuniga-Galindo, Wilson Barry University. Algebraic geometry, number theory, padic analysis. http://euclid.barry.edu/~zuniga/

29. 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.

30. The Origins Of Proof In the beginning euclid s geometry. euclid was born about 365 BC in euclid goes on in his Elements to present various geometric propositions, http://plus.maths.org/issue7/features/proof1/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 7 January 1999 Contents Features Unspinning the boomerang Bang up a boomerang! Galloping gyroscopes Time and motion ... The origins of proof Career interview Career interview: Games developer Regulars Plus puzzle Pluschat Mystery mix Letters Staffroom Introducing the MMP Geometer's corner International Mathematics Enrichment Conference News from January 1999 ... posters! January 1999 Features The origins of proof by Kona Macphee What is proof? Philosophers have argued for centuries about the answer to this question, and how (and if!) things can be proven; no doubt they will continue to do so! Mathematicians, on the other hand, have been using "working definitions" of proof to advance mathematical knowledge for equally long. Starting in this issue, PASS Maths is pleased to present a series of articles introducing some of the basic ideas behind proof and logical reasoning and showing their importance in mathematics.

31. GAEL - Géometrie Algébrique En Liberté A series of conferences aimed at researchers in Algebraic geometry at the beginning of their scientific career. http://www-euclid.mathematik.uni-kl.de/~gael/

The success of GAEL as a young people's conference was recently recognised by David Eisenbud, president of the American Mathematical Society, in an interview in Notices of the AMS . His comments about GAEL are copied here ; the full article can be read on the AMS webpage GAEL XIV : Provisional details GAEL XIII : Details now available The dates have been set for Gael XIII. It will be Monday, 21st - Friday, 25th March, 2005. More details are in the announcement Some General Remarks on GAEL Future Editions of GAEL Information on GAEL XIII (March 2005) Previous Editions of GAEL Participants and Scientific Programme of all Editions of GAEL (GAEL I - VII) Information on GAEL VI (March 1998) Information on GAEL VII (March 1999) Information on GAEL VIII (March 2000) ... Information on GAEL XII (April 2004) This page is maintained by Elizabeth Baldwin It has not been changed since 14th March 2005.

32. 'Euclid's Window' euclid s Window The Story of geometry from Parallel Lines to Hyperspace. By Leonard Mlodinow. Anyone who thought geometry was boring or dry should prepare http://plus.maths.org/issue22/reviews/book4/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 22 November 2002 Contents Features More or Less In a spin The golden ratio and aesthetics The best medicine? Career interview Career interview: Medical statistician Regulars Plus puzzle Pluschat Mystery mix Reviews 'The Golden Ratio' 'Euclid's Window' 'Elements of Grace' and 'Copernican Notes' 'Calculus' ... posters! November 2002 Reviews 'Euclid's Window' reviewed by Rachel Thomas Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace By Leonard Mlodinow Anyone who thought geometry was boring or dry should prepare to be amazed. Despite its worthy cover this book is exactly what its title says - a story - and the plot of this story involves life, death and revolutions of understanding and belief, and stars the some of the most famous names in history. The book opens with Aristotle watching ships at sea disappearing hull first over the horizon. "On a flat earth, ships should dwindle evenly until they disappear", and so he came to the realisation that the earth must be curved. This sets the scene for Mlodinow's tale of how geometry has shaped human history - "to observe the large scale structure of our planet, Aristotle had looked through the window of geometry." The book recounts how we have continued to look through this window to understand the reality we live in, and how the window has changed along the way.

33. Thabit Gives information on background and contributions to noneuclidean geometry, spherical trigonometry, number theory and the field of statics. Was an important translator of Greek materials, including euclid's Elements, during the Middle Ages. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thabit.html

Al-Sabi Thabit ibn Qurra al-Harrani Born: 836 in Harran, Mesopotamia (now Turkey) Died: 18 Feb 901 in Baghdad, (now in Iraq) Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

34. Untitled About 300 BC, euclid organized all of the geometry and much of the And so persuasive and logically compelling was euclid s geometry that it took over http://www.southernct.edu/~grant/nicolai/history.html

A Brief History of Geometry Leading to non-Euclidean Geometry Much of the following is excerpted, with permission, from A Mathematics Sampler: Topics for the Liberal Arts, Fourth Edition About 300 BC, Euclid organized all of the geometry and much of the arithmetic and number theory that was known (some 300 years of work by earlier Greek mathematicians) into a single, cohesive work, The Elements . Euclidean geometry is the geometry we learn informally as children and somewhat more formally in high school geometry; for most, it is just "geometry." Euclid's goal was to systematize the various relationships that had been observed among spatial figures, which he, like Plato and Aristotle, regarded as ideal representations of physical entities. Euclid's organizational scheme, the axiomatic method, was so ingenious that it has remained the paradigm for all of mathematics and much of science. And so persuasive and logically compelling was Euclid's geometry that it took over two thousand years before mathematicians began to suspect that there might be other ways of looking at geometry, that perhaps Euclid's geometry was not the geometry, but

35. EAGER Activities European Algebraic geometry Research Training Network. Activities of or related to the network. http://euclid.mathematik.uni-kl.de/activities/

EAGER ACTIVITIES Research Research objectives and division of among the nodes Training Predoc and Postdoc positions Annual schools and conferences General propaganda EAGER annual Euroconference GAEL Trento schools ... VBAC meetings RELATED ACTIVITIES Schools and meetings September schools, Poland MRI spring schools, Netherland Nordfjordeid summer schools, Norway COW (Cambridge Oxford Warwick algebraic geometry seminar), England ... Scuola Matematica Interuniversitaria, Italy Summer schools in mathematics in Cortona and Perugia. Check also our algebraic geometry conference list Student programs International Master's Programme at Kaiserslautern, Germany MRI Master classes Netherland MSc program at Warwick MSc program at Cambridge

36. Properties Of Space euclid s geometry had done more than help architects and cartographers. The confidence in euclid s geometry was starting to be undermined. http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Properties-of-Space.

Click here to download a Printable pdf version of this page. Oh, for heavens sake, Norman! You act as if you have never seen a hole in the time-space continuum before. Three properties of space will be discussed: Geometry, Topology and Dimensionality Euclidean and Non-Euclidean Geometry In one area of human inquiry there had long existed a quiet confidence in our ability to fathom something of the ultimate truth about the universe. People thought that if this success was possible in one area of inquiry then perhaps it was true in others. The source of this confidence was the age-old study of geometry that Euclid and the ancient Greeks had placed upon a firm logical foundation. Euclidean geometry is a geometry where the Pythagoras Theorem for triangles holds. The theorem gives the distance-squared between two points (c in the diagram) as the sum of the squares of the other two sides (a and b ). Any space where this Euclidean distance function holds is said to be spatially flat.

37. Trento Schools Intended for European doctoral students and postdoctoral fellows in algebraic geometry. http://euclid.mathematik.uni-kl.de/activities/trento.html

Trento schools These schools are a continuation of more than 10 previous schools. The Program Management Committee chooses a topic in the light of recent developements and selects the best experts for the scientific organization of the school. The purpose is either to provide young researchers with a basic but sophisticated technique or to present them with a coherent overview of some developing area. These schools are intended for European doctoral students and post-doctoral fellows in algebraic geometry. Previous schools Trento school 1997 Trento school 1998 Trento school 1999 ... Trento school 2002 reports on problems to wwwadmin@euclid.mathematik.uni-kl.de back to main page

38. What Really Is Geometry? The geometry taught today in school is a confused mixture of euclid s and Descartes But the beauty of euclid s geometry is that it does not make use of http://www.mathpath.org/concepts/geometries.htm

A summer program and resource for middle school students showing high promise in mathematics What is Geometry? The nature and inter-relationship of various geometries The geometry taught today in school is a confused mixture of Euclid's and Descartes'. But the teacher is not to blame. Having evolved from antiquity from often-used methods for measurement of figures drawn mainly on plain surfaces, the methods and principles became distilled, for ready reference and use, as mathematical propositions, particularly in Greece in the peace and prosperity of the few centuries following the rule of Pericles. Then Euclid, in around 300 B.C., gathered, improved, and systematically wrote down all that was known in Geometry to his day. The work - called The Elements - attempted to develop Geometry from the firm foundation of axioms and succeeded in great measure to provide rigorous demonstrations - proof - of the mathematical results loosely proved by his predecesors. While most of the proofs in Euclid's work were correct, blemishes were discovered in some proofs one of which being the very first proposition in the Elements. However, these blemishes were not due to erroneous deduction but tacit assumptions or "intuitively obvious" facts that were not justified by the axioms. Considerations of these blemishes culminated in 1899 A.D. with David Hilbert's proposal of a revised axiom system that would not only preserve the validity of the proofs in the Elements but which was in conformity with the modern notion of the axiomatic method as proceeding from a set of undefined terms, definitions, and the axiom statements on the undefined terms. The Euclidean Geometry of today is the Geometry based on this revised axiom system or other equivalent systems since proposed.

39. Euclid Mathematician Picture Math Gift Shirt Mathematicians Famous euclid s geometry was one of construction, and the circle and radius were central elements to euclid s constructions. http://www.mathematicianspictures.com/Mathematicians/Euclid.htm

Home about The Mathematicians Math Gift Shop about us ... Composers T shirts THE MATHEMATICIANS About The Mathematicians Index Page TShirts Index page Famous Mathematician ... Property of Math Dept MATH POSTERS Posters Index page The Mathematicians Pi Posters Pi Day Posters ... Posters MATH MUGS Riemann Mugs Pi Mugs Pi Day Mugs PI STORE Pi Store Index page Pi Posters, Tshirts, Mugs Pi Day Posters, Tshirts, Mugs Pi Scroll Posters ... PI OF THE MONTH CLUB CLOCKS Mathematician Desk Clocks CUSTOM ORDERS Custom Orders FEATURED MATH EMATICS BOOK AUTHOR Ask the Author ABOUT US About Us C ustomer Coments Page Contact SHOPPING CART View Shopping Cart THE MATHEMATICIANS The Mathematicians Index Page Pythagoras of Samos Zeno of elea Archimedes ... Founders of America Euclid Gift items available include: Euclid Poster Euclid All items carry our Total Satisfaction Guarantee . If you are dissatisfied with any item you purchase, simply advise us and return it within 15 days for replacement or refund.

40. NonEuclid - Hyperbolic Geometry Article & Applet Hyperbolic geometry is a geometry of Einstein s General Theory of Relativity Axioms and Theorems euclid s Postulates, Hyperbolic Parallel Postulate, http://www.cs.unm.edu/~joel/NonEuclid/

NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the for use in High School and Undergraduate Education. Hyperbolic Geometry is a geometry of Einstein's General Theory of Relativity and Curved Hyperspace. Authors: Joel Castellanos - Graduate Student, Dept. of Computer Science , University of New Mexico Joe Dan Austin - Associate Professor, Dept. of Education, Rice University Ervan Darnell - Graduate Student, Dept. of Computer Science, Rice University Italian Translation by Andrea Centomo, Scuola Media "F. Maffei", Vicenza Funding for NonEuclid has been provided by: CRPC, Rice University Institute for Advanced Study / Park City Mathematics Institute Run NonEuclid Applet (click button below): If you do not see the button above, it means that your browser is not Java 1.3.0 enabled. This may be because: 1) you are running a browser that does not support Java 1.3.0, 2) there is a firewall around your Internet access, or 3) you have Java deactivated in the preferences of your browser. Both and Microsoft Internet Explorer 6.0

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