61. Richard Taylor's Home Page Harvard. Arithmetic algebraic geometry, automorphic forms. Preprints. http://abel.math.harvard.edu/~rtaylor/

R I C H A R D T A Y L O R Here are some recent papers. They are available either as dvi or as postscript files. They may be very slightly different from the published versions, e.g. they may not include corrections made to the proofs. Galois representations. (Review article.) R.Taylor Proceedings of ICM 2002, volume I, 449-474. dvi Postscript Galois representations. (Long version of above review article.) R.Taylor to appear Annales de la Faculte des Sciences de Toulouse. dvi Postscript Galois representations. R.Taylor slides for talk at ICM 2002. dvi Postscript On the meromorphic continuation of degree two L-functions. R.Taylor preprint. dvi Postscript Remarks on a conjecture of Fontaine and Mazur. R.Taylor Journal of the Institute of Mathematics of Jussieu 1 (2002), 1-19. dvi Postscript On icosahedral Artin representations. II R.Taylor American Journal of Mathematics 125 (2003), 549-566. dvi Postscript On the modularity of elliptic curves over Q. C.Breuil, B.Conrad, F.Diamond and R.Taylor

62. What Is GHL? A library for 2D and 3-D geometric calculation in C, with functions for shape generation, geometric evaluation, intersection, and offsetting and filleting. http://www.pml.co.jp/ghl/index.html

Geometry Handling Library Japanese Contents What is GHL? Release Notes More Details Demo Version ... GHL Users What is GHL? This is a complete C functions library of 2-D and 3-D geometric calculation. The library includes functions which calculate the following items for analytical and free-formed shapes, including NURBS, with high reliability and precision. Shape generation Evaluation of generated geometric elements Intersection of any combination of analytical and free-formed shapes Offsetting and filleting (2-D and 3-D) More than 2,000 external routines are included in this library. This library is written in standard C language, and thus portable to most of the workstations and personal computers working under various operating sysytems as follows. SGI IRIX Sun Solaris HP HP-UX Various PC Unixes Apple Mac OS X This product is used by various application systems which require precise geometric operations from 1992. GHL will be revised continuously to incorporate newly developed theory and algorithms. GHL 3.4.7 : latest version (shipped on Nov. '03 GHL 3.4.7 Release Note

63. Math Forum Internet Mathematics Library: New Location geometry Step by Step from the Land of the Incas, Intro. Antonio geometry problems involving circles and triangles, with animated proofs. Antonio Gutierrez. Inca geometry, Inca City on Mars Nasa. http://forum.swarthmore.edu/~steve/

The Forum Internet Resource Collection has become The Internet Mathematics Library Please change your links and bookmarks to: http://mathforum.org/library/ Library Home Full Table of Contents Suggest a Link ... Library Help We now offer many more categories, selected starting points, updated entries, and powerful search and browse functions. We hope you find this enhanced presentation helpful as you search for mathematics sites on the Internet. Please search and browse the new Library. Here are a few shortcuts: Mathematics Topics, from Algebra and Arithmetic to Statistics and Topology... Resource Types Lesson Plans and Activities Problems and Puzzles Mathematics Education Topics - Teaching Issues and Strategies, Research and Reform... About the Internet Mathematics Library We are now cataloguing only mathematics and math education sites. Suggestion Box Home The Math Library Help Desk ... Search http://mathforum.org/ webmaster@mathforum.org

64. Graphics Group Conducts research in realtime 3D model aquisition, shape-based retrieval and analysis, video mosaics, lapped textures, texture mapping for cel animation, and algorithm animation. http://www.cs.princeton.edu/gfx/

Princeton CS Dept Local Access Princeton CS Dept Local Access

65. Geometry From The Land Of The Incas. Problems, Theorems, Proofs, Quizzes, With A Presents geometry problems, with proofs, animation and sound Poncelet, Napoleon, Eyeball, Steiner, Carnot, Sangaku, Morley, Langley, Varignon, Wittenbauer http://agutie.homestead.com/files/

Presents geometry problems, with proofs, animation and sound: Poncelet, Napoleon, Eyeball, Steiner, Carnot, Sangaku, Morley, Langley and the Butterfly Theorem. Also, Inca Geometry (Cuzco, Machu Picchu, Incan Quipu, Nazca Lines, Lord of Sipan); quotes from Descartes, Galileo, Newton, Pappus, Plato, Poincare, Voltaire; and quizzes.

66. The Geometry Junkyard: Knot Theory A page of links on geometric questions arising from knot embeddings. http://www.ics.uci.edu/~eppstein/junkyard/knot.html

Knot Theory There is of course an enormous body of work on knot invariants, the 3-manifold topology of knot complements , connections between knot theory and statistical mechanics, etc. I am instead interested here primarily in geometric questions arising from knot embeddings. Animated 3d curves and knots , Jos Leys. Atlas of oriented knots and links , Corinne Cerf extends previous lists of all small knots and links, to allow each component of the link to be marked by an orientation. Borromean rings don't exist . Geoff Mess relates a proof that the Borromean ring configuration (in which three loops are tangled together but no pair is linked) can not be formed out of circles. Dan Asimov discusses some related higher dimensional questions. Matthew Cook conjectures the converse Are Borromean links so rare? S. Javan relates the history of the links and describes various generalizations with more than three rings. For more history and symbolism of the Borromean rings, see Peter Cromwell's web site . See also Paul Bourke's Borromean rings page A Brunnian link . Cutting any one of five links allows the remaining four to be disconnected from each other, so this is in some sense a generalization of the Borromean rings. However since each pair of links crosses four times, it can't be drawn with circles.

67. Funbrain.com Shape Surveyor Geometry Game Improve your geometry skills. Fun game teaches area and perimeter of rectangles and squares with an archeology twist. For kids and http://www.funbrain.com/poly/

Pick the difficulty level you wish to play. Easy Medium Hard Super Brain Pick if you would like to play perimeters and/or areas and hit "Start Digging" to begin the game. Area and Perimeter Area Perimeter Instructions You will be shown a rectangle with the dimensions labeled. You must calculate the area or perimeter of the rectangle. For each problem you get correct, you will receive a piece of an archeological puzzle. The game is over when you get all the puzzle pieces. Parents Teachers Quiz Lab MyGradeBook ... Privacy

68. Nineteenth Century Geometry By Roberto Torretti, Universidad de Chile. http://plato.stanford.edu/entries/geometry-19th/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAR Nineteenth Century Geometry 1. Lobachevskian geometry 2. Projective geometry 3. Klein's Erlangen program 4. Axiomatics perfected ... Related Entries 1. Lobachevskian geometry Euclid (fl. 300 b.c.) placed at the head of his Elements aitemata 1. To draw a straight line from any point to any point. 3. To draw a circle with any center and any radius. Figure 1 In the darker ages that followed, Euclid's sense of mathematical freedom was lost and philosophers and mathematicians expected geometry to rest on self-evident grounds. Now, if a is perpendicular and b is almost perpendicular to PQ, a and b approach each other very slowly on one side of PQ and it is not self-evident that they must eventually meet somewhere on that side. After all, the hyperbole indefinitely approaches its asymptotes and yet, demonstrably, never meets them. Through the centuries, several authors demanded-and attempted-a proof of Euclid's Postulate. John Wallis (b. 1616, d. 1703) derived it from the assumption that there are polygons of different sizes that have the same shape. But then this assumption needs proof in turn. Girolamo Saccheri (b. 1667, d. 1733) tried reductio . He inferred a long series of propositions from the negation of Euclid's Postulate, until he reached one which he pronounced "repugnant to the nature of the straight line". But Saccheri's understanding of this "nature" was nourished by Euclidean geometry and his conclusion begged the question.

69. Amnon Besser: Homepage Ben Gurion University. Number theory, algebraic cycles, algebraic Ktheory and arithmetic geometry. Research, publications, course information, and links. http://www.cs.bgu.ac.il/~bessera/

Dr. Amnon Besser Address Department of Mathematics Ben Gurion University Be'er Sheva 84105 Israel Phone Fax E-mail: bessera@math.bgu.ac.il Room NO. Office hours : Monday 14-16 Education B.Sc. : Tel Aviv University 1985 M.Sc. : Tel Aviv University 1987 Ph.D. : Tel Aviv University 1993 Research Research Interests: Number theory, Arithmetic geometry, p-adic integration, p-adic cohomology, Shimura varieties, Automorphic forms, Algebraic cycles, Algebraic K-theory. List of publications from mathscinet (requires mathscinet authorization) Research profile Research Group: Number Theory and Algebraic Geometry Postdoctoral positions in the group Number theory and Algebraic geometry seminar Publications On the measure of large trigonometric sums , Astererisque 258 (1999) 35-76 CM cycles over Shimura Curves , Journal of Algebraic geometry 4 (1995) 659-691 Elliptic fibrations of K3 surfaces and QM kummer surfaces , Math. Zeitschrift 228 (1998), No. 2, 283-308 On the Kolyvagin cup product , Transactions of the Amer. Math. Soc. 349 (1997), No. 11, 4635-4657 , Doc. Math. 2 (1997), No. 02, 31-46 (electronic)

70. Geometry Algorithm Home Resources for computational geometry algorithm software programming including monthly algorithms with C++ code and an archive, AND a short history of geometry http://www.geometryalgorithms.com/

Geometry Algorithms [Home] Overview History Algorithms Books ... Web Sites Steiner's Porism Welcome to Dan Sunday's Geometry Algorithms web site. Here you will find resources for developing geometry algorithm and computer graphics software. Whether you're just interested in learning about this class of algorithms, or have a real problem to solve, we may have what you need. Look around. Visit our Geometry Gift Shop Hot Books (Click on Cover for Info) Computational Geometry in C Reviews: Computational Geometry Reviews: Geometric Tools Reviews: Geometry Revisited Reviews: Overview Linear Algebra (PDF) Geometry History Geometers History Books Web Sites ... Videos Featured Item Pavilion Brain Benders Puzzle Box Average Customer Review: Need Help? Contact us at: services@softsurfer.com Help SUPPORT This Site Please make purchases through this site to help support us. The cost is the same to you, but we get a small commission. Email comments and suggestions to feedback@softsurfer.com

71. Veys University of Leuven. Algebraic geometry, singularity theory, applications in number theory. Papers and preprints. http://www.wis.kuleuven.ac.be/algebra/veys.htm

Home Page of Wim Veys Contents Work Information Contact Information Publications with available DVI- and PS-file Previous publications Work Information Professor at the University of Leuven (K.U.Leuven), Department of Mathematics, Section of Algebra Fields of Research Algebraic Geometry, Singularity Theory, applications in Number Theory Specific Research Topics Exceptional divisor of an embedded resolution, Zeta Functions (Igusa, topological, motivic), Monodromy, configurations of curves on surfaces, Stringy invariants, Principal value integrals Ph.D. Students Bart Rodrigues : Geometric determination of the poles of motivic and topological zeta functions may 2002 Dirk Segers : Smallest poles of zeta functions and solutions of polynomial congruences, april 2004 Jan Schepers : On stringy invariants Ann Lemahieu : On possible poles of zeta functions Filip Cools Back to top Contact Information Address University of Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium. Electronic mail address wim.veys@wis.kuleuven.ac.be

72. Shape And Space In Geometry geometry is the mathematics of shape and space. For many of us, the geometry course sounded the death knell for our progress—and interest—in mathematics. http://www.learner.org/teacherslab/math/geometry/

Geometry is the mathematics of shape and space. It's about the properties of objects (their angles and surfaces, for instance) and the consequences of how these objects are positioned (where their shadows fall, how people must move around them). Here's a chance to put those memories to rest, to experience geometry anew. At its roots, geometry is not abstract. Rather, it's fun and colorful, instructive and practical. Geometry is about real things: how big they are, whether they fit, how to find them, what they look like in a mirror. Geometry is naturally concrete. This lab divides activities into two broad categories. Activities about shape center on identifying properties of various shapes and measuring their dimensions. Activities about space Simply put, geometry is important to real life. Before you start the activities, read this background to find out why. Home Channel Catalog About Us ... Legal Policy

73. Topology And Geometry A collection of educational, graphical and research software by Jeff Weeks. http://www.geometrygames.org/

Jeff Weeks' Topology and Geometry Software Fun and Games for ages 10 and up Torus and Klein Bottle games (online) Kali (Windows, Macintosh) KaleidoTile (Windows, Macintosh) Classroom Materials for teachers grades 6-10 Exploring the Shape of Space Curved Spaces for software developers Computer Graphics in Curved Spaces (OpenGL, Direct3D) Research Software for mathematicians SnapPea (Linux, Macintosh, Windows) Comments? Problems? Suggestions? Contact Jeff Weeks awards and links

74. Areas, Volumes, Surface Areas textAreas, Volumes, Surface Areas. (pi = pi = 3.141592 ) textAreas. textsquare = a^{2}. textrectangle = ab. textparallelogram = bh. http://www.math2.org/math/geometry/areasvols.htm

[text:Areas, Volumes, Surface Areas pi = [pi] = 3.141592...) [text:Areas] [text:rectangle] = ab [text:parallelogram] = bh [text:trapezoid] = h/2 (b + b [text:circle] = pi r [text:ellipse] = pi r r [text:triangle] = (1/2) b h [text:equilateral triangle] = (1/4) [text:triangle given SAS] = (1/2) a b sin C [text:triangle given a,b,c] = [sqrt][s(s-a)(s-b)(s-c)] [text:when] s = (a+b+c)/2 ([text:Heron's formula]) [text:when n = # of sides and S = length from center to a corner] [text:Volumes] [text:rectangular prism] = a b c [text:irregular prism] = b h [text:cylinder] = b [text:pyramid] = (1/3) b h [text:cone] = (1/3) b [text:ellipsoid] = (4/3) pi r r r [text:Surface Areas] [text:prism]: ([text:lateral area]) = [text:perimeter]( b ) L ([text:total area]) = [text:perimeter]( b ) L + 2 b

75. PROJECTIVE GEOMETRY Projective geometry is a beautiful subject which has some remarkable applications beyond those in standard textbooks. These were http://www.anth.org.uk/NCT/

Projective geometry is a beautiful subject which has some remarkable applications beyond those in standard textbooks. These were pointed to by Rudolf Steiner who sought an exact way of working scientifically with aspects of reality which cannot be described in terms of ordinary physical measurements. His colleague George Adams worked out much of this and pointed the way to some remarkable research done by Lawrence Edwards in recent years. Steiner's spiritual research showed that there is another kind of space in which more subtle aspects of reality such as life processes take place. Adams took his descriptions of how this space is experienced and found a way of specifying it geometrically, which is dealt with in the Counter Space Page A brief introduction to the basics of the subject is given in the Basics Page The work of Lawrence Edwards is introduced in the Path Curves Page , and some explorations of his work on further aspects is described in the Pivot Transforms Page . This is mostly pictorial, with reference to documentation. YOU ARE INVITED TO EXPLORE!

76. String Theory: A Happy Marriage Of Geometry And Physics An introductory description of this theory with references to current work being done in the Netherlands. http://www.math.leidenuniv.nl/~stieltjes/archief/biennial9596/frame/node5.html

Next: Strings in physics and Up: No Title Previous: Research Highlights String Theory: A Happy Marriage of Geometry and Physics Research Programme: Algebraic and Analytic Geometry Researcher: R.H. Dijkgraaf J.H.M.Dassen Fri Mar 20 16:01:06 MET 1998

77. Beiträge Zur Algebra Und Geometrie Homepage Beiträge zur Algebra und Geometrie Contributions to Algebra and geometry. ISSN 01384821 · Electronic Edition Managing Editors. http://www.emis.de/journals/BAG/

Contributions to Algebra and Geometry Managing Editors The mathematical Journal was founded in 1971 on the occasion of the 65th birthday of O.-H. Keller. It publishes research articles in the areas of algebra, geometry, algebraic geometry and related fields , preferably in English language. For fastest access: Choose your nearest server! Editorial Contents Volume 34 (1993): No. 1 No. 2 Volume 35 (1994): No. 1 No. 2 Volume 36 (1995): No. 1 No. 2 Volume 37 (1996): No. 1 No. 2 Volume 38 (1997): No. 1 No. 2 Volume 39 (1998): No. 1 No. 2 Volume 40 (1999): No. 1 No. 2 Volume 41 (2000): No. 1 No. 2 Volume 42 (2001): No. 1 No. 2 Volume 43 (2002): No. 1 No. 2 Volume 44 (2003): No. 1 No. 2 Volume 45 (2004): No. 1 Technical Notes Last modified 5 Mar 2004 Heldermann Verlag ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition

78. Hyperbolic Geometry Cabri constructions for the demonstration of the basic concepts of hyperbolic geometry in the Poincare disc model. http://mcs.open.ac.uk/tcl2/nonE/nonE.html

Hyperbolic Geometry using Cabri This page and links maintained by Tim Lister, t.c.lister@open.ac.uk Last updated: A tessellation of the hyperbolic plane H Full screen version of diagram During the summer of 97 I had great fun playing with some marvelous software, Cabri Geometry , and devising constructions for use in teaching the basic ideas of a geometry course put on by the Open University. These started with some figures to demonstrate the transformations of Inversive Geometry, and progressed to figures for the Arbelos, the inversors of Peucellier and Hart, Coaxial Circles and so on, much of which was driven by the discovery of a Dover edition of a small pearl of a book Advanced Euclidean Geometry (Modern Geometry) An elementary Treatise on the Geometry of the triangle and the Circle (to give its full title) written by Roger A. Johnson and first published in 1929. It had languished on my bookshelves, having been bought years ago for 20 cents (South African) in some sale or other. I can recommend it as a fascinating read, or just for taking in the breathtaking complexity of the many hand crafted diagrams to be found on its pages.

79. Balkan Journal Of Geometry And Its Applications Balkan Journal of geometry and Its Applications. 1 No. 2. Published by BALKAN SOCIETY OF GEOMETERS geometry Balkan Press Bucharest, ROMANIA http://www.emis.de/journals/BJGA/

Balkan Journal of Geometry and Its Applications Managing Editor: V. Balan (Bucharest) Editorial board Promoters and Founders: R. Miron (Iassy), C. Udriste (Bucharest), Gr. Tsagas (Thessaloniki) Editor-in-Chief: C. Udriste (Bucharest) Members: I.D. Albu (Timisoara), M. Anastasiei (Iassy), D. Andrica (Cluj), Gh. Atanasiu (Brasov), V. Balan (Bucharest), D. E. Blair (East Lansing), B.-Y. Chen (East Lansing), J. Dorfmeister (Lawrence), A. Jannussis (Patras), V. Obadeanu (Timisoara), Gh. Pitis (Brasov), P. Popescu (Craiova), G. Pripoaie (Bucharest), P. C. Stavrinos (Athens), L. Tamassy (Debrecen), Gr. Tsagas (Thessaloniki), L. Vanhecke (Leuven), E. Vassiliou (Athens) Managing Editor for the Electronic Version of BJGA: V. Balan (Bucharest) For fastest access: Choose your nearest server! Contents Volume 7 (2002): No. 1 No. 2 Volume 6 (2001): No. 1 No. 2 Volume 5 (2000): No. 1 No. 2 Volume 4 (1999): No. 1 No. 2 Volume 3 (1998): No. 1 No. 2 Volume 2 (1997): No. 1 No. 2 Volume 1 (1996): No. 1 No. 2 Published by BALKAN SOCIETY OF GEOMETERS Geometry Balkan Press Bucharest, ROMANIA

80. Diophantine Geometry GeorgAugust-Universit¤t, G¶ttingen, Germany; 1722 June 2004. http://www.uni-math.gwdg.de/yuri/SS04/conference.html

<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> Conference "Diophantine Geometry Mathematisches Institut Organizer: Yuri Tschinkel Program Useful information Contact us Short Courses: J.-B. Bost , (Orsay): Foliations on algebraic varieties over number fields: algebraicity and transcendence B. Hassett , (Rice University): Equations of universal torsors and Cox rings R. Pink Special points and subvarieties of abelian varieties Other participants include: V. Abrashkin , (University of Durham) V. Batyrev

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