61. 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 content revised 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.

62. PROJECTIVE GEOMETRY Rudolf Steiner's approach.Category Science Math geometry Projective......Projective geometry is a beautiful subject which has some remarkableapplications 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!

63. 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. 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. Colinear points on knots Greg Kuperberg shows that a non-trivial knot or link in R necessarily has four colinear points.

64. Computational Geometry Elsevier journal edited by JörgRüdiger Sack and Kurt Mehlhorn.Category Science Math geometry Computational geometry Journals...... http://www.elsevier.nl/locate/comgeo

Home Search What's New Electronic Services ... Links Computational Geometry Journal Information Description Audience Abstracting/Indexing Bibliographic and Ordering Information ... Dispatch Dates Authors Author Gateway The fast and efficient new author service for this journal Online submission of papers Editors Information and services for Editors Contents Services ContentsDirect Full text Articles, Tables of Contents, Abstracts Free Sample Copy News/Related Websites MathematicsWeb The Mathematics Preprint Server Related Info ELSEVIER Last update: 06 May 2003

65. Anngeo Trento, Italy; 1115 June 2001. http://www.science.unitn.it/cirm/anngeo.html

66. Journal For Geometry And Graphics Biannual journal about graphics and graphics-related geometry, published by Heldermann Verlag. Includes Category Science Math geometry Journals......Journal for geometry and Graphics. ISSN 14338157 · Electronic EditionEditorial Board G. Bertoline (West Lafayette), Y. Charit http://www.emis.de/journals/JGG/

Journal for Geometry and Graphics Editorial Board G. Bertoline (West Lafayette), Y. Charit (Haifa), Chen Jiannan (Beijing), L. D. Goss (Evansville), J. Hoschek (Darmstadt), S. Ino (Hokkaido), R. D. Jenison (Ames), C. Leopold (Kaiserslautern), E. Molnár (Budapest), S. Nagano (Tokyo), M. Palej (Gliwice), K. Suzuki (Tokyo), J. P. Tschupik (Innsbruck), G. Weiß (Dresden), K. Yoshida (Osaka) Managing Editors R. E. Barr (Austin), M. Kato (Tokyo), H. Stachel (Vienna) The concern of this international scientific journal is to stimulate scientific research and teaching methodology in the field of graphics and graphics-related geometry by the dissemination of new results. The published papers are ordered into three groups: Theoretical Graphics (Section 1), Applications (Section 2), Graphics Education (Section 3). For fastest access: Choose your nearest server! Editorial Contents Volume 5 (2001) Number 1 Number 2 Volume 4 (2000) Number 1 Number 2 Volume 3 (1999) Number 1 Number 2 Volume 2 (1998) Number 1 Number 2 Volume 1 (1997) Number 1 Number 2 ELibM and Heldermann Verlag

67. Graphics & Geometry 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 Graphics: Search CS website:

68. Bubble Geometry - Science Museum Of Minnesota Thinking Fountain image (17k), Bubble geometry. Have you ever seena square bubble? Experiment with bubbles. Create bubble wands out http://www.smm.org/sln/tf/b/bubblegeometry/bubblegeometry.html

Bubble Geometry Have you ever seen a square bubble? Experiment with bubbles. Create bubble wands out of found objects (straws, pipe cleaners, strawberry baskets and coathangers) and have your own bubble festival. How can you catch a bubble? The secret is the soap solution. Try catching a bubble with a dry hand versus a wet hand. Which lasts longer? This activity is included in the Shapes cluster developed with K-2 teachers at the Ross School in San Francisco. What could you use to make lots of tiny bubbles? How could you measure a bubble? Why do bubbles fall towards the ground? Bubbles Soap bubbles are so fun! Make your own bubble prints Gathered by topic Connected together Index of ideas Try something new Science Learning Network

69. Geometry Formulas And Facts An excerpt from the 30th Edition of the CRC Standard Mathematical Tables and Formulas. http://freeabel.geom.umn.edu/docs/reference/CRC-formulas/

Next: Part I: Two-Dimensional Geometry Up: Geometry Reference Archives Geometry Formulas and Facts Silvio Levy This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas , published in late 1995 by CRC press This completely rewritten and updated edition of CRC's classical reference work is edited by Dan Zwillinger, and boasts the participation of dozens of distinguished contributors in all fields of mathematics. Ordering information is available here The present excerpt covers the area of Geometry (minus differential geometry). It was written by Silvio Levy and is reproduced here with permission. All the figures were made by the author using Mathematica , except those in Section , which were made using kali This online version was prepared with the help of Nikos Drakos's converter; for compatibility of text and formulas, choose a largish text font with your browser. A button in the text indicates a cross-reference. Part I: Two-Dimensional Geometry 1 Coordinate Systems in the Plane 1.1 Substitutions and Transformations 1.2 Cartesian Coordinates in the Plane ... 16 Quadrics Next: Part I: Two-Dimensional Geometry Up: Geometry Reference Archives The Geometry Center Home Page Silvio Levy Wed Oct 4 16:41:25 PDT 1995 This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas CRC Press ). Unauthorized duplication is forbidden.

70. Computational Geometry, Algorithms And Applications Recent book with a focus on applications, by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Category Science Math geometry Computational geometry Books...... Comments to geobook@cs.uu.nl. Last modified Oct 9, 2000. Computational geometryAlgorithms and Applications. Second Edition. Computational geometry. http://www.cs.uu.nl/geobook/

About the book Cover Table of contents Errata (1st edition) Errata (2nd edition) ... Order Implementation CGAL LEDA More software Further reading Books Bibliography Web sites Comments to geobook@cs.uu.nl Last modified Oct 9, 2000 Computational Geometry: Algorithms and Applications Second Edition Mark de Berg Otfried Schwarzkopf TU Eindhoven (the Netherlands) Marc van Kreveld Mark Overmars Utrecht University (the Netherlands) published by Springer-Verlag 2nd rev. ed. 2000. 367 pages, 370 fig. Hardcover DM 59 ISBN: 3-540-65620-0 You can order the book here This textbook on computational geometry has 367 pages. The pages are almost square with a large margin containing over 370 figures. To get an idea about the style and format, take a look at the Introduction or chapter 7 on Voronoi diagrams Computational geometry Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains-computer graphics, geographic information systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self study.

71. Recognition Systems - Hand Geometry Biometric HandKey and HandPunch terminals utilizing hand geometry for identification. http://www.recogsys.com/

Hand Geometry Technology Press Releases Recognition Systems' HandReader Technology verifies identities by the size and shape of the hand. No fingerprints or palm prints are utilized. Applications / Products HandPunch 4000 HandPunch 3000 HandPunch 2000 HandPunch 1000 ... MORE

72. The Former CGAL Home Page The CGAL project is a collaborative effort to develop a robust, easy to use, and efficient C++ software Category Science Math geometry Computational geometry Software......The CGAL web pages have moved to http//www.cgal.org/. http://www.cs.uu.nl/CGAL/

The CGAL web pages have moved to http://www.cgal.org/

73. Piguy 's Math Javascripts Page This page has dozens of math calculators, making all sorts of math, from algebra to arithmetic to geometry, easier. Also, 50,000 decimals of pi and a logarithm table. http://www.geocities.com/CapeCanaveral/Hall/1216/

Click above for more info about making money surfing... by the way, I have PROOF that you actually get paid piguy's Math Page Search this page! This search engine hasn't been working that well, so if you don't get good results, you aren't alone. It will be fixed soon (hopefully). Howdy! Thanks for coming to my web page. I am working on getting more stuff, but it is a slow process. JavaScript Things Logarithm Stuff Links Math Forum ... Webrings If you have any kind of complaint, comment, or hint, Please and let me know. Don't forget to sign my guestbook! Have a good Day! Take my poll! Click here to vote for other things. My website quality check How good is this website Totally, 100% AWESOME !!! If I liked Math, It would be pretty cool Decent, not great, but pretty good Not very good, needs work, probably in bottom 30% of websites Where in the world did you learn how to make a website?!?! Current Results FastCounter by LinkExchange people have visited this Math page since Sept. 18th, 1998 Sorry, you do not have a javascript compatible browser. You will not be able to see the beauty of this website. Find out about me and my family by clicking here

74. Cabri Geometry The home site for Cabri geometry, a dynamic geometry package .Category Science Math geometry Software......Parlezvous français ? About Products Origins Books Webs News Contacts Cabrilog CabriJava CabriWorld 2001 Last http://www-cabri.imag.fr/index-e.html

About Products Origins News ... CabriWorld 2001 Last updated: 10 April 2003 webadmin@cabri.net

75. Notes On Differential Geometry By B. Csikós Notes by Bal¡zs Csik³s. Chapters in PostScript. http://www.cs.elte.hu/geometry/csikos/dif/dif.html

Differential Geometry Budapest Semesters in Mathematics Lecture Notes by Balázs Csikós FAQ: How to read these files? Answer: The files below are postscript files compressed with gzip . First decompress them by gunzip , then you can print them on any postscript printer, or you can use ghostview to view them and print selected (or all) pages on any printer. CONTENTS Unit 1. Basic Structures on R n , Length of Curves. Addition of vectors and multiplication by scalars, vector spaces over R, linear combinations, linear independence, basis, dimension, linear and affine linear subspaces, tangent space at a point, tangent bundle; dot product, length of vectors, the standard metric on R n ; balls, open subsets, the standard topology on R n , continuous maps and homeomorphisms; simple arcs and parameterized continuous curves, reparameterization, length of curves, integral formula for differentiable curves, parameterization by arc length. Unit 2. Curvatures of a Curve Convergence of k-planes, the osculating k-plane, curves of general type in R n , the osculating flag, vector fields, moving frames and Frenet frames along a curve, orientation of a vector space, the standard orientation of R n , the distinguished Frenet frame, Gram-Schmidt orthogonalization process, Frenet formulas, curvatures, invariance theorems, curves with prescribed curvatures.

76. Arithmetic Algebraic Geometry A European network of 12 working groups from 6 countries. http://www.maths.univ-rennes1.fr/arithgeom/

A Research Training Network of the European Community Overview Partners Programme Post-docs Activities Project overview Developing powerful methods taken from geometry to study the arithmetical properties of algebraic equations Algebraic equations and their arithmetical properties have interested mankind since antiquity. One has only to think of the works of Pythagoras and Diophantus, which were a milestone in their time. For many centuries such problems have fascinated both serious mathematicians (Fermat, Gauss, ...) and amateurs alike. However, developments in recent years have transformed the subject into one of the central areas of mathematical research, which has relations with, or applications to, virtually every mathematical field, as well as an impact to contemporary everyday life (for example, the use of prime numbers and factorisation for encoding "smart" cards). The classical treatment of equations by analysis and geometry in the realm of complex numbers in this century has found a counterpart, in the similar theories over finite and p -adic fields, which have particular significance for arithmetic questions. The study of certain functions encoding arithmetic information and generalising the Riemann zeta-function (

77. Geometry Facts about geometry illustrated by using online interactive lessons,exercises, practice and games for grades K8. geometry. These http://www.aaamath.com/B/geo.htm

Geometry These pages teach geometry facts covered in K8 math courses. Each page has an explanation, interactive practice and challenge games about geometry. Geometry Facts and Calculations Polygons Polygons II Classifying Triangles by Angles Classifying Triangles by Sides ... Finding the Fourth Angle of a Quadrilateral Area Area of a Square Area of a Rectangle Area of a Parallelogram Area of a Trapezoid ... Area of a Circle Perimeter and Circumference Perimeter of a Square Perimeter of a Rectangle Perimeter of a Parallelogram Circumference of a Circle Surface Area Surface Area of a Cube Surface Area of a Rectangular Prism Surface Area of a Cylinder Volume Volume of a Cube Volume of a Rectangular Prism Volume of a Triangular Prism Volume of a Cone ... Learning Aids Grade School Levels: Kindergarten First Second Third ... World Levels Arithmetic Topics: Addition Algebra Comparing Counting ... Subtraction

78. Alg_arith.icm98 (ICM 1998 Satellite Conference) Essen, Germany; 1015 August 1998. http://www.exp-math.uni-essen.de/zahlentheorie/Alg_Arith_Geo_ICM98/index.html

ICM 1998 SATELLITE CONFERENCE ALGEBRAIC and ARITHMETIC GEOMETRY August 10-15, 1998 Essen, Germany Third announcement There will be a satellite conference on algebraic and arithmetic geometry at the university of Essen, Germany, from August 10 until August 15, 1998. Arrival: Sunday, August 9, afternoon Departure: Saturday, August 15, afternoon Nearest airport: Program: There will be plenary sessions (55 min.) and two parallel series of main lectures (45 min.), one on Geometry and one on Arithmetic. At present the following speakers accepted the invitation: V. Alexeev, V. Batyrev, K. Behrend, S. Bloch, J.-B. Bost, C. Deninger, A. Goncharov, R. Hain, D. Harbater, Y. Ihara, J. de Jong, Y. Kawamata, F. Oort, R. Pink, F. Pop, M. Raynaud, K. Ribet, S. Saito, T. Saito, In addition there will be up to four parallel series of seminar talks (35 min.). The subjects of the seminars include Arithmetic and Arakelov geometry Galois theory Algebraic cycles Birational geometry Geometry and physics Projective geometry and vector bundles Preliminary schedule (new): as ps.file

79. Computational Geometry On The WWW Computational geometry on the World Wide Web Starting Point ApplicationChallenges to Computational geometry CG Impact Task Force Report http://www.dcc.unicamp.br/~guialbu/geompages.html

Computational Geometry on the World Wide Web Starting Point Bibliography, Journals ... Computational Geometers Software, Libraries, Codes ... Starting Point Application Challenges to Computational Geometry - CG Impact Task Force Report Computational Geometry Pages - Jeff Erickson Computational Geometry Resources - Carleton Univ. Geometry in Action - David Eppstein ... The Geometry Center - Univ. of Minnesota Bibliography, Journals ... Computational Geometry: Theory and Applications Computer Science Journals - Univ. of Dortmund International Journal of Computational Geometry and Applications Unified Computer Science Technical Report Index ... BSP Tree Freq. Asked Questions - Qualia, Inc. Computational Geometers let me know if you want your name in/out this list A B C D ... Univ. of Baltimore . See also his nice Bibliography for Optimization Asano, Tetsuo JAIST, Japan Atallah, Mikhail ... Charles Univ., Czech Republic . See also his nice Davenport-Schinzel Sequences pages Klein, Rolf Kranakis, Evangelos Carleton Univ. ... Otto-von-Guericke-Univ. Magdeburg. See also his nice Packomania (packing of circles) Stiller, Peter F.

80. [physics/9709045] An Introduction To Noncommutative Geometry A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics. http://arxiv.org/abs/physics/9709045

Physics, abstract physics/9709045 An Introduction to Noncommutative Geometry Authors: Joseph C. Varilly Comments: 85 pages, Plain TeX, lectures at EMS Summer School on NCG and Applications, Sept 1997 Report-no: UCR-FM-12-97 Subj-class: Mathematical Physics; Differential Geometry; Quantum Algebra These are lecture notes for a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997. 1. Commutative geometry from the noncommutative point of view. 2. Spectral triples on the Riemann sphere. 3. Real spectral triples, the axiomatic foundation. 4. Geometries on the noncommutative torus. 5. The noncommutative integral. 6. Quantization and the tangent groupoid. 7. Equivalence of geometries. 8. Action functionals. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv physics find abs

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