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Séminaire MaMuX
Mathématiques, musique et relations avec d'autres disciplines


Géométrie - Geometry

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University of California, Irvine.



<http://www.noncommutativegeometry.net/> <http://www-cabri.imag.fr/abracadabri/GeoNonE/GeoNonE.htm> <http://www.geom.umn.edu/>
Les activités du projet PRISME sont centrées sur la géométrie algorithmique et ses applications, et sur les aspects géométriques de la robotique.
David Eppstein
Geometry Junkyard <http://www.ics.uci.edu/~eppstein/geom.html>
Nicolas Hannachi
Polyèdres. Spheres (sphere packing). Images 3D animées à l'aide de LiveGraphics3D
A generalization of Doyle Spirals. A. I. Bobenko and T. Hoffmann
There is a printable PostScript version. Visit the Applets.
The document is shown by JDvi a dvi file viewer written in JAVA.
<http://www-sfb288.math.tu-berlin.de/Publications/online/cscpOnline/> <http://compgeom.cs.uiuc.edu/~jeffe/compgeom/> <http://www.geom.uiuc.edu/apps/gallery.html>
The Topological Zoo is designed a resource for mathematicians and educators. It is a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures.
<http://www.geom.umn.edu/zoo/> <http://www-sop.inria.fr/saga/saga.html>
The CGAL project is a collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms.
Technique for curved folds (As used in teabag folding)This is a graphical illustration of how folds along curved lines work. It was used in a couple of my contributions to the teabag problem, and also appears in Tom Longtin's teabag, based on a McDonalds' container for french fries.
Proofs and Refutations in Geometry ...
<http://www-cgrl.cs.mcgill.ca/~godfried/research.html> <http://www.ac-noumea.nc/maths/amc/polyhedr/> <http://perso.wanadoo.fr/challenge.en.geometrie/>
I've written four applets. The fourth (Feb. 1996) deals with geometry. I'm using it to illustate Euclid's Elements, as well as other pages on geometry (very much in progress) such as the one illustrating the Euler line of a triangle.
Déclic est un logiciel qui permet de construire à la souris toute figure de géométrie euclidienne. Les éléments de bases sont le point, la droite et le cercle. Mais tous les outils de la 6ème à la Terminale sont disponibles.
<http://home.nordnet.fr/~eostenne/declic.htm> <http://www.stetson.edu/~efriedma/packing.html>
Xah Lee



Art, Architecture, Fractals, Teacher Surfing Sites, Software
The goal of this project was to collect and organize available INTERNET resources on Authentic Mathematical Assessment applicable to Secondary Schools. What is it? Are there examples? Where can I find additional information?
Les activités du projet PRISME sont centrées sur la géométrie algorithmique et ses applications, et sur les aspects géométriques de la robotique.



I figure out algorithms for solving geometric problems on the computer and try to prove that they're the best possible.
<http://www.geom.umn.edu/~nina/> <http://www-sop.inria.fr/prisme/personnel/bronnimann/index.html> <http://www.cs.twsu.edu/~gao/gao.html>
Documents Cours au Collège de France (en français), articles ...
Department of mathematics University of Tennessee Knoxville
Circle Packing papers, Circle Packing Bibliography, The Zoo, Cortical cartography, Curvature Flow, A "Regular" Pentagonal Tiling of the Plane
A circle packing is a configuration of circles with a specified pattern of tangencies. See the examples below; the circles typically must assume a variety of different sizes in order to fit together in a prescribed tangency pattern. Papers



by Shalosh B. Ekhad, XIV, downloaded from the Future by Doron Zeilberger In addition to its geometrical interest, this textbook gives a glimpse of how math articles and books would look like in fifty years (and perhaps much sooner!). Maple (or some variant of it) will become the lingua-franca of math, and this will improve communications between humans and machines, and even between humans and other humans.



This page lists "small" pieces of geometric software available on the Internet. Most of the software is available free of charge. Unless otherwise specified, C or C++ source code is available for all programs.
Paul Leopardi



Following the example of Paul Erdös, mathematicians sometimes offer rewards to the first person to publish a solution of a previously unsolved problem. Below are listed several problems which may be difficult to solve. I am pleased to offer monetary rewards for first publications of solutions.



Thomas Chomette
Ce problème de géométrie assez classique à été remis au goût du jour par le président chinois, à l'occasion du congrès international des mathématiciens (Pékin, août 2002)... ps






page de liens
<liens_pict.html#SOFT> <http://www.geom.umn.edu/apps/gallery.html> <http://www.geom.umn.edu/software/download/> <http://www.geom.umn.edu/software/cglist/>
sets the X root window to an image of the Earth, as seen from your favorite vantage point in space, correctly shaded for the current position of the Sun
<http://www.cs.colorado.edu/~tuna/xearth/index.html> <http://www.inria.fr/Information/logiciels-fra.html>
bibliothèque pour le calcul géométrique
<http://www-sop.inria.fr/prisme/CGAL/CGAL.html> <http://members.xoom.com/FeYiLai/dr_geo/last_version.html>
by Nina Amenta of the Geometry Center (World Wide Web interface by Paul Burchard via W3Kit)
<http://www.geom.umn.edu/apps/kali/about.html> <http://www.susqu.edu/brakke/evolver/examples/examples.htm> <http://www.geom.umn.edu/software/download/geomview.html> <http://www.geomview.org>
DOME is a freeware DOS utility for generating the coordinates of a geodesic dome or sphere. DOME will output a "camera-ready" POV-Ray script file. DOME 4.6 is freeware according to the terms of the standard GNU license agreement.
Rick Bono
GeoGebra est un logiciel dynamique de mathématiques réunissant géométrie, algèbre et calcul.
Si Java 1.4.2 (ou plus) est installé sur votre machine, vous pouvez démarrer GeoGebra tout de suite.
Laboratoire de mathematiques   du Musée Universitaire de l'Histoire des Sciences et des Instruments Scientifiques
Dans le laboratoire de Mathématiques du Musée Universitaire de l'Histoire des Sciences et des Instruments Scientifiques il y a environ 160 machines mathématiques construites par les enseignants du Liceo A.Tassoni dans le cadre d'un projet innovateur pour l'enseignement de la géométrie, développé par le Nucleo di Ricerca in Storia e Didattica della Matematica (University of Modena) . Le projet, coordonné par le Professeur. Mariolina Bartolini Bussi (bartolini@unimo.it) a produit des machines mathématiques, des progressions didactiques, des films d'animation, et des simulations informatiques.






<http://perso.wanadoo.fr/jpq/gava/index.htm> <http://aleph0.clarku.edu/~djoyce/java/Geometry/Geometry.html> <http://www.dynamicgeometry.com/JavaSketchpad/About_JavaSketchpad.html> <http://www.geom.umn.edu/java/> <http://www.geom.umn.edu/java/Kali/> <http://www.dynamicgeometry.com/JavaSketchpad/Gallery/Other_Explorations_and_Amusements/Vasarely_Bubble.html> <http://www-cgrl.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Fabienne/Game.html>
a non-commercial Java 1.1 applet by Martin Kraus
<http://wwwvis.informatik.uni-stuttgart.de/~kraus/LiveGraphics3D/index.html> <http://www.geom.umn.edu/java/> <http://www.saliege.com/dynamique/projet/cbparam/arcparam.html> <http://www.keypress.com/sketchpad/> <http://www.cabri.net/cabrijava/index.html>
JavaView -  Interactive 3D Geometry and Visualization



by Steven Richard Hollasch
Arizona State University August 1991
Implementation Notes : 4D Wireframe Display Program and 4D Raytracer



by Joseph O'Rourke
B. Polster and G. F. Steinke
The Euclidean plane and the geometry of circles on a sphere have a number of features in common... These two geometries are just two examples of a host of classical examples of geometries on surfaces... Our book tries to summarize all major results about geometries on surfaces. It also includes many results about these geometries that will appear for the first time in this book.



David Madore (Page maths de Gro-Tsen) fichier pdf
James W. Cannon, William J. Floyd, Richard Kenyon, and Walter R. Parry
Flavors of Geometry MSRI Publications Volume 31, 1997 (115 pages)
Tomás García-Salgado
Nexus Network Journal, vol. 5 no. 1(Spring 2003),
Jorge Sotomayor
Materials Matemàtics Revista Electrònica de Divulgació Matemàtica Editada pel Departament de Matemàtiques de la Universitat Autònoma de Barcelona



R. Mahmoodi Baram and H. J. Herrmann (Stuttgart), N. Rivier (Strasbourg)
We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops of an even number of spheres can be constructed in a self-similar way and that it can act as a three-dimensional bearing in which spheres can rotate without slip and with negligible torsion friction.
The most essential contribution towards its rigorous proof was given in 1841 and is due to Jacob Steiner (1796-1863).
<http://www.cut-the-knot.com/do_you_know/isoperimetric.html> <http://www.math.fsu.edu/~marcolli/NCGindex.html>
Evangelos Kranakis Danny Krizanc Jorge Urrutia
J. Czyzowicz, E. Kranakis, J. Urrutia,Applied Mathematical Sciences, Vol. 1, 2007, no. 52, pp. 2593 - 2600
by Erik D. Demaine, Martin L. Demaine, Erich Friedman Z
Hinged dissection of polypolyhedra (2005) by Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy, Diane L. Souvaine



a freely accessible electronic journal on classical euclidean geometry and related areas, aims at bringing to a wide, international readership the beauty, elegance, and usefulness of elementary geometry, in research and in teaching.
Edited by Dénes Nagy and György Darvas - Journals of the International Society for the Interdisciplinary Study of Symmetry



Jacques-Olivier Moussafir - Introduction. Contenu. Ce document introduit donc succinctement quelques notions de géométrie, aussi visuellement que possible, à un niveau élémentaire. On a ajouté au texte de nombreux dessins, exercices et problèmes. Ceux-ci sont parfois franchement difficiles.
<http://www.ceremade.dauphine.fr/~msfr/ens/geo.pdf> <http://bigbox.unl.edu/plane/bin/index_a.htm> <http://gauss.math.ucl.ac.be/~alvarez/teaching/projective-geometry/project.html>
An Introduction to Riemannian Geometry S. Gudmundsson,
Differentialgeometri 1 U. Hamenstädt,
Foundations of Differential Geometry P. Michor,
Differential Geometry S. Yakovenko,
Complex manifolds and Hermitian Geometry A. D. Wang
Minimal surfaces in Euclidean spaces G. Weinstein
Hal Schenck
The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms over the last quarter century have revolutionized the area, making many (formerly inaccessable) problems tractable, and providing a fertile ground for experimentation and conjecture. We'll begin by studying some basic commutative algebra and connections to geometry; i.e. rings, and ideals, varieties, the Hilbert basis theorem and nullstellensatz. Then we'll discuss graded objects and varieties in projective space; the Hilbert syzygy theorem says (basically) we can approximate a graded module with a finite sequence of free modules (a finite free resolution). The Grobner basis algorithm (which we'll study) actually lets us compute these things; and so we have a great source of examples. The real objective of the course is to bring whatever we choose to study next to life by doing lots of examples. There are many paths we can take; a homological direction (free resolutions, Tor and Ext, Hilbert syzygy theorem), a combinatorial direction (Stanley-Reisner rings, upper bound theorem, applications to polytopes and discrete geometry); or an applied direction (coding theory, integer programming, mathematical modelling, and robot control). Or we can take a tapas approach, and study some of everything.
The course will examine a number of issues concerning the mathematical and philosophical foundations of the special theory of relativity. The emphasis throughout will be on the "geometric" approach to the theory, and considerable class time will be devoted to a careful study of Minkowski geometry, and its relations to both Euclidean and non-Euclidean (Lobatchevskian) plane geometry. (One of the nicest routes to the latter is via special relativity.



John C. Polking Rice University
<http://math.rice.edu/~pcmi/sphere/> <http://www-sop.inria.fr/prisme/manifestations/journees98/supports/>
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.






Pauline Romera-Lebret Archives Audiovisuelles de la Recherche
Le séminaire, mis en place à la FMSH, se veut largement ouvert. Non seulement il est un lieu de rencontre d'excellence entre mathématiciens, philosophes et historiens des sciences, mais il s'ouvre également à un public de "curieux", plus dispersés culturellement. Cet éclatement disciplinaire, voulu, apporte avec lui en retour un enrichissement de la réflexion portée sur les entités géométriques et, plus largement, sur le sens et la signification des mathématiques. Des spécialistes de grande valeur interviennent ici, où l'occasion leur est donnée de faire connaître leurs travaux de manière approfondie. Leurs exposés, à l'intention d'une large audience, sont accessibles au public non versé dans les matières formelles ou de pure philosophie. Des thèmes plus techniques sont aussi abordés, sans pour autant déroger aux deux premières exigences.
Ce séminaire est organisé par l'Equipe F2DS & le Centre Charles Morazé, avec le soutien du Centre National de la Recherche Scientifique (CNRS) et de la Fondation Maison des Sciences de l'Homme (FMSH).
Marcel Berger - IHES - Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France - ancien directeur
Archives Audiovisuelles de la Recherche Histoires de géométries 2008






Le Modulor    Le Corbusier
Dick Termes
traduction française Imaginez que vous êtes à l'intérieur d'une sphère transparente, suspendue à 150 mètres au-dessus du fond du Grand Canyon aux Etats- Unis. Vous vous trouvez au cSur des falaises, au-dessus de certaines, endessous d autres. Vous disposez de pinceaux et de peinture et vous vous mettez à peindre le paysage sur la surface intérieure de la sphère...
by Mizuta Tasogare May, 1995
Pencil carvings feature in the exhibition that we JAD Project hold. They are mainly produced by Mizuta Tasogare and Kato Jado.
Fractals by Jos Leys



<http://math.rice.edu/~joel/NonEuclid/reference.html> <http://www-leibniz.imag.fr/ATINF/Dongming.Wang/GRBib/> <http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Chou:Shang=Ching.html>






<liens_math.html> <http://www.scs.carleton.ca/~csgs/resources/cg.html>
Geometry Center Downloadable Software
<http://www.geom.umn.edu/software/cglist/> <http://www.ics.uci.edu/~eppstein/junkyard/model.html> <http://www-unix.mcs.anl.gov/AR/others.html> <http://www.matem.unam.mx/~urrutia/CompGeomInfo/People.html>

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