Auteur
THÈME
GÉNÉRALITÉS - VUES D'ENSEMBLE
Banchoff.T.F. Beyond the third dimension, Scientific American Library, Freeman &Co, New York, 1990
Berger M. Géométrie Vivante ou l'Echelle de Jacob, Cassini, Paris, 2009 ISBN978-2-84225-035-5
Bruter C.P. Deux universaux de la décoration, Saverne
Dürer A. Géométrie, Préface J. Peiffer, Editions du Seuil, Paris, 1995
Emmer M. The Visual Mind I, Leonardo, The MIT Press, Cambridge, 1993
Emmer M. The Visual Mind II, Leonardo, The MIT Press, Cambridge, 2006
Holden A. Shapes, Space, and Symmetry, Columbia University Press, New-York- London, 1971
Ghyka M. Le Nombre d'Or, Gallimard, Paris, 1931-1959
Glaeser G.
Polthier K.
A Mathematical Picture Book, Springer-Verlag, Berlin, 2013 ISBN 978-3-642-14647-3
Pacioli L. Divine Proportion, Librairie du Compagnonnage, Paris, 1998, ISBN 2-901362-11-7
Speiser D. Crossroads: History of Science, History of Art, Kim Williams Editor, Birkhauser, Bâle, 2011
Weyl H. Symmetry, Princeton University Press, 1952
Symétrie et mathématique moderne, Flammarion, Paris, 1964
Liens historiques entre Arts et Mathématiques
Alberti L.B. De la Peinture, De Pictura, Paris Macula Dédale, 1992
Armann B. Roman Dodecahedron, The Math. Intelligencer 15 (1993), 52-53
Armann B. A Roman icosahedron discovered, Am. Math. Monthly 103 (1996), 132-133.
Armann B. Pictures of the Projective Plane
Bessot D.
Hellegouarch Y.
Le Goff J.-P.
Destin de l'Art, Desseins de la Science (Actes du Colloque A.D.E.R.H.E.M., Université de Caen, 24-29 Octobre 1986), ADERHEM-CNRS, 1991
Cubisme http://fr.wikipedia.org/wiki/Cubisme
Gillings R. J. Mathematics in the time of the Pharaohs, Dover, New-York, 1982
Mirgidicyan E. Les surfaces réglées dans l'art du xxème siècle. Regards croisés sur les constructions d'Antoine Pevsner et de Naum Gabo, Thèse 2010, Bibliothèque Institut H. Poincaré
Von Petzinger G. Geometric signs
Texier P. et Alii A Howiesons Poort tradition of engraving ostrich eggshell containers dated to 60,000 years ago at Diepkloof Rock Shelter, South Africa, PNAS, April 6, 2010 | vol. 107 | no. 14, 6180–6185.
Vitruve Architecture ou Art de bien Bâtir
PEINTURE et GRAVURE
Ouvrages
Dali S. Oui, Méthode paranoïaque-critique et autres textes, Denoël/Gonthier, Paris, 1971
Jeener P. Espaces gravés, Cedic/Nathan Paris, 1986
Kadinski W. Point et ligne sur un plan Gallimard, Paris, 1991
Du Spirituel dans l'art, et dans la peinture en particulier , Denoël, Paris, 1989
De Vinci L. Traité de la Peinture, Jean de Bonnot, Paris, 1977
PEINTURE et GRAVURE
Pavages
Castera J.M.
Jolis H.
Géométrie douce, Atelier 6 1/2, 1991 , ISBN 2950538908
P.N. Chung, M.A. Fernandez, Y. Li, M.Marz, F.Morgan, I. R. Plata, N. Shah, L.S. Vieira Isoperimetric Pentagonal Tilings, Notices AMS, May 2012, Vol. 59 (5), 632-640.
Deledicq R.
Raba R.
Le monde des pavages, ACL - Editions du Kangourou, Paris, 1977
Dunham D. M.C. Escher's Use of the Poincaré Models of Hyperbolic Geometry in Mathematics
and Modern Art
(C.P. Bruter Ed. Springer 2012) 69-77.
Field M. The Design of 2-colour Wallpapers Patterns Using Mehtods Based on Chaotic Dynamics and Symmetry, in Mathematics and Art (C.P. Bruter Ed., Springer 2002) 43-60.
Field M.
Golubtiski M.
Symmetry in Chaos, Oxford University Press, 1992
Grünbaum B.
Shephard G.C.
Tilings and Patterns, Freeman and Co, New York, 1989
Munford D.
Series C.-Wright D.
Indra Pearls, The Vision of Felix Klein, Cambridge University Press, 2002
Raba R. Zoo mathématique, ACL - Editions du Kangourou, Paris, 1998
Redondo Buitrago A.
Reyes Iglesias E.
Geometry and Art from the Cordovan Proportion, in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012) 117-129
Tard F. Rhombopolyclonic Polygonal Rosettes Theory, in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012) 167-176
PEINTURE et GRAVURE
Perspective
Bessot D.
Hellegouarch Y.
Le Goff J.-P.
Destin de l'Art, Desseins de la Science (Actes du Colloque A.D.E.R.H.E.M., Université de Caen, 24-29 Octobre 1986), ADERHEM-CNRS, 1991
Bruter C.P. Inititiation à la Perspective
Termes D. http://www.termespheres.com/ | http://termespheres.com/termesphere-that-show-how-perspective-works/
PEINTURE et GRAVURE
Surfaces
Faber E.-Hauser H. Today's menu: Geometry and resolutions of singular algebraic surfaces, Bull. Am. Math. Soc. 47(3) 2010, 373-417
Franzoni G. The Klein Bottle: Variations on a Theme, Notices of the AMS, vol 59, 8, 1076-1082.
Hunt B. A Gallery of Algebraic Surfaces in Mathematics and Art (C.P. Bruter Ed.), Springer 2002, 237-266
Jeener P. Graveur de Surfaces in Mathematics and Modern Art(C.P. Bruter Ed.) Springer 2012, 85-104
Jeener P. My Mathematical Engravings in Mathematics and Modern Art(C.P. Bruter Ed.) Springer 2012, 85-104
Palais R. A Mathematician and an Artist. The Story of a Collaboration in Mathematics and Modern Art (C.P. Bruter Ed.) Springer 2012, 1-9
Glaeser G.
Polthier K.
A Mathematical Picture Book, Springer-Verlag, Berlin, 2013 ISBN 978-3-642-14647-3
Polthier K. Polyhedral Surfaces of Constant Mean Curvature
Salamon S. Dynamic Surfaces in Mathematics and Modern Art (C.P. Bruter Ed.) Springer 2012, 131-151
Sullivan J.M. Pleasing Shapes for Topological Objects in Mathematics and Modern Art (C.P. Bruter Ed.) Springer 2012, 153-165
Papers on algebraic surfaces http://www.imaginary-exhibition.com/mathematik.php?lang=en
Websites
EG-Models http://www.eg-models.de/models.html, look for Surfaces (52) : The list includes Algebraic, Mean Curvature, Minimal, Polyhedral, Riemann surfaces.
3D-XplorMath http://3d-xplormath.org/, look for Surfaces.
Weber M. Matthias Weber's Minimal Surface Site
MATHCURVE http://www.mathcurve.com/
DESSINER ET PEINTRE
TO DRAW AND TO PAINT
Here is a list of some main public softwares for drawing and painting. Of course, to create the best original works, it might sometimes be better to write one's own software ... Several software in that list are free of charge and labelled F.
General
Javaview http://www.javaview.de/ F
Maple http://www.maplesoft.com/
Mathematica http://www.wolfram.com/mathematica/
Mathlab http://www.mathworks.fr/products/matlab/
Oorange http://www.polthier.info/articles/oorange/index.html
Algebraic surfaces
Surfer http://www.imaginary-exhibition.com/surfer.php F
jsurfer http://www.imaginary-exhibition.com/jsurfer.php F
Curves and surfaces
3D-XplorMath http://3d-xplormath.org/ F
Plane Curves
Space Curves
Surfaces
Conformal Maps
Polyhedra
ODE
Central Forces
Lattice Models
Waves
Fractals & Chaos
Differential geometry Grape F
Knots http://knotplot.com/download/
Entrelacs http://www.entrelacs.net/ F
http://hypatiasoft.pagesperso-orange.fr/F_index.html#mozTocId14585 F/NF
Plane geometry Geogebra F
Cinderella
Vectorial drawing Inkskape F
Illustrator F/NF
Painting Power Ray
Painter
Photos Retouching Gimp F
ANALYSIS and "FREQUENTIAL" REPRESENTATION
Cheng X.
Hart J.V.
WalkerJ.S
Time frequency analysis of musical rhythm, Notices of the AMS 56 (3) 2009, 344-360
Colonna J.F. Signal Processing [Traitement du Signal]
Daubechies I. Van Eyck's Mystic Lamb
Desolneux A.
Mumford D.
Pattern Theory, The Stochastic Analysis of Real World Signals AK Peters, 2010, ISBN 978-1-56881-579-4
3D-OBJECTS and SCULPTURES
Apéry F. Constructing Wire Models in Mathematics and Art, (C.P. Bruter Ed., Springer 2002), 179-200
Apéry F. Old and New Mathematical Models: Saving the Heritage of the Institut Henri Poincaré, in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012), 17-27
Charbonneau Ph. Rules Sculptures in Mathematics and Art, (C.P. Bruter Ed., Springer 2002), 233-236
Dickson S. Tactile Mathematics in Mathematics and Art, (C.P. Bruter Ed., Springer 2002), 213-222
Ferguson H. and C. Celebrating Mathematics in Stone and Bronze, Notices of the AMS, 57, 7 840-850
Hart. G.W. Solid-Segment Sculptures in Mathematics and Art , (C.P. Bruter Ed., Springer 2002), 17-27
Holden A. Shapes, Space, and Symmetry, Columbia University Press, New-York- London, 1971
Kozlov D. Knots and Links As Form-Generating Structures in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012), 105-115
Mirgidicyan E. Les surfaces réglées dans l'art du xxème siècle. Regards croisés sur les constructions d'Antoine Pevsner et de Naum Gabo, Thèse 2010, Bibliothèque Institut H. Poincaré
Rips Ph. Gallery 1 | Gallery 2 | Gallery 3 | Gallery 4
Robinson J. Symbolic Sculptures in Mathematics and Art C.P. Bruter Ed., Springer 2002), 148-152
Sullivan J. Minimal Flowers, Bridges Proceedings 2010, 395-398
Termes D. http://www.termespheres.com
POLYHEDRA
Alexanderson G. Luca da Pacioli and Leonardo's drawings of polyhedra, Bull. AMS, 47, 3, 553-556.
Cromwell P. R. Polyhedra, Cambridge University Press, 1997
De Clipperleir X. Transforming Polyhedra
Dezarnaud C.- Sevin A. Histoire des polyèdres, Vuibert, Paris, 2009.
Hart. G.W. Solid-Segment Sculptures in Mathematics and Art , (C.P. Bruter Ed., Springer 2002), 17-27
Pacioli L. Divine Proportion, Librairie du Compagnonnage, Paris, 1998, ISBN 2-901362-11-7
POPULARISATION and PEDAGOGY
Andreatta M. Activités pédagogiques et transmission des savoirs en mathématique/musique
Baka P. http://www.mathsdance.com/
Bruter C.P. Comprendre les Mathématiques Odile Jacob, Paris 1996, Introduction et Chapitre I : Sur la pertinence des mathématiques, Chapitre II : La mathématique, science expérimentale ? Chapitre III : Les leçons pédagogiques d'Henri Poincaré Chapitre IV : Degrés de rationalité en mathématiques
Bruter C.P. Deux universaux de la décoration, Saverne
Bruter C.P. Bonne Année | Part I | Part II | Part III | Part IV | Part V |
Bruter C.P. Pâtisserie Mathématique | Part I | Part II | Part III | Part IV |
Bruter C.P. An Introduction to the Construction of Some Mathematical Objects, in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012) 29-46
Bruter C.P. L'oeuvre d'art mathématique, un outil pédagogique efficace
Budin M. www.mathema.si
Chartier T. Envisionning the Invisible Notices of the AMS, 57(1) 2010 24-28
Constant J. Structure of Visualisation and Symmetry in Iterated Function Systems in Mathematics and Modern Art (C.P. Bruter Ed. Springer 2012) 53-67
Centre for the
(C.P. Bruter Ed. Springer 2012) 53-67 Popularisation
of Mathematics
http://www.popmath.org.uk/centre/index.html
Dedò M. Machines for Building Symmetries in Mathematics and Art, (C.P. Bruter Ed., Springer 2002) 61-77 Maria Dedò
Forum How Art Can Help the Teaching of Mathematics ? in Mathematics and Art, (C.P. Bruter Ed., Springer 2002)(with the participation of Claude-Paul Bruter (153-154), Ronnie Brown (155-159), Manuel Arala-Chaves (160-165), Michele Emmer (166-167), Michael Field (168-172)) R. Brown, C.P. Bruter, M. Chaves, M. Emmer, M. Field.
Guedj D. Le Théorème du Perroquet Le Seuil, Paris, 1998
Guedj D. Zéro, ou les cinq vies d'Aémer Robert Laffont, Paris, 2005
Kalantari B. Polynomial Root-Finding and Polynomiography, World Scientific, 2009.
Gruel G.-M.
Matt A.D.
Imaginary Travelling Exhibition Catalogue Mathematisches Forschunginstitut Oberwolfach 2008 ISBN 978-3-00-026939-4
Mayer M.Reflex
Sylvander B. L'île logique
VISUALIZATION TOWARDS MATHEMATICS
Crass S. Solving Polynomial by Iteration, An Aesthetic Approach in Mathematics and Art, (C.P. Bruter Ed., Springer 2002) 95-104
Hubbard J. Visualization and Dynamical Systems in Mathematics and Art (C.P. Bruter Ed., Springer 2002) 91-94
Polthier K. Visualizing Mathematics-Online in Mathematics and Art (C.P. Bruter Ed., Springer 2002) 29-42
Sazdanovic R. Diagrammatics in Art and Mathematics Symmetry 2012, 4(2), 285-301
Wegert E.-Semmler G. Phase Plots of Complex Functions: A journey in Illustration, Notices of the A.M.S., 58 (6) 2011, 768-780.
VISUALIZATION, FILMS and VIDEOS
Looking for instance at The Optiverse, you will find a large collection of mathematical videos on youtube
Alvarez A.-Ghys E.-Leys J. Dimensions, une promenade mathématique
Brunet J. Like a Dream
De Clippeleir X. Animated gifs of the transforming cube
Francis G.-Levy. S.-Sullivan J.M. The Optiverse
Polthier K. Videos
MUSIQUE et INSTRUMENTS
Agon C.
Amiot E.
Andreatta M.
Assayag G.
Bresson J.
Manderau J.(Ed.)
Mathematics and Computation in Music. Proceedings of the third International Conference of the Mathematics and Computation in Music. Paris, June 15-17, 2011 Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence, Springer, 2011
Andreatta M. Mathematica est exercitium musicae, la recherche mathémusicale et ses interactions avec les autres disciplines
Bruner R. Mathematical music visualization: the sphere, the Moore space, the Joker
Celibidache S. La Musique n'est Rien Actes Sud, Paris, 2012
Charnoz G. Démystifier la Théorie musicale Editions du Makar, Paris, 2001
Cheng X.
Hart J.V.
WalkerJ.S
Time frequency analysis of musical rhythm, Notices of the AMS 56 (3) 2009, 344-360
Daniélou A. Sémantique Musicale, Hermann, Paris, 1967
Don G.W.
Muir K.K.
Volk G.B.
Walker J.S.
Music: Broken symmetry, geometry, and complexity, Notices of the AMS 57 (1) 2010, 30-49
Goodman J.E. On Hearing the Sound of a Theorem, Notices of the AMS 58 (10) 2011, 1409
Hart V. Mathematics and Music Boxes in Mathematics and Modern Art , (C.P. Bruter Ed.) Springer 2012, 79-83
Hellegouarch Y. L'Essai d'un nouvelle théorie de la musique" de Léonhard Euler in Destin de l'Art, Desseins de la Science, (Actes du Colloque A.D.E.R.H.E.M., Université de Caen, 24-29 Octobre 1986), ADERHEM-CNRS, 1991 pp 46-88
Hellegouarch Y. A Mathematical Interpretation of Expressive Intonation in Mathematics and Art (C.P. Bruter Ed.), Springer 2002, 141-148
Hoffman-Jablan J. Symmetry of Musical Work
Johnson T. Mathematical musical archives
Machabey A. Quelques savants-musiciens à l'époque de Mersenne Revue d'histoire des Sciences et de leur applications, 11 (3) 1958, 193-206
Neuwirth E. The Mathematics of Tuning Musical Instruments - a Simple Toolkit for Experiments in Mathematics and Art (C.P. Bruter Ed.), Springer 2002, 79-88
Schneiderman R. Can One Hear the Sound of a Theorem, Notices of the AMS 58 (7) 2011, 929-937
Schneiderman R. Response to Tymocko, Notices of the AMS 58 (10) 2011, 1048
Simoes C. Mathematical Aspects of the Second Viennese School of Music in Mathematics and Art (C.P. Bruter Ed.), Springer 2002, 105-117
Tymoczko D. The Geometry of Musical Chords, Science 313 (2006) 72-74
Tymoczko D. A Geometry of Music, Oxford University Press, 2011
Walker J.S. On the article of Schneiderman, Notices of the AMS 58 (10) 2011, 1408-1409
Xenakis I. Musiques formelles, Le Revue Musicale, double numéro spécila 253-254, Paris, 1963