Custom cover image
Mathematics and Modern Art : Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010 / edited by Claude Bruter
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Proceedings in Mathematics ; 18 | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: Online-Ressource (VIII, 178p. 221 illus., 145 illus. in color, digital)ISBN:- 9783642244971
- 700.105
- 519
- NX180.M33
Contents:
Summary: Preface -- A Mathematician and an Artist. The Story of a Collaboration by R.Palais -- Dimensions, a Math Movie by A.Alvarez, J.Leys -- Old and new Mathematical Models: saving the Heritage of the Institute Henri Poincaré by F.Apéry -- An Introduction to the Construction of some Mathematical Objects by C.P.Bruter -- Computer, Mathematics and Art by J.-F.Colonna -- Structure of Visualization and Symmetry in iterated Function Systems by J.Constant -- Polyhedral eversions of the sphere; gastrulation by R.Denner -- M.C. Escher’s Use of the Poincaré Models of Hyperbolic Geometry by D.Dunham -- Mathematics and Music Boxes by V.Hart -- Mes Gravures Mathématiques by P.Jeener -- Knots and Links As Form-Generating Structures by D.Kozlov -- Geometry and Art from the Cordovan Proportion by A.Redondo-Buitrago, E.Reyes -- Dynamic Surfaces by S. Salamon -- Pleasing Shapes for Topological Objects by J.Sullivan -- Rhombopolyclonic Polygonal Rosettes Theory by F.Tard .Summary: The link between mathematics and art remains as strong today as it was in the earliest instances of decorative and ritual art. Arts, architecture, music and painting have for a long time been sources of new developments in mathematics, and vice versa. Many great painters have seen no contradiction between artistic and mathematical endeavors, contributing to the progress of both, using mathematical principles to guide their visual creativity, enriching their visual environment with the new objects created by the mathematical science. Owing to the recent development of the so nice techniques for visualization, while mathematicians can better explore these new mathematical objects, artists can use them to emphasize their intrinsic beauty, and create quite new sceneries. This volume, the content of the first conference of the European Society for Mathematics and the Arts (ESMA), held in Paris in 2010, gives an overview on some significant and beautiful recent works where maths and art, including architecture and music, are interwoven. The book includes a wealth of mathematical illustrations from several basic mathematical fields including classical geometry, topology, differential geometry, dynamical systems. Here, artists and mathematicians alike elucidate the thought processes and the tools used to create their work.PPN: PPN: 1651475059Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
Mathematics and Modern Art; Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010; Preface; Contents; A Mathematician and an Artist. The Story of a Collaboration; 1 Appreciation; 2 Introduction; 3 The Five Glasses Surface; 4 Kuen´s Surface; 5 Triply Periodic Surface WP; 6 A Fractal Basin; 7 Two Cyclides; 8 Tunnel 5B; 9 Lya Poster; 10 Wohlgemuth-Thayer; Dimensions, a Math Movie; 1 Introduction: The Start of a Film Project; 2 The Scenario; 3 The Production; 4 A Non-profit Project; 5 The Website [6]; 6 Results; 7 Conclusion; References
Old and New Mathematical Models: Saving the Heritage of the Institut Henri Poincaré1 Introduction; 2 The Klein Bottle; 3 The One-Sided Cyclid; 4 The Poinsot Great Dodecahedron; 5 Smooth Cubic with Seven Real Lines; 6 Dandelin Model; 7 A Model of Descriptive Geometry; 8 Sievert Surface; 9 Two Recent Models; References; An Introduction to the Construction of Some Mathematical Objects; 1 Generalities; 1.1 Introduction; 1.2 Shapes as a Restricted Class of Mathematical Objects; 1.3 Characteristic Features of a Shape; 2 Internal Modifications; 2.1 Pinching; 2.2 Inflations; 2.2.1 Singular Inflations
2.2.2 Regular Inflations and Desinflations2.3 Folding; 2.4 Cutting and Opening; 3 External Modifications; 4 Synthesis; References; Computer, Mathematics and Art; 1 Chess and Math; 2 Mathematics are the Reality; 3 Art and Computer; 4 Art and Mathematics; Structure of Visualization and Symmetry in Iterated Function Systems; 1 Introduction; 2 Methodology; 2.1 Data Collection: Mathematical Iteration Systems; 2.2 Graphic Manipulation; 2.2.1 Vector Outline; 2.2.2 Optical Illusion; Hermann Grid; The Hering Illusion; The Wundt Illusion; The Aitken Wheel; The Ebbinghaus; 2.2.3 Color Scheme
2.3 Dissemination2.3.1 Multimedia; Visual Component; Audio Track; 2.3.2 Deployment; 3 Conclusion; References; M.C. Escher´s Use of the Poincaré Models of Hyperbolic Geometry; 1 Introduction; 2 A Brief History of Hyperbolic Art; 3 Repeating Patterns and the Poincaré Disk and Half Plane Models; 4 Patterns in the Poincaré Disk Model; 5 Patterns in the Poincaré Half-Plane Model; 6 Future Work; References; Mathematics and Music Boxes; 1 Introduction; 2 Related Work; 3 Transforming a Piece; 4 Loops; 5 Canons; 6 Types of Canons; References; My Mathematical Engravings
1 Introduction: The Engraver´s Job2 Minimal Surfaces; 2.1 Enneper Surface; 2.2 Formulas of Monge and Weierstraß; 2.3 Catalan Surface; 2.4 Jeener Surface; 2.5 Minimal Surface with a Family of Parabolas; 2.6 Bonnet Surface; 2.7 Henneberg Surface; 3 Topology of Closed Surfaces Without Singularities; 3.1 Surfaces with Constant Total Curvature; 3.1.1 The Pseudo-sphere (K = -1); 3.1.2 Dini Helicoid (K = -1); 3.1.3 Kuen Surface (K = -1); 3.1.4 Sievert Surface (K = +1); 3.1.5 Surfaces of Zero Curvature (K = 0); 4 Bi-periodical Functions; 4.1 Jacobi Functions; 4.2 Weierstraß Functions; References
Knots and Links As Form-Generating Structures
No physical items for this record