Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work. This book emphasizes and renews the deep relation between Mathematics and Art. The Forum Discussion suggests to develop a deeper interpenetration between these two cultural fields, notably in the teaching of both Mathematics and Art.
Author(s): Claude-Paul Bruter (auth.), Claude P. Bruter (eds.)
Series: Mathematics and Visualization
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2002
Language: English
Pages: 337
Tags: Visualization; Geometry; Topology; Computer Imaging, Vision, Pattern Recognition and Graphics
Front Matter....Pages I-X
Presentation of the Colloquium. The ARPAM Project....Pages 1-15
Solid-Segment Sculptures....Pages 17-27
Visualizing Mathematics — Online....Pages 29-42
The Design of 2-Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry....Pages 43-60
Machines for Building Symmetry....Pages 61-77
The Mathematics of Tuning Musical Instruments — a Simple Toolkit for Experiments....Pages 79-88
The Garden of Eden....Pages 89-90
Visualization and Dynamical Systems....Pages 91-94
Solving Polynomials by Iteration....Pages 95-104
Mathematical Aspects in the Second Viennese School of Music....Pages 105-117
Mathematics and Art: The Film Series....Pages 119-133
Guided Tours of Buried Galleries (Inside a Computer)....Pages 135-139
A Mathematical Interpretation of Expressive Intonation....Pages 141-148
Symbolic Sculptures....Pages 149-152
FORUM: How Art Can Help the Teaching of Mathematics?....Pages 153-154
Forum Discussion....Pages 155-159
Forum Discussion: Presentation of the Atractor ....Pages 160-165
Forum Discussion....Pages 166-167
Forum Discussion....Pages 168-172
Getting Out of the Box and Into the Sphere....Pages 173-177
Constructing Wire Models....Pages 179-200
Sphere Eversions: from Smale through “The Optiverse”....Pages 201-212
Tactile Mathematics....Pages 213-222
Hyperseeing, Knots, and Minimal Surfaces....Pages 223-232
Ruled Sculptures....Pages 233-236
A Gallery of Algebraic Surfaces....Pages 237-266
The Mathematical Exploratorium....Pages 267-272
Copper Engravings....Pages 273-274
Back Matter....Pages 275-337
