The Visual Mind II (Hardcover)

Description:

Mathematical forms rendered visually can give aesthetic pleasure; certain works of art -- Max Bill's Moebius band sculpture, for example -- can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.

Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians -- not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema.

Michele Emmer is Professor of Mathematics at the University of Rome "La Sapienza."

 

Table of Contents:

Introduction Michele Emmer	xi
	Section 1. Mathematics and Aesthetics	1
1.	The Phenomenology of Mathematical Beauty Gian-Carlo Rota	3
2.	Mathematical Beauty and the Evolution of the Standards of Mathematical Proof James W. McAllister	15
3.	Aesthetics for Computers, or How to Measure Harmony Jaroslav Nesetril	35
4.	Visual Mathematics: Mathematics and Art Michele Emmer	59
	Section 2. Geometry and Art	91
5.	Life Through Art Carmen Bonell	95
6.	John Robinson's Symbolic Sculptures: Knots and Mathematics Ronald Brown	125
7.	Geometries of Curvature and Their Aesthetics Brent Collins	141
8.	Poetry in Curves: The Guggenheim Museum in Bilbao Giusppa Di Cristina	159
9.	Eightfold Way: The Sculpture Helaman Ferguson and Claire Ferguson	187
10.	The Geometric Aesthetic George W. Hart	215
11.	Art and the Age of the Sciences Charles Perry	235
12.	Some Aspects of the Use of Geometry in My Artistic Work Sylvie Pic	253
	Section 3. Mathematics and Art	269
13.	Local/Global in Mathematics and Painting Capi Corrales Rodriganez and Laura Tedeschini-Lalli	273
14.	Visual Knots: Concerning Geometry and Visuality in the Work of Marcel Duchamp Manuel Corrada	309
15.	Lunda Symmetry: Where Geometry Meets Art Paulus Gerdes	335
16.	Four-Dimensional Space or Space-Time? The Emergence of the Cubism-Relativity Myth in New York in the 1940s Linda Dalrymple Henderson	349
17.	"Reverse Perspective": Historical Fallacies and an Alternative View Clemena Antonova and Martin Kemp	399
18.	Four-Dimensional Projection: Art and Reality Tony Robbin	433
19	Rational Design versus Artistic Intuition in Stained-Glass Art Tomas Garcia Salgado	449
	Section 4. Geometry, Computer Graphics, and Art	469
20	Dynamics, Chaos, and Design Michael Field	473
21.	Paul Klee on Computer: Biomathematical Models Help Us Understand His Work Roberto Giunti	495
22.	Parameterized Sculpture Families Carlo H. Sequin	527
23.	The Aesthetic Value of Optimal Geometry John M. Sullivan	547
	Section 5. Mathematics, Visualization, and Cinema	565
24.	Mathematics and Cinema Michele Emmer	569
25.	Some Organizing Principles Peter Greenaway	601
26.	Figures and Characters in the Great Book of Nature Jean-Marc Levy-Leblond
27.	Circle Packings and the Sacred Lotus Tibor Tarnai and Koji Miyazaki	647
28.	Meander Mazes on Polysphericons Anthony Phillips	667
	Contributors	685
	Name Index	689
	Subject Index	697