The Visual Mind II

by Emmer, Michele

• ISBN13: 9780262550635
• ISBN10: 0262550636
• Format: Paperback
• Copyright: 2006-10-01
• Publisher: Mit Pr

Summary

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 Mindin 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 Mindproposes 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.

Table of Contents

Introduction	xi
Michele Emmer
Section 1 Mathematics and Aesthetics	1	(90)
The Phenomenology of Mathematical Beauty	3	(12)
Gian-Carlo Rota
Mathematical Beauty and the Evolution of the Standards of Mathematical Proof	15	(20)
James W. McAllister
Aesthetics for Computers, or How to Measure Harmony	35	(24)
Jaroslav Nesetril
Visual Mathematics: Mathematics and Art	59	(32)
Michele Emmer
Section 2 Geometry and Art	91	(178)
Life Through Art	95	(30)
Carmen Bonell
John Robinson's Symbolic Sculptures: Knots and Mathematics	125	(16)
Ronald Brown
Geometries of Curvature and Their Aesthetics	141	(18)
Brent Collins
Poetry in Curves: The Guggenheim Museum in Bilbao	159	(28)
Giuseppa Di Cristina
Eightfold Way: The Sculpture	187	(28)
Helaman Ferguson
Claire Ferguson
The Geometric Aesthetic	215	(20)
George W. Hart
Art and the Age of the Sciences	235	(18)
Charles Perry
Some Aspects of the Use of Geometry in My Artistic Work	253	(16)
Sylvie Pic
Section 3 Mathematics and Art	269	(200)
Local/Global in Mathematics and Painting	273	(36)
Capi Corrales Rodriganez
Laura Tedeschini-Lalli
Visual Knots: Concerning Geometry and Visuality in the Work of Marcel Duchamp	309	(26)
Manuel Corrada
Lunda Symmetry: Where Geometry Meets Art	335	(14)
Paulus Gerdes
Four-Dimensional Space or Space-Time? The Emergence of the Cubism-Relativity Myth in New York in the 1940s	349	(50)
Linda Dairymple Henderson
``Reverse Perspective'': Historical Fallacies and an Alternative View	399	(34)
Clemena Antonova
Martin Kemp
Four-Dimensional Projection: Art and Reality	433	(16)
Tony Robbin
Rational Design Versus Artistic Intuition In Stained-Glass Art	449	(20)
Tomas Garcia Salgado
Section 4 Geometry, Computer Graphics, and Art	469	(96)
Dynamics, Chaos, and Design	473	(22)
Michael Field
Paul Klee on Computer: Biomathematical Models Help Us Understand His Work	495	(32)
Roberto Giunti
Parameterized Sculpture Families	527	(20)
Carlo H. Sequin
The Aesthetic Value of Optimal Geometry	547	(18)
John M. Sullivan
Section 5 Mathematics, Visualization, and Cinema	565	(120)
Mathematics and Cinema	569	(32)
Michele Emmer
Some Organizing Principles	601	(22)
Peter Greenaway
Figures and Characters in the Great Book of Nature	623	(24)
Jean-Marc Levy-Leblond
Circle Packings and the Sacred Lotus	647	(20)
Tibor Tarnai
Koji Miyazaki
Meander Mazes on Polysphericons	667	(18)
Anthony Phillips
Contributors	685	(4)
Name Index	689	(8)
Subject Index	697