Mathematics And the Aesthetic

by Sinclair, Nathalie; Pimm, David; Higginson, William

• ISBN13: 9780387305264
• ISBN10: 0387305262
• Format: Hardcover
• Copyright: 2006-11-30
• Publisher: Springer Verlag

Summary

The essays in this book explore the ancient affinity between the mathematical and the aesthetic, focusing on the fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine the ways in which the aesthetic is ever present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Table of Contents

Notes about Authors	xiii
Chapter α A Historical Gaze at the Mathematical Aesthetic
Nathalie Sinclair and David Pimm	1	(19)
Section A: The Mathematician's Art
Introduction to Section A	20	(1)
Chapter 1 Aesthetics for the Working Mathematician
Jonathan M. Borwein	21	(20)
Chapter 2 Beauty and Truth in Mathematics
Doris Schattschneider	41	(17)
Chapter 3 Experiencing Meanings in Geometry
David W. Henderson and Daina Taimina	58	(28)
Section B: A Sense for Mathematics
Introduction to Section B	86	(1)
Chapter 4 The Aesthetic Sensibilities of Mathematicians
Nathalie Sinclair	87	(18)
Chapter 5 The Meaning of Pattern
Martin Schiralli	105	(21)
Chapter 6 Mathematics, Aesthetics and Being Human
William Higginson	126	(18)
Section C: Mathematical Agency
Introduction to Section C	144	(1)
Chapter 7 Mechanism and Magic in the Psychology of Dynamic Geometry
R. Nicholas Jackiw	145	(15)
Chapter 8 Drawing on the Image in Mathematics and Art
David Pimm	160	(30)
Chapter 9 Sensible Objects
Dick Tahta	190	(33)
Chapter ω Aesthetics and the 'Mathematical Mind'
David Pimm and Nathalie Sinclair	223	(32)
References	255	(22)
Index of Names	277	(4)
Index	281