Visual Thinking in Mathematics by Marcus Giaquinto

Visual Thinking in Mathematics

byMarcus Giaquinto

Paperback | September 26, 2011

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Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemologicalfunctions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually hasepistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows howwe can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures.Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal toscholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.

About The Author

Marcus Giaquinto is a Reader in Philosophy at University College London.

Details & Specs

Title:Visual Thinking in MathematicsFormat:PaperbackDimensions:300 pages, 9.21 × 6.14 × 0.03 inPublished:September 26, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199575533

ISBN - 13:9780199575534

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Extra Content

Table of Contents

1. Introduction2. Simple Shapes: Vision and Concepts3. Basic Geometrical Knowledge4. Geometrical Discovery by Visualizing5. Diagrams in Geometric Proofs6. Mental Number Lines7. Visual Aspects of Calculation8. General Theorems from Specific Images9. Visual Thinking in Basic Analysis10. Symbol Manipulation11. Cognition of Structure12. Mathematical Thinking: Algebraic v. Geometric?

Editorial Reviews

`Review from previous edition The author shows great ambition in tackling such an interesting topic with an interdisciplinary spirit.' Sun-Joo Shin, Notre Dame Philosophical Reviews