Visual Thinking in Mathematics

Visual Thinking in Mathematics

AngličtinaPevná vazbaTisk na objednávku
Giaquinto Marcus
Oxford University Press
EAN: 9780199285945
Tisk na objednávku
Předpokládané dodání v úterý, 10. prosince 2024
1 781 Kč
Běžná cena: 1 979 Kč
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Podrobné informace

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 epistemological functions, 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 has epistemological 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 how we 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 to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
EAN 9780199285945
ISBN 0199285942
Typ produktu Pevná vazba
Vydavatel Oxford University Press
Datum vydání 5. července 2007
Stránky 298
Jazyk English
Rozměry 241 x 162 x 23
Země United Kingdom
Autoři Giaquinto Marcus
Ilustrace numerous line figures