Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.
Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.
Marcus Giaquinto is a Reader in Philosophy at University College London.
Inhaltsangabe
1: Introduction 2: Simple Shapes: Vision and Concepts 3: Basic Geometrical Knowledge 4: Geometrical Discovery by Visualizing 5: Diagrams in Geometric Proofs 6: Mental Number Lines 7: Visual Aspects of Calculation 8: General Theorems from Specific Images 9: Visual Thinking in Basic Analysis 10: Symbol Manipulation 11: Cognition of Structure 12: Mathematical Thinking: Algebraic v. Geometric?
1: Introduction 2: Simple Shapes: Vision and Concepts 3: Basic Geometrical Knowledge 4: Geometrical Discovery by Visualizing 5: Diagrams in Geometric Proofs 6: Mental Number Lines 7: Visual Aspects of Calculation 8: General Theorems from Specific Images 9: Visual Thinking in Basic Analysis 10: Symbol Manipulation 11: Cognition of Structure 12: Mathematical Thinking: Algebraic v. Geometric?
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