Math Made Visual数学创作视觉

2006-4  

Mathematical Assn of Amer  

Alsina, Claudi/ Nelsen, Roger B.  

172  

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The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

Introduction; PartⅠ： Visualizing Mathematics by Creating Pictures　1. Representing numbers by graphical elements　2. Representing numbers by lengths of segments　3. Representing numbers by areas of plane figures　4. Representing numbers by volumes of bodies　5. Identifying key elements　6. Employing isometry　7. Employing similarity　8. Area preserving transformations　9. Escaping from the plan　10. Overlaying tiles　11. Playing with several copies　12. Sequential frames　13. Geometric dissections　14. Moving frames　15. Iterative procedures　16. Introducing colors　17. Visualization by inclusion　18. Ingenuity in 3D　19. Using 3D models　20. Combining techniquesPartⅡ： Visualization in the ClassroomPartⅢ： Hints and Solutions to the ChallengesReferencesIndex

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