Math Made Visual数学创作视觉
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作者： Roger Nelsen，Claudi Alsina著
出 版 社：
出版时间： 2006-4-1字数：版次： 1页数： 172印刷时间： 2006/04/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780883857465包装： 精装编辑推荐
作者简介：Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. He did Post-doctoral studies at the University of Massachusetts, Amherst. Currently he is a Professor of mathematics at the Technical University of Catalonia. He participates in a a wide range of international activities, and has written several research papers and publications on mathematics and mathematics education.
内容简介
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.
目录
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 techniques
PartⅡ： Visualization in the Classroom
PartⅢ： Hints and Solutions to the Challenges
References
Index
