Math Made Visual: Creating Images for Understanding Mathematics

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MAA, Jul 6, 2006 - Mathematics - 173 pages
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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.
 

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Contents

Visualizing Mathematics by Creating Pictures
1
Representing Numbers by Lengths of Segments
7
Representing Numbers by Areas of Plane Figures
13
Representing Numbers by Volumes of Objects
19
Identifying Key Elements
23
Employing Similarity
31
Escaping from the Plane
43
Playing with Several Copies
55
Moving Frames
69
Introducing Colors
79
Ingenuity in 3D
87
Using 3D Models
97
Combining Techniques
109
Visualization in the Classroom 117
119
Hints and Solutions to the Challenges
143
References
161

Sequential Frames
59

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