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. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea 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.…mehr
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. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea 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.
Roger B. Nelson, geb. 1942 in Chicago, Illinois, erhielt seinen B.A. in Mathematik 1964 von der DePauw University und 1969 promovierte er in Mathematik an der Duke University. Er ist gewähltes Mitglied der akademischen Phi-Beta-Kappa-Gesellschaft sowie der wissenschaftlichen Vereinigung Sigma Xi und unterrichtete rund vierzig Jahre Mathematik und Statistik am Lewis & Clark College bevor er im Jahre 2009 in den Ruhestand ging. Er hat etliche mathematische Werke geschrieben.
Inhaltsangabe
Introduction; Part I. 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 plane; 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; Part II. Visualization in the Classroom; Part III. Hints and Solutions to the Challenges; References; Index.
Introduction; Part I. 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 plane; 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; Part II. Visualization in the Classroom; Part III. Hints and Solutions to the Challenges; References; Index.
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