Fractals, Graphics, and Mathematics Education
by Frame, Michael; Mandelbrot, Benoit B.; Steen, Lynn ArthurFormat: Paperback
Pub. Date: 2003-01-01
Publisher(s): Mathematical Assn of Amer
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Summary
Fractal Geometry is a recent edition to the collection of mathematical tools for describing nature, and is the first to focus on roughness. Fractal geometry also appears in art, music and literature, most often without being consciously included by the artist. Consequently, through this we may uncover connections between the arts and sciences, uncommon for students to see in maths and science classes. This book will appeal to teachers who have wanted to include fractals in their mathematics and science classes, to scientists familiar with fractal geometry who want to teach a course on fractals, and to anyone who thinks general scientific literacy is an issue important enough to warrant new approaches.
Table of Contents
| Part I. Introductory Essays: 1. Some reasons for the effectiveness of fractal geometry in mathematics education Benoit B. Mandelbrot and Michael Frame | |
| 2. Unsolved problems and still emerging concepts Benoit B. Mandelbrot | |
| 3. Fractals, graphics and mathematics education Benoit B. Mandelbrot | |
| 4. Mathematics and society in the twentieth century Benoit B. Mandelbrot | |
| Part II. Classroom Experiences: 5. Teaching fractals and dynamical systems at the Hotchkiss school Melkana Brakalova and David Coughlin | |
| 6. Reflection on Wada basins: some fractals with a twist Dane Camp | |
| 7. Learning and teaching about fractals Donald M. Davis | |
| 8. The fractal geometry of the Mandelbrot set Robert L. Devaney | |
| 9. Fractals - energizing the mathematics classroom Viki Fegers and Mary Beth Johnson | |
| 10. Other chaos games Sandy Fillebrown | |
| 11. Creating and teaching undergraduate courses in fractal geometry: a personal experience Michel Lapidus | |
| 12. Exploring Fractal dimensions by experiment Ron Lewis | |
| 13. Fractal themes on all levels Kenneth G. Monks | |
| 14. Art and fractals: artistic explorations of natural self-similarity Brianna Murati and Michael Frame | |
| 15. Order and chaos, art and magic: a first college course in quantitative reasoning based on fractals and chaos David Peak and Michael Frame | |
| 16. A software driven undergraduate fractals course Douglas C. Ravenel | |
| Part III. A Final Word: 17. The fractal ring from art to art through mathematics, finance and the sciences Benoit B. Mandelbrot | |
| Part IV. Appendices: 18. Panorama of fractals and their uses. An alphabetic workbook-index Michael Frame and Benoit B. Mandelbrot | |
| 19. Reports of some field experiences. |
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