## Fractals, Graphics, and Mathematics EducationFractal 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. |

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### Contents

Some Reasons for the Effectiveness of Fractals in Mathematics Education by Benoit B Mandelbrot Michael Frame | 3 |

Unsolved Problems and StillEmerging Concepts in Fractal Geometry by Benoit B Mandelbrot | 11 |

Fractals Graphics and Mathematics Education by Benoit B Mandelbrot | 21 |

Mathematics and Society in the 20th Century by Benoit B Mandelbrot | 29 |

CLASSROOM EXPERIENCES | 33 |

Teaching Fractals and Dynamical Systems at The Hotchkiss School by Melkana Brakalova David Coughlin | 35 |

Considering Change in the Undergraduate Mathematics Major John A Dossey Editor | 45 |

Scaling the Heights Deborah Nolan Editor | 46 |

A Report on Evaluation Efforts and National Impact from 1988 to 1998 Susan L Ganter | 56 |

Resources for Professional Development Matthew Delong and Dale Winter | 57 |

Fractals Graphics and Mathematics Education Benoit Mandelbrot and Michael Frame Editors | 58 |

Assets for Undergraduate Mathematics David Carlson Charles R Johnson David C Lay and A Duane Porter Editors | 59 |

Periods of the Bulbs by Robert L Devaney | 61 |

FractalsEnergizing the Mathematics Classroom by Vicki Fegers Mary Beth Johnson | 69 |

Other Chaos Games by Sandy Fillebrown | 105 |

a Personal Experience by Michel Lapidus | 111 |

Innovative Programs Using Technology Susan Lenker Editor | 47 |

Writing in the Teaching and Learning of Mathematics John Meier and Thomas Rishel | 48 |

Assessment Practices in Undergraduate Mathematics Bonnie Gold Editor | 49 |

Exploring ODEs with Modern Technology Michael J Kallaher Editor | 50 |

An International Perspective Victor J Katz Editor | 51 |

Resources for Undergraduate Instructors Thomas L Moore Editor | 52 |

Papers in Applied Geometry Catherine A Gorini Editor | 53 |

A Guide for New Mathematicians Thomas W Rishel | 54 |

Issues That Matter and Strategies That Work Elizabeth C Rogers Barbara E Reynolds Neil A Davidson and Anthony D Thomas Editors | 55 |

Exploring Fractal Dimensions by Experiment by Ron Lewis | 117 |

Fractal Themes at Every Level by Kenneth G Monks | 139 |

Artistic Explorations of Natural SelfSimilarity by Brianna Murratti Michael Frame | 149 |

a First College Course in Quantitative Reasoning Based on Fractals and Chaos by David Peak Michael Frame | 157 |

200901 1 12 | 164 |

A Software Driven Undergraduate Fractals Course by Douglas C Ravenel | 171 |

The Fractal Ring from Art to Art through Mathematics Finance and the Sciences | 179 |

About the Editors and Other Contributors | 201 |

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