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Fractals, graphics, and mathematics education

Author: Michael Frame; Benoit B Mandelbrot
Publisher: [Washington, DC] : Mathematical Association of America, ©2002.
Series: MAA notes, no. 58.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Fractal geometry is a recent addition to the collection of mathematical tools for describing nature and the works of Man. It made possible for the first time a national study of roughness. Fractals are encountered in mathematics and many natural sciences, but also in finance and in art, music and literature most often without being consciously included by anyone. Therefore, fractals interconnect the arts and the  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michael Frame; Benoit B Mandelbrot
ISBN: 0883851695 9780883851692
OCLC Number: 50032121
Description: xiii, 206 p. : ill. (some col.) ; 28 cm.
Contents: Some reasons for the effectiveness of fractals in mathematics education / Benoit Mandelbrot. Michael Frame --
Unsolved problems and still-emerging concepts in fractal geometry ; Fractals, graphics, and mathematics education ; Mathematics and society in the 20th century / Benoit Mandelbrot --
Teaching fractals and dynamical systems at the Hotchkiss school / Melkana Brakalova, David Coughlin --
Reflecting on wada basins : some fractals with a twist / Dane Camp --
Learning and teaching about fractals / Donald M. Davis --
The Fractal geometry of the Mandelbrot set: periods of the bulbs / Robert L. Devaney --
Fractals : energizing the mathematics classroom / Vicky Fegers, Mary Beth Johnson --
Other chaos games / Sandy Fillebrown --
Creating and teaching undergraduate courses and seminars in fractal geometry : a personal experience / Michel Lapidus --
Exploring fractal dimensions by experiment / Ron Lewis --
Fractal themes at every level / Kenneth G. Monks --
Art and fractals : artistic explorations of natural self-similarity / Brianna Murratti, Michael Frame --
Order and chaos, art and magic : a first college course in quantitiative reasoning based on fractals and chaos / David Peak, Michael Frame --
A Software driven undergraduate fractals course / Douglas C. Ravenel --
The Fractal ring from art to art through mathematics, finance, and the sciences / Benoit B. Mandelbrot --
Panorama of fractals and their uses : an alphabetic wordbook-index / Michael Frame, Benoit B. Mandelbrot --
Report of some field experiences.
Series Title: MAA notes, no. 58.
Other Titles: Fractals, graphics, & mathematics education
Responsibility: Michael Frame and Benoit B. Mandelbrot, editors ; foreword by Lynn Arthur Steen.
More information:

Abstract:

Fractal geometry is a recent addition to the collection of mathematical tools for describing nature and the works of Man. It made possible for the first time a national study of roughness. Fractals are encountered in mathematics and many natural sciences, but also in finance and in art, music and literature most often without being consciously included by anyone. Therefore, fractals interconnect the arts and the natural and social sciences in many intrinsic ways. Rarely, if ever, are students exposed to anything like this in mathematics and science classes. This book collects essays about fractal's role in mathematics and science education. In the first four chapters, the editors address general issues. The next twelve chapters are invited case studies authored by educators who began years ago to use fractal geometry in classes that range from second grade elementary school, through public and private high schools, to state universities and private colleges. Some contributors survey literature and software they have used, others present detailed sample lessons. The chapter for Florida Atlantic University reports on a program training teachers in Florida. Many teachers developed fractals courses on their own in isolation from one another. This book is a token of how widespread such courses have become. The common themes that appear throughout mark the coming of age of this subject. - Publisher.

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