Fractals for the classroom : strategic activities

Author(s)

• Peitgen, Heinz-Otto

Bibliographic Information

Fractals for the classroom : strategic activities

Heinz-Otto Peitgen ... [et al.]

Springer-Verlag, c1991-c1999

• v. 1 : us
• v. 1 : gw
• v. 2 : us
• v. 2 : gw
• v. 3 : us

Note

"Published in cooperation with the National Council of Teachers of Mathematics (NCTM)" -- t.p. verso

Description and Table of Contents

Volume

v. 1 : us ISBN 9780387973463

Description

There are many reasons for writing this first volume of strategic activities on fractals. The most pervasive is the compelling desire to provide students of mathematics with a set of accessible, hands-on experiences with fractals and their underlying mathematical principles and characteristics. Another is to show how fractals connect to many different aspects of mathematics and how the study of fractals can bring these ideas together. A third is to share the beauty of their structure and shape both through what the eye sees and what the mind visualizes. Fractals have captured the attention, enthusiasm, and interest of many people around the world. To the casual observer, their color, beauty, and geometric structure captivates the visual senses like few other things they have ever experienced in mathematics. To the computer scientist, fractals offer a rich environment in which to explore, create, and build a new visual world as an artist creating a new work. To the student, fractals bring mathematics out of past history and into the twenty-first century. To the mathematics teacher, fractals offer a unique, new opportunity to illustrate both the dynamics of mathematics and its many connecting links.

Table of Contents

Unit 1 Self-Similarity.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 1.1 Sierpinski Triangle and Variations.- 1.2 Number Patterns and Variations.- 1.3 Square Gasket.- 1.4 Sierpinski Tetrahedron.- 1.5 Trees.- 1.6 Self-Similarity: Basic Properties.- 1.7 Self-Similarity: Specifics.- 1.8 Box Self-Similarity: Grasping the Limit.- 1.9 Pascal's Triangle.- 1.10 Sierpinski Triangle Revisited.- 1.11 New Coloring Rules and Patterns.- 1.12 Cellular Automata.- Unit 2 The Chaos Game.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 2.1 The Chaos Game.- 2.2 Simulating the Chaos Game.- 2.3 Addresses in Triangles and Trees.- 2.4 Chaos Game and Sierpinski Triangle.- 2.5 Chaos Game Analysis.- 2.6 Sampling and the Chaos Game.- 2.7 Probability and the Chaos Game.- 2.8 Trees and the Cantor Set.- 2.9 Trees and the Sierpinski Triangle.- Unit 3 Complexity.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 3.1 Construction and Complexity.- 3.2 Fractal Curves.- 3.3 Curve Fitting.- 3.4 Curve Fitting Using Logs.- 3.5 Curve Fitting Using Technology.- 3.6 Box Dimension.- 3.7 Box Dimension and Coastlines.- 3.8 Box Dimension for Self-Similar Objects.- 3.9 Similarity Dimension.- Answers.

Volume

v. 2 : us ISBN 9780387975542

Description

The same factors that motivated the writing of our first volume of strategic activities on fractals continued to encourage the assembly of additional activities for this second volume. Fractals provide a setting wherein students can enjoy hands-on experiences that involve important mathematical content connected to a wide range of physical and social phenomena. The striking graphic images, unexpected geometric properties, and fascinating numerical processes offer unparalleled opportunity for enthusiastic student inquiry. Students sense the vigor present in the growing and highly integrative discipline of fractal geom etry as they are introduced to mathematical developments that have occurred during the last half of the twentieth century. Few branches of mathematics and computer science offer such a contem porary portrayal of the wonderment available in careful analysis, in the amazing dialogue between numeric and geometric processes, and in the energetic interaction between mathematics and other disciplines. Fractals continue to supply an uncommon setting for animated teaching and learn ing activities that focus upon fundamental mathematical concepts, connections, problem-solving techniques, and many other major topics of elementary and advanced mathematics. It remains our hope that, through this second volume of strategic activities, readers will find their enjoyment of mathematics heightened and their appreciation for the dynamics of the world in creased. We want experiences with fractals to enliven curiosity and to stretch the imagination.

Table of Contents

Unit 4 Iteration.- Unit 5 Chaos.- Unit 6 The Mandelbrot Set.- Answers.

Volume

v. 3 : us ISBN 9780387984209

Description

Written by the award winning authors of Chaos and Fractals (0-387-97903-4), this work introduces the reader to iterated function systems through a lively, interactive approach. This well-written, clearly illustrated book explores the history and the unlimited potential of fractals, while developing a basic mathematical understanding and appreciation for the topics.

Table of Contents

Preface.- Authors.- Connections to the Curriculum.- Foreword (by Jana Wallace).- IFS in Two Dimensions.- IFS and Geometric Genetic Codes.- Answers.

Volume

v. 1 : gw ISBN 9783540973461

Description

This first volume of strategic classroom activities is designed to develop, through a hands-on approach, a basic mathematical understanding and appreciation of fractals. The concepts presented on fractals include self-similarity, the chaos game and complexity as it relates to fractal dimension. Where appropriate, the activities take advantage of the technological power of the graphics calculator. The slide package that accompanies this first volume includes high quality fractal images.

Table of Contents

1: Self-Similarity. 2: The Chaos Game. 3: Complexity.

Volume

v. 2 : gw ISBN 9783540975540

Description

This second volume of practical activities is designed to develop a basic mathematical understanding of fractals. Concepts addressed include self-similarity, the chaos game and complexity as it relates to fractal dimension. The book is accompanied by a slide pack of fractal images. The material has been put together with reference to the National Council for Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Where appropriate, the activities can be used in conjunction with a graphics calculator.

by "Nielsen BookData"

Details

• NCID: BA12901264
• ISBN:
  • 038797346X
  • 354097346X
  • 0387975543
  • 3540975543
  • 0387984208
• LCCN: 91011998
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York ; Tokyo
• Pages/Volumes: 3 v.
• Size: 28 cm
• Classification:
  • LCC : QA614.86
  • DC20 : 514/.74
• Subject Headings:
  • LCSH : Fractals