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＜電子ブック＞
Fractals for the Classroom: Strategic Activities Volume One / by Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, Evan Maletsky, Terry Perciante, Lee Yunker

版	1st ed. 1991.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1991
本文言語	英語
大きさ	XII, 129 p. 37 illus : online resource
冊子体	Fractals for the classroom : strategic activities / Heinz-Otto Peitgen ... [et al.] ; v. 1 : us - v. 3 : us
著者標目	*Peitgen, Heinz-Otto author Jürgens, Hartmut author Saupe, Dietmar author Maletsky, Evan author Perciante, Terry author Yunker, Lee author SpringerLink (Online service)
件　名	LCSH:Topology FREE:Topology
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4613-9047-3

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