Fractals for the Classroom: Strategic Activities Volume Three (Google eBook)
Springer Science & Business Media, Mar 1, 1999 - Education - 107 pages
This third and final volume of Strategic Activities on fractal geometry and chaos theory focuses upon the images that for many people have provided a compelling lure into an investigation of the intricate properties embedded within them. By themselves the figures posses fascinating features, but the mechanisms by which they are formed also highlight significant approaches to modeling natural processes and phenomena. The general pattern and specific steps used to construct a fractal image illustrated throughout this volume, comprise an iterated function system. The objective of this volume is to investigate the processes and often surprising results of applying such systems. These strategic activities have been developed from a sound instructional base, stressing the connections to the contemporary curriculum as recommended in the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics. Where appropriate, the activities take advantage of the technological power of the graphics calculator. The contents of this volume joined with the details contained in the prior two books. Together they provide a comprehensive survey of fractal geometry and chaos theory. The dynamic nature of the research and the experimental characteristics of related applications provides an engaging paradigm for classroom activity.
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270 degrees Activities 8.4 affine transformation algebraically algorithm applied ation Off Hori Base Copy Scale binary coordinates CD CD CD chaos game chaos theory combinations conjugate Coords corresponding decimal coordinate diagonal digits eight motions eight possible eight symmetries entries equations family of fractals final image formula fractal image fractals shown Function Composition geometric genetic code Goto Gotol graphing calculator grid Heinz-Otto Hori set Vert horizontal identify image figure image point Implicit Discoveries initial figure iterated function system Kummer's Criterion line symmetry linear lines of symmetry mathematics matrix NESTED ADDRESS Orient original figure Pascal's triangle pixel position ratio reduced copies replica San Juan College Saupe screen self-similarity structure sequence set Vert Base shaded cells Sierpinski Curve Sierpinski triangle Specific Directions square back Stage 1 Stage Strategic Activities symmetry computer symmetry transformations three cells University of Bremen Vert Base Copy vertical whole image whole object
Page x - The mathematics curriculum should include investigation of the connections and interplay among various mathematical topics and their applications so that all students can — use and value the connections among mathematical topics; use and value the connections between mathematics and other disciplines.
Page xiv - ... hopeful and constructive in approach, though taking a clear look at debit sides; and (5) to offer possible solutions for a free citizen's choice. All of us here know that no kind of education or learning is actually an end in itself, but rather should suggest how doors may be opened to a richer life, to a better understanding and appreciation of the world in which we live. All subjects presented on TV should be vital to the viewer, and rewarding in further investigation on his own initiative....