Fractals for the Classroom: Strategic Activities Volume One
Springer Science & Business Media, Dec 6, 2012 - 129 pages
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.
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Activity Sheets algorithm area at stage box dimension branches Cantor set Cellular automata chaos game coloring look-up table completed tree CONNECTIONS construction process corresponding Count the number e e e e e e e e e e e e e e e e º e o e endpoints exponential function fractal dimension fractal shape fully grown geometric sequence graphing calculator Implicit Discoveries iterative process Koch curve Koch snowflake large without bound line segment linear graph mathematics midpoints move halfway number of pixels number of rolls number of shaded number of triangles number patterns º e e º e e e º e º º e o e º Pascal's triangle pixels lit power function power relationship Sierpinski tetrahedron Sierpinski triangle slope Specific Directions Stage 1 Stage stage-2 triangle standard graph paper straight line strictly self-similar string subsquares subtriangles variables vertical visual