Fractals for the Classroom: Strategic Activities Volume OneSpringer New York, 1991 - 129 páginas 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. |
Términos y frases comunes
algebraic algorithm attractor binary numbers binary subdivision box dimension Cantor set cell chaos game coloring complete complex number composition of functions compression connected copies corresponding critical point curve decimal diagonal digits disconnected Disp equation error escape to infinity figure fixed point fractal image function f(x geometric genetic code given Goto graphical iteration graphing calculator grid Implicit Discoveries initial point input intersection point invariant interval iteration behavior iteration path iteration pattern iterative process Julia sets kneading linear long term behavior Mandelbrot set mapping mathematics parabola Pascal's triangle periodic points pixels plot preimages prisoner set quadratic function question repeating repeller rotation saw-tooth function segment self-similarity sequence of iterates shaded shown Sierpinski triangle sin² slope Specific Directions spiral square Stage 1 Stage stage-3 staircase steps of graphical stretch-and-cut-and-paste stretch-and-fold subinterval subtriangles tent function tree unit interval vertical visual x-axis хо