Fractals for the Classroom: Strategic Activities Volume TwoSpringer Science & Business Media, 2013 M06 29 - 187 páginas 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. |
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Fractals for the Classroom: Strategic Activities Volume Two Heinz-Otto Peitgen,Hartmut Jurgens,Dietmar Saupe Sin vista previa disponible - 2014 |
Términos y frases comunes
absolute error activity algebraic attractor binary numbers binary subdivision Cantor set chaos complex number composition machine composition of functions Compute connected corresponding curve decimal places determine diagonal Disp domain draw equation escape to infinity fails to escape form f(x fractals Function Composition geometric given Goto graphical iteration graphing calculator grid imag Implicit Discoveries initial point initial value xo input intersection point Interval width invariant interval iteration behavior iteration path iteration pattern iteration process Julia sets kneading locate long term behavior Mandelbrot set mathematical number of iterations numerical iteration parabola parabola f(x parameter values periodic points preimages prisoner set quadratic function question relative error repeller saw-tooth function segments sensitivity sequence of iterates shown sin² slope Specific Directions spiral stack staircase steps of graphical stretch-and-cut-and-paste stretch-and-fold successive iterates T-icons tent and saw-tooth tent function TEXAS INSTRUMENTS totally disconnected transformed unit interval visually x-axis x²+c хо