Mathematica® in Action: Problem Solving Through Visualization and Computation

In this third edition of __Mathematica® in Action__, award-winning author Stan Wagon guides beginner and veteran users alike through __Mathematica's__ powerful tools for mathematical exploration. The transition to __Mathematica__ 7 is made smooth with plenty of examples and case studies that utilize __Mathematica's__ newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. __Mathematica in Action__ also emphasizes the breadth of __Mathematica__ and the impressive results of combining techniques from different areas. This material enables the reader to use __Mathematica__ to solve a variety of complex problems. Case studies ranging from elementary to sophisticated are provided throughout. Whenever possible, the book shows how __Mathematica__ can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, an illustration of the Banach—Tarski Paradox via hyperbolic geometry, new and surprising formulas for p, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics. Visualization is emphasized throughout, with finely crafted graphics in each chapter. Wagon is the author of eleven books on mathematics, including __A Course in Computational Number Theory__, named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of __Mathematica__, including the books __VisualDSolve: Visualizing Differential Equations with Mathematica__, and __Animating Calculus: Mathematica Notebooks for the Laboratory__. **From reviews of the second edition:** "In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics." **—Richard Walker, __The Mathematical Gazette__** "The bottom line is that __Mathematica in Action__ is an outstanding book containing many examples of real uses of __Mathematica__ for the novice, intermediate, and expert user." **—Mark McClure, __Mathematica in Education and Research__** In this third edition of Mathematica in Action, award-winning author Stan Wagon guides beginner and veteran users alike through Mathematica's powerful tools for mathematical exploration. The transition to Mathematica 7 is made smooth with plenty of examples and case studies that utilize Mathematica's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Mathematica in Action also emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. This material enables the reader to use Mathematica to solve a variety of complex problems of mathematics. Case studies ranging from elementary to sophisticated are provided throughout. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, an illustration of the Banach-Tarski Paradox via hyperbolic geometry, new and surprising formulas for p, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics. Visualization is emphasized throughout, with finely crafted graphics in each chapter. Wagon is the author of nine books on mathematics, including A Course in Computational Number Theory, named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, including the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From reviews of the second edition: "In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics." --Richard Walker, The Mathematical Gazette "The bottom line is that Mathematica in Action is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user." --Mark McClure, Mathematica in Education and Research iJournal Front Matter....Pages i-xi A Brief Introduction....Pages 1-22 Plotting....Pages 23-52 Prime Numbers....Pages 53-76 Rolling Circles....Pages 77-111 Three-Dimensional Graphs....Pages 113-140 Dynamic Manipulations....Pages 141-167 The Cantor Set, Real and Complex....Pages 169-178 The Quadratic Map....Pages 179-208 The Recursive Turtle....Pages 209-234 Parametric Plotting of Surfaces....Pages 235-265 Penrose Tiles....Pages 267-275 Complex Dynamics:Julia Sets and the Mandelbrot Set....Pages 277-300 Solving Equations....Pages 301-328 Optimization....Pages 329-362 Differential Equations....Pages 363-397 Computational Geometry....Pages 399-422 Check Digits and the Pentagon....Pages 423-429 Coloring Planar Maps....Pages 431-472 New Directions For π....Pages 473-490 The Banach–Tarski Paradox....Pages 491-504 The Riemann Zeta Function....Pages 505-522 Miscellany....Pages 523-556 Back Matter....Pages 557-578 Case studies ranging from elementary to sophisticated are provided throughout. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, an illustration of the Banach-Tarski Paradox via hyperbolic geometry, new and surprising formulas for & pi;, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics. Visualization is emphasized throughout, with finely crafted graphics in each chapter. All Mathematica code is included on a CD, allowing the reader to easily use the code in further experiments or other applications Plenty of examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, and new and surprising formulas for p. Visualization is emphasized throughout, with finely crafted graphics in each chapter.