## Mathematica in Action"Mathematica in Action, 2nd Edition," is designed both as a guide to the extraordinary capabilities of Mathematica as well as a detailed tour of modern mathematics by one of its leading expositors, Stan Wagon. Ideal for teachers, researchers, mathematica enthusiasts. This second edition of the highly sucessful W.H. Freeman version includes an 8 page full color insert and 50% new material all organized around Elementary Topics, Intermediate Applications, and Advanced Projects. In addition, the book uses Mathematica 3.0 throughtout. Mathematica 3.0 notebooks with all the programs and examples discussed in the book are available on the TELOS web site (www.telospub.com). These notebooks contain materials suitable for DOS, Windows, Macintosh and Unix computers. Stan Wagon is well-known in the mathematics (and Mathematica) community as Associate Editor of the "American Mathematical Monthly," a columnist for the "Mathematical Intelligencer" and "Mathematica in Education and Research," author of "The Banach-Tarski Paradox" and "Unsolved Problems in Elementary Geometry and Number Theory (with Victor Klee), as well as winner of the 1987 Lester R. Ford Award for Expository Writing. |

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### Contents

A Brief Introduction | 1 |

Basic Concepts | 19 |

Plotting | 21 |

Prime Numbers | 47 |

Rolling Circles | 75 |

Surfaces | 103 |

Graphics Issues and Applications | 127 |

The Cantor Set Real and Complex | 129 |

Number Theory | 313 |

PublicKey Encryption | 315 |

Egyptian Fractions | 321 |

The Ancient and Modern Euclidean Algorithm | 331 |

Imaginary Primes and Prime Imaginaries | 361 |

Certifying Primality | 385 |

Check Digits and the Pentagon | 409 |

Advanced Projects | 417 |

The Quadratic Map | 139 |

The Recursive Turtle | 167 |

Parametric Plotting of Surfaces | 187 |

Penrose Tiles | 215 |

Fractals Ferns and Julia Sets | 225 |

Numerical Mathematics | 254 |

Custom Curves | 255 |

Solving Equations | 277 |

Differential Equations | 293 |

New Directions for 𝛑 | 419 |

Rearrangement of Series | 445 |

Eschers Patterns | 455 |

Computational Geometry | 485 |

Coloring Planar Maps and Graphs | 507 |

The Riemann Zeta Function | 539 |

The BanachTarski Paradox | 555 |

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### Common terms and phrases

approximations argument AspectRatio Automatic Axes Bezier curve bifurcation Cantor set chapter circle code that follows color plate complex numbers computation congruent continued fraction contour plot convergence cycloid default define digits discussed DisplayFunction divisors Epilog Escher's Euclidean algorithm example EXERCISE fact False Fibonacci Figure fixed point formula four-color fraction Frame FrameTicks function Gaussian integers Gaussian primes graph Graphics GrayLevel Identity input interpolating iterations Julia set Kempe chain linear look Mathematica Mathematical matrix method Module motif NestList option opts orbit output package pairs parameter ParametricPlot pattern Perrin pseudoprimes planar planar graph plane PlotPoints PlotRange polygon polynomial Pratt certificate prime number PrimeQ problem proof pseudoprime quadratic map quotients random Range recursive result Riemann hypothesis root rotation routine sequence shows signature simple solution Solve space-filling curve square starting value surface theorem True variable vertex vertices wheel yields zeros