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Mrs. Perkins's Electric Quilt

Book Description

What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself.

In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end.

Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. For the Reader
  7. Preface
  8. Chapter 1 - Three Examples of the Mutual Embrace
    1. 1.1 Unphysical Laws
    2. 1.2 When Math Goes Wrong
  9. Chapter 2 - Measuring Gravity
    1. 2.1 First, a Little Theory
    2. 2.2 Out in the Author’s Garage
  10. Chapter 3 - Feynman’s Infinite Circuit
    1. 3.1 An Infinity of Resistors
    2. 3.2 An Infinity of Reactances, and Recursion
    3. 3.3 Convergence—or Not?
    4. 3.4 Three More Infinite, All-Resistor Networks
  11. Chapter 4 - Air Drag—A Mathematical View
    1. 4.1 Air Drag Treated Broadly
    2. 4.2 Air Drag Treated with Some Detail
  12. Chapter 5 - Air Drag—A Physical View
    1. 5.1 The Quadratic Force Law
    2. 5.2 Long Falls through a Real Atmosphere
  13. Chapter 6 - Really Long Falls
    1. 6.1 Falling into the Sun
    2. 6.2 Falling from Heaven to Hell
  14. Chapter 7 - The Zeta Function—and Physics
    1. 7.1 A Curious Double Integral
    2. 7.2 Fourier Series and the Zeta Function
    3. 7.3 The Zeta Function in Physics
  15. Chapter 8 - Ballistics — With No Air Drag (Yet)
    1. 8.1 Shooting a Cannon in a Vacuum
    2. 8.2 What Makes a Champion Shot-Putter?
    3. 8.3 Another Cannon Question
  16. Chapter 9 - Ballistics—With Air Drag
    1. 9.1 Thin Air Cannot Be Ignored!
    2. 9.2 Air Drag and Baseball
  17. Chapter 10 - Gravity and Newton
    1. 10.1 The Beginnings of Modern Gravity
    2. 10.2 Newton’s Superb Theorems
    3. 10.3 The Moon Test and Blowing-Up Planets
    4. 10.4 A Surprising Gravity Calculation
    5. 10.5 Gravitational Contraction
  18. Chapter 11 - Gravity Far Above the Earth
    1. 11.1 Kepler’s Laws of Planetary Motion
    2. 11.2 Weighing the Planets
  19. Chapter 12 - Gravity Inside the Earth
    1. 12.1 Newton’s Experiment
    2. 12.2 Gravity Inside the Earth
    3. 12.3 Pressure at the Center of the Earth
    4. 12.4 Travel Inside the Earth
    5. 12.5 Epilogue
  20. Chapter 13 - Quilts & Electricity
    1. 13.1 Recreational Mathematics
    2. 13.2 Electric Quilts
    3. 13.3 Three Impossibility Proofs
  21. Chapter 14 - Random Walks
    1. 14.1 Ronald Ross and the Flight of Mosquitoes
    2. 14.2 Karl Pearson Formulates a Famous Problem
    3. 14.3 Gambler’s Ruin
    4. 14.4 The Monte Carlo Method
  22. Chapter 15 - Two More Random Walks
    1. 15.1 Brownian Motion
    2. 15.2 Shrinking Walks
  23. Chapter 16 - Nearest Neighbors
    1. 16.1 Cannibals Can Be Fun!
    2. 16.2 Neighbors Beyond the Nearest
    3. 16.3 What Happens When We Have Lots of Cannibals
    4. 16.4 Serious Physics
  24. Chapter 17 - One Last Random Walk
    1. 17.1 Resistor Mathematics
    2. 17.2 Electric Walks
    3. 17.3 Monte Carlo Circuit Simulation
    4. 17.4 Symmetry, Superposition, and Resistor Circuits
  25. Chapter 18 - The Big Noise
    1. 18.1 An Interesting Textbook Problem
    2. 18.2 The Polar Equations of the Big-Noise Flight
    3. 18.3 The Acceleration on a Big-Noise Flight Path
  26. Chapter 19 - Electricity in the Fourth Dimension
    1. 19.1 The Tesseract
    2. 19.2 Connecting a Tesseract Resistor Cube
  27. Acknowledgments
  28. Index
  29. Also by Paul J. Nahin