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# Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics

Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics available in Hardcover, NOOK Book

- ISBN-10:
- 0691135401
- ISBN-13:
- 9780691135403
- Pub. Date:
- 08/17/2009
- Publisher:
- Princeton University Press

## Overview

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.

## Product Details

ISBN-13: | 9780691135403 |
---|---|

Publisher: | Princeton University Press |

Publication date: | 08/17/2009 |

Pages: | 424 |

Sales rank: | 590,610 |

Product dimensions: | 6.40(w) x 9.30(h) x 1.40(d) |

## Read an Excerpt

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.

## First Chapter

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

For the Reader xi

Preface xiii

Chapter 1: Three Examples of the Mutual Embrace 1

1.1 Unphysical Laws 1

1.2 When Math Goes Wrong 6

1.3 Math from Physics 13

Chapter 2: Measuring Gravity 18

2.1 First, a Little Theory 18

2.2 Out in the Author's Garage 21

Chapter 3: Feynman's Infinite Circuit 24

3.1 An Infinity of Resistors 24

3.2 An Infinity of Reactances, and

Recursion 27

3.3 Convergence—or Not? 32

3.4 Three More Infinite, All-Resistor

Networks 36

Chapter 4: Air Drag—A Mathematical View 44

4.1 Air Drag Treated Broadly 44

4.2 Air Drag Treated with Some Detail 51

Chapter 5: Air Drag—A Physical View 62

5.1 The Quadratic Force Law 62

5.2 Long Falls through a Real Atmosphere 70

Chapter 6: Really Long Falls 82

6.1 Falling into the Sun 82

6.2 Falling from Heaven to Hell 86

Chapter 7: The Zeta Function—and Physics 94

7.1 A Curious Double Integral 94

7.2 Fourier Series and the Zeta Function 95

7.3 The Zeta Function in Physics 100

Chapter 8: Ballistics—With No Air Drag (Yet) 107

8.1 Shooting a Cannon in a Vacuum 107

8.2 What Makes a Champion Shot-Putter? 112

8.3 Another Cannon Question 116

Chapter 9: Ballistics—With Air Drag 120

9.1 Thin Air Cannot Be Ignored! 120

9.2 Air Drag and Baseball 126

Chapter 10: Gravity and Newton 136

10.1 The Beginnings of Modern Gravity 136

10.2 Newton's Superb Theorems 140

10.3 The Moon Test and Blowing-Up Planets 148

10.4 A Surprising Gravity Calculation 152

10.5 Gravitational Contraction 157

Chapter 11: Gravity Far Above the Earth 170

11.1 Kepler's Laws of Planetary Motion 170

11.2 Weighing the Planets 175

Chapter 12: Gravity Inside the Earth 186

12.1 Newton's Experiment 186

12.2 Gravity Inside the Earth 191

12.3 Pressure at the Center of the Earth 200

12.4 Travel Inside the Earth 203

12.5 Epilogue 209

Chapter 13: Quilts & Electricity 215

13.1 Recreational Mathematics 215

13.2 Electric Quilts 220

13.3 Three Impossibility Proofs 225

Chapter 14: Random Walks 233

14.1 Ronald Ross and the Flight of Mosquitoes 233

14.2 Karl Pearson Formulates a Famous Problem 236

14.3 Gambler's Ruin 241

14.4 The Monte Carlo Method 245

Chapter 15: Two More Random Walks 261

15.1 Brownian Motion 261

15.2 Shrinking Walks 269

Chapter 16: Nearest Neighbors 285

16.1 Cannibals Can Be Fun! 285

16.2 Neighbors Beyond the Nearest 291

16.3 What Happens When We Have Lots of Cannibals 294

16.4 Serious Physics 296

Chapter 17: One Last Random Walk 299

17.1 Resistor Mathematics 299

17.2 Electric Walks 301

17.3 Monte Carlo Circuit Simulation 305

17.4 Symmetry, Superposition, and Resistor Circuits 313

Chapter 18: The Big Noise 321

18.1 An Interesting Textbook Problem 321

18.2 The Polar Equations of the Big-Noise Flight 322

18.3 The Acceleration on a Big-Noise Flight Path 328

SOLUTIONS TO THE CHALLENGE PROBLEMS 333

SPECIAL BONUS DISCUSSION 371

Warning: Do Not Read before Reading Disscussion 17 373

Chapter 19: Electricity in the Fourth Dimension 373

19.1 The Tesseract 373

19.2 Connecting a Tesseract Resistor Cube 376

Acknowledgments 385

Index 387

## What People are Saying About This

**Desmond Higham**

This is an excellent piece of work, well up to Nahin's very high standards. It contains a wealth of interesting examples, simple but clever ideas, and surprising conclusions. The book demonstrates why basic calculus is fascinating, beautiful, and relevant to the world around us--and why it is infinitely more accurate and powerful than intuition when it comes to explaining nature. Another fine addition to the Nahin canon.

— *Desmond Higham, University of Strathclyde*

**Ford**

If you like mathematics, you will love this book. If you like physics, you will love it even more. A treasure trove for students of any age, and a marvelous resource for teachers.

— *Kenneth W. Ford, author of "The Quantum World: Quantum Physics for Everyone"*

**Lawrence Weinstein**

I greatly enjoyed this delightful book, which nicely mixes elegant mathematics, intriguing physics, interesting history and personalities, and useful numerical simulation. The book applies these in order to examine a wide range of fascinating and fun phenomena, from trajectory motion to electrical networks to random walks, in new and different ways.

— *Lawrence Weinstein, coauthor of "Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin"*

## Reading Group Guide

For the Reader xi

Preface xiii

Chapter 1: Three Examples of the Mutual Embrace 1

1.1 Unphysical Laws 1

1.2 When Math Goes Wrong 6

1.3 Math from Physics 13

Chapter 2: Measuring Gravity 18

2.1 First, a Little Theory 18

2.2 Out in the Author's Garage 21

Chapter 3: Feynman's Infinite Circuit 24

3.1 An Infinity of Resistors 24

3.2 An Infinity of Reactances, and

Recursion 27

3.3 Convergence—or Not? 32

3.4 Three More Infinite, All-Resistor

Networks 36

Chapter 4: Air Drag—A Mathematical View 44

4.1 Air Drag Treated Broadly 44

4.2 Air Drag Treated with Some Detail 51

Chapter 5: Air Drag—A Physical View 62

5.1 The Quadratic Force Law 62

5.2 Long Falls through a Real Atmosphere 70

Chapter 6: Really Long Falls 82

6.1 Falling into the Sun 82

6.2 Falling from Heaven to Hell 86

Chapter 7: The Zeta Function—and Physics 94

7.1 A Curious Double Integral 94

7.2 Fourier Series and the Zeta Function 95

7.3 The Zeta Function in Physics 100

Chapter 8: Ballistics—With No Air Drag (Yet) 107

8.1 Shooting a Cannon in a Vacuum 107

8.2 What Makes a Champion Shot-Putter? 112

8.3 Another Cannon Question 116

Chapter 9: Ballistics—With Air Drag 120

9.1 Thin Air Cannot Be Ignored! 120

9.2 Air Drag and Baseball 126

Chapter 10: Gravity and Newton 136

10.1 The Beginnings of Modern Gravity 136

10.2 Newton's Superb Theorems 140

10.3 The Moon Test and Blowing-Up Planets 148

10.4 A Surprising Gravity Calculation 152

10.5 Gravitational Contraction 157

Chapter 11: Gravity Far Above the Earth 170

11.1 Kepler's Laws of Planetary Motion 170

11.2 Weighing the Planets 175

Chapter 12: Gravity Inside the Earth 186

12.1 Newton's Experiment 186

12.2 Gravity Inside the Earth 191

12.3 Pressure at the Center of the Earth 200

12.4 Travel Inside the Earth 203

12.5 Epilogue 209

Chapter 13: Quilts & Electricity 215

13.1 Recreational Mathematics 215

13.2 Electric Quilts 220

13.3 Three Impossibility Proofs 225

Chapter 14: Random Walks 233

14.1 Ronald Ross and the Flight of Mosquitoes 233

14.2 Karl Pearson Formulates a Famous Problem 236

14.3 Gambler's Ruin 241

14.4 The Monte Carlo Method 245

Chapter 15: Two More Random Walks 261

15.1 Brownian Motion 261

15.2 Shrinking Walks 269

Chapter 16: Nearest Neighbors 285

16.1 Cannibals Can Be Fun! 285

16.2 Neighbors Beyond the Nearest 291

16.3 What Happens When We Have Lots of Cannibals 294

16.4 Serious Physics 296

Chapter 17: One Last Random Walk 299

17.1 Resistor Mathematics 299

17.2 Electric Walks 301

17.3 Monte Carlo Circuit Simulation 305

17.4 Symmetry, Superposition, and Resistor Circuits 313

Chapter 18: The Big Noise 321

18.1 An Interesting Textbook Problem 321

18.2 The Polar Equations of the Big-Noise Flight 322

18.3 The Acceleration on a Big-Noise Flight Path 328

SOLUTIONS TO THE CHALLENGE PROBLEMS 333

SPECIAL BONUS DISCUSSION 371

Warning: Do Not Read before Reading Disscussion 17 373

Chapter 19: Electricity in the Fourth Dimension 373

19.1 The Tesseract 373

19.2 Connecting a Tesseract Resistor Cube 376

Acknowledgments 385

Index 387

## Interviews

For the Reader xi

Preface xiii

Chapter 1: Three Examples of the Mutual Embrace 1

1.1 Unphysical Laws 1

1.2 When Math Goes Wrong 6

1.3 Math from Physics 13

Chapter 2: Measuring Gravity 18

2.1 First, a Little Theory 18

2.2 Out in the Author's Garage 21

Chapter 3: Feynman's Infinite Circuit 24

3.1 An Infinity of Resistors 24

3.2 An Infinity of Reactances, and

Recursion 27

3.3 Convergence—or Not? 32

3.4 Three More Infinite, All-Resistor

Networks 36

Chapter 4: Air Drag—A Mathematical View 44

4.1 Air Drag Treated Broadly 44

4.2 Air Drag Treated with Some Detail 51

Chapter 5: Air Drag—A Physical View 62

5.1 The Quadratic Force Law 62

5.2 Long Falls through a Real Atmosphere 70

Chapter 6: Really Long Falls 82

6.1 Falling into the Sun 82

6.2 Falling from Heaven to Hell 86

Chapter 7: The Zeta Function—and Physics 94

7.1 A Curious Double Integral 94

7.2 Fourier Series and the Zeta Function 95

7.3 The Zeta Function in Physics 100

Chapter 8: Ballistics—With No Air Drag (Yet) 107

8.1 Shooting a Cannon in a Vacuum 107

8.2 What Makes a Champion Shot-Putter? 112

8.3 Another Cannon Question 116

Chapter 9: Ballistics—With Air Drag 120

9.1 Thin Air Cannot Be Ignored! 120

9.2 Air Drag and Baseball 126

Chapter 10: Gravity and Newton 136

10.1 The Beginnings of Modern Gravity 136

10.2 Newton's Superb Theorems 140

10.3 The Moon Test and Blowing-Up Planets 148

10.4 A Surprising Gravity Calculation 152

10.5 Gravitational Contraction 157

Chapter 11: Gravity Far Above the Earth 170

11.1 Kepler's Laws of Planetary Motion 170

11.2 Weighing the Planets 175

Chapter 12: Gravity Inside the Earth 186

12.1 Newton's Experiment 186

12.2 Gravity Inside the Earth 191

12.3 Pressure at the Center of the Earth 200

12.4 Travel Inside the Earth 203

12.5 Epilogue 209

Chapter 13: Quilts & Electricity 215

13.1 Recreational Mathematics 215

13.2 Electric Quilts 220

13.3 Three Impossibility Proofs 225

Chapter 14: Random Walks 233

14.1 Ronald Ross and the Flight of Mosquitoes 233

14.2 Karl Pearson Formulates a Famous Problem 236

14.3 Gambler's Ruin 241

14.4 The Monte Carlo Method 245

Chapter 15: Two More Random Walks 261

15.1 Brownian Motion 261

15.2 Shrinking Walks 269

Chapter 16: Nearest Neighbors 285

16.1 Cannibals Can Be Fun! 285

16.2 Neighbors Beyond the Nearest 291

16.3 What Happens When We Have Lots of Cannibals 294

16.4 Serious Physics 296

Chapter 17: One Last Random Walk 299

17.1 Resistor Mathematics 299

17.2 Electric Walks 301

17.3 Monte Carlo Circuit Simulation 305

17.4 Symmetry, Superposition, and Resistor Circuits 313

Chapter 18: The Big Noise 321

18.1 An Interesting Textbook Problem 321

18.2 The Polar Equations of the Big-Noise Flight 322

18.3 The Acceleration on a Big-Noise Flight Path 328

SOLUTIONS TO THE CHALLENGE PROBLEMS 333

SPECIAL BONUS DISCUSSION 371

Warning: Do Not Read before Reading Disscussion 17 373

Chapter 19: Electricity in the Fourth Dimension 373

19.1 The Tesseract 373

19.2 Connecting a Tesseract Resistor Cube 376

Acknowledgments 385

Index 387

## Recipe

For the Reader xi

Preface xiii

1.1 Unphysical Laws 1

1.2 When Math Goes Wrong 6

1.3 Math from Physics 13

Chapter 2: Measuring Gravity 18

2.1 First, a Little Theory 18

2.2 Out in the Author's Garage 21

3.1 An Infinity of Resistors 24

3.2 An Infinity of Reactances, and

Recursion 27

3.3 Convergence—or Not? 32

3.4 Three More Infinite, All-Resistor

Networks 36

4.1 Air Drag Treated Broadly 44

4.2 Air Drag Treated with Some Detail 51

5.1 The Quadratic Force Law 62

5.2 Long Falls through a Real Atmosphere 70

Chapter 6: Really Long Falls 82

6.1 Falling into the Sun 82

6.2 Falling from Heaven to Hell 86

7.1 A Curious Double Integral 94

7.2 Fourier Series and the Zeta Function 95

7.3 The Zeta Function in Physics 100

8.1 Shooting a Cannon in a Vacuum 107

8.2 What Makes a Champion Shot-Putter? 112

8.3 Another Cannon Question 116

9.1 Thin Air Cannot Be Ignored! 120

9.2 Air Drag and Baseball 126

10.1 The Beginnings of Modern Gravity 136

10.2 Newton's Superb Theorems 140

10.3 The Moon Test and Blowing-Up Planets 148

10.4 A Surprising Gravity Calculation 152

10.5 Gravitational Contraction 157

11.1 Kepler's Laws of Planetary Motion 170

11.2 Weighing the Planets 175

12.1 Newton's Experiment 186

12.2 Gravity Inside the Earth 191

12.3 Pressure at the Center of the Earth 200

12.4 Travel Inside the Earth 203

12.5 Epilogue 209

13.1 Recreational Mathematics 215

13.2 Electric Quilts 220

13.3 Three Impossibility Proofs 225

14.1 Ronald Ross and the Flight of Mosquitoes 233

14.2 Karl Pearson Formulates a Famous Problem 236

14.3 Gambler's Ruin 241

14.4 The Monte Carlo Method 245

Chapter 15: Two More Random Walks 261

15.1 Brownian Motion 261

15.2 Shrinking Walks 269

16.1 Cannibals Can Be Fun! 285

16.2 Neighbors Beyond the Nearest 291

16.3 What Happens When We Have Lots of Cannibals 294

16.4 Serious Physics 296

17.1 Resistor Mathematics 299

17.2 Electric Walks 301

17.3 Monte Carlo Circuit Simulation 305

17.4 Symmetry, Superposition, and Resistor Circuits 313

18.1 An Interesting Textbook Problem 321

18.2 The Polar Equations of the Big-Noise Flight 322

18.3 The Acceleration on a Big-Noise Flight Path 328

SPECIAL BONUS DISCUSSION 371

Warning: Do Not Read before Reading Disscussion 17 373

19.1 The Tesseract 373

19.2 Connecting a Tesseract Resistor Cube 376

Acknowledgments 385

Index 387