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

by Paul Nahin

Overview

An incomparable collection of stimulating math puzzles from bestselling author Paul Nahin

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:	9781400833467
Publisher:	Princeton University Press
Publication date:	08/17/2009
Sold by:	Barnes & Noble
Format:	eBook
Pages:	424
File size:	9 MB

About the Author

Paul J. Nahin is the author of many best-selling popular math books, including Digital Dice, Chases and Escapes, Dr. Euler's Fabulous Formula, When Least is Best, Duelling Idiots and Other Probability Puzzlers, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

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"

From the Publisher

"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

"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

"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

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"

Editorial Reviews

"Mrs. Perkins's Electric Quilt is a great book for anyone interested in the connections between mathematics and physics. Along the way, Nahin, author of many popular math books, shares many historical anecdotes about the problems and the people who studied them. . . . A teacher of general physics or introductory calculus will find many interesting discussions that can be included in an introductory course."

Choice

"Overall, this book is a really fun read. The combination of mathematics applied to real physics problems and the historical fabric within which they are woven proved a winner for me. I could write more about this volume, but I think I'll quit here—I want to get to work on some of the challenge problems."—-Barry R. Holstein, American Journal of Physics

"This book shows mathematics and physics at their very best, united to explore fascinating phenomena with astonishing results."—-Linda Kallam, Mathematics Teacher

From the Publisher

This book shows mathematics and physics at their very best, united to explore fascinating phenomena with astonishing results.

Mathematics Teacher - Linda Kallam

Overall, this book is a really fun read. The combination of mathematics applied to real physics problems and the historical fabric within which they are woven proved a winner for me. I could write more about this volume, but I think I'll quit here—I want to get to work on some of the challenge problems.

American Journal of Physics - Barry R. Holstein

This book shows mathematics and physics at their very best, united to explore fascinating phenomena with astonishing results.
— Linda Kallam

Mathematics Teacher

Overall, this book is a really fun read. The combination of mathematics applied to real physics problems and the historical fabric within which they are woven proved a winner for me. I could write more about this volume, but I think I'll quit here—I want to get to work on some of the challenge problems.
— Barry R. Holstein

American Journal of Physics