Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics
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...
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"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 Choice 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.
For the Reader xi Preface xiiiChapter 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 13Chapter 2: Measuring Gravity 18 2.1 First, a Little Theory 18 2.2 Out in the Author's Garage 21Chapter 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 36Chapter 4: Air Drag--A Mathematical View 44 4.1 Air Drag Treated Broadly 44 4.2 Air Drag Treated with Some Detail 51Chapter 5: Air Drag--A Physical View 62 5.1 The Quadratic Force Law 62 5.2 Long Falls through a Real Atmosphere 70Chapter 6: Really Long Falls 82 6.1 Falling into the Sun 82 6.2 Falling from Heaven to Hell 86Chapter 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 100Chapter 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 116Chapter 9: Ballistics--With Air Drag 120 9.1 Thin Air Cannot Be Ignored! 120 9.2 Air Drag and Baseball 126Chapter 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 157Chapter 11: Gravity Far Above the Earth 170 11.1 Kepler's Laws of Planetary Motion 170 11.2 Weighing the Planets 175Chapter 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 209Chapter 13: Quilts & Electricity 215 13.1 Recreational Mathematics 215 13.2 Electric Quilts 220 13.3 Three Impossibility Proofs 225Chapter 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 245Chapter 15: Two More Random Walks 261 15.1 Brownian Motion 261 15.2 Shrinking Walks 269Chapter 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 296Chapter 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 313Chapter 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 328SOLUTIONS TO THE CHALLENGE PROBLEMS 333 SPECIAL BONUS DISCUSSION 371 Warning: Do Not Read before Reading Disscussion 17 373Chapter 19: Electricity in the Fourth Dimension 373 19.1 The Tesseract 373 19.2 Connecting a Tesseract Resistor Cube 376Acknowledgments 385 Index 387
\ American Journal of PhysicsOverall, 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\ \ \ \ \ Mathematics TeacherThis book shows mathematics and physics at their very best, united to explore fascinating phenomena with astonishing results.\ — Linda Kallam\ \ \ American Journal of Physics\ - Barry R. Holstein\ 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.\ \ \ \ \ Mathematics Teacher\ - Linda Kallam\ This book shows mathematics and physics at their very best, united to explore fascinating phenomena with astonishing results.\ \ \ \ \ ChoiceMrs. 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.\ \ \ \ \ ChoiceMrs. 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.\ \
