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

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 problemssome three dozen in allthat 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 classand anyone who enjoys popular math books. Mrs. Perkins's Electric Quilt and Other Intriguing Stories of Mathematical Physics Title page For the Reader Preface 1 Three Examples of the Mutual Embrace 1.1 Unphysical Laws 1.2 When Math Goes Wrong 1.3 Math from Physics 2 Measuring Gravity 2.1 First, a Little Theory 2.2 Out in the Author’s Garage 3 Feynman’s Infinite Circuit 3.1 An Infinity of Resistors 3.2 An Infinity of Reactances, and Recursion 3.3 Convergence—or Not? 3.4 Three More Infinite, All-Resistor Networks 4 Air Drag—A Mathematical View 4.1 Air Drag Treated Broadly 4.2 Air Drag Treated with Some Detail 5 Air Drag—A Physical View 5.1 The Quadratic Force Law 5.2 Long Falls through a Real Atmosphere 6 Really Long Falls 6.1 Falling into the Sun 6.2 Falling from Heaven to Hell 7 The Zeta Function—and Physics 7.1 A Curious Double Integral 7.2 Fourier Series and the Zeta Function 7.3 The Zeta Function in Physics 8 Ballistics—With No Air Drag (Yet) 8.1 Shooting a Cannon in a Vacuum 8.2 What Makes a Champion Shot-Putter? 8.3 Another Cannon Question 9 Ballistics—With Air Drag 9.1 Thin Air Cannot Be Ignored! 9.2 Air Drag and Baseball 10 Gravity and Newton 10.1 The Beginnings of Modern Gravity 10.2 Newton’s Superb Theorems 10.3 The Moon Test and Blowing-Up Planets 10.4 A Surprising Gravity Calculation 10.5 Gravitational Contraction 11 Gravity Far Above the Earth 11.1 Kepler’s Laws of Planetary Motion 11.2 Weighing the Planets 12 Gravity Inside the Earth 12.1 Newton’s Experiment 12.2 Gravity Inside the Earth 12.3 Pressure at the Center of the Earth 12.4 Travel Inside the Earth 12.5 Epilogue 13 Quilts & Electricity 13.1 Recreational Mathematics 13.2 Electric Quilts 13.3 Three Impossibility Proofs 14 Random Walks 14.1 Ronald Ross and the Flight of Mosquitoes 14.2 Karl Pearson Formulates a Famous Problem 14.3 Gambler’s Ruin 14.4 The Monte Carlo Method 15 Two More Random Walks 15.1 Brownian Motion 15.2 Shrinking Walks 16 Nearest Neighbors 16.1 Cannibals Can Be Fun! 16.2 Neighbors Beyond the Nearest 16.3 What Happens When We Have Lots of Cannibals 16.4 Serious Physics 17 One Last Random Walk 17.1 Resistor Mathematics 17.2 Electric Walks 17.3 Monte Carlo Circuit Simulation 17.4 Symmetry, Superposition, and Resistor Circuits 18 The Big Noise 18.1 An Interesting Textbook Problem 18.2 The Polar Equations of the Big-Noise Flight 18.3 The Acceleration on a Big-Noise Flight Path SOLUTIONS TO THE CHALLENGE PROBLEMS SPECIAL BONUS DISCUSSION Warning: Do Not Read before Reading Disscussion 17 19 Electricity in the Fourth Dimension 19.1 The Tesseract 19.2 Connecting a Tesseract Resistor Cube Acknowledgments Index

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.

What does quilting have to do with electric circuit theory? This book presents an exploration of some of the many ways that math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself.