Mrs. Perkins's Electric Quilt

For the Reader xiPreface xiiiChapter 1: Three Examples of the Mutual Embrace 11.1 Unphysical Laws 11.2 When Math Goes Wrong 61.3 Math from Physics 13Chapter 2: Measuring Gravity 182.1 First, a Little Theory 182.2 Out in the Author's Garage 21Chapter 3: Feynman's Infinite Circuit 243.1 An Infinity of Resistors 243.2 An Infinity of Reactances, andRecursion 273.3 Convergence--or Not? 323.4 Three More Infinite, All-ResistorNetworks 36Chapter 4: Air Drag--A Mathematical View 444.1 Air Drag Treated Broadly 444.2 Air Drag Treated with Some Detail 51Chapter 5: Air Drag--A Physical View 625.1 The Quadratic Force Law 625.2 Long Falls through a Real Atmosphere 70Chapter 6: Really Long Falls 826.1 Falling into the Sun 826.2 Falling from Heaven to Hell 86Chapter 7: The Zeta Function--and Physics 947.1 A Curious Double Integral 947.2 Fourier Series and the Zeta Function 957.3 The Zeta Function in Physics 100Chapter 8: Ballistics--With No Air Drag (Yet) 1078.1 Shooting a Cannon in a Vacuum 1078.2 What Makes a Champion Shot-Putter? 1128.3 Another Cannon Question 116Chapter 9: Ballistics--With Air Drag 1209.1 Thin Air Cannot Be Ignored! 1209.2 Air Drag and Baseball 126Chapter 10: Gravity and Newton 13610.1 The Beginnings of Modern Gravity 13610.2 Newton's Superb Theorems 14010.3 The Moon Test and Blowing-Up Planets 14810.4 A Surprising Gravity Calculation 15210.5 Gravitational Contraction 157Chapter 11: Gravity Far Above the Earth 17011.1 Kepler's Laws of Planetary Motion 17011.2 Weighing the Planets 175Chapter 12: Gravity Inside the Earth 18612.1 Newton's Experiment 18612.2 Gravity Inside the Earth 19112.3 Pressure at the Center of the Earth 20012.4 Travel Inside the Earth 20312.5 Epilogue 209Chapter 13: Quilts & Electricity 21513.1 Recreational Mathematics 21513.2 Electric Quilts 22013.3 Three Impossibility Proofs 225Chapter 14: Random Walks 23314.1 Ronald Ross and the Flight of Mosquitoes 23314.2 Karl Pearson Formulates a Famous Problem 23614.3 Gambler's Ruin 24114.4 The Monte Carlo Method 245Chapter 15: Two More Random Walks 26115.1 Brownian Motion 26115.2 Shrinking Walks 269Chapter 16: Nearest Neighbors 28516.1 Cannibals Can Be Fun! 28516.2 Neighbors Beyond the Nearest 29116.3 What Happens When We Have Lotsof Cannibals 29416.4 Serious Physics 296Chapter 17: One Last Random Walk 29917.1 Resistor Mathematics 29917.2 Electric Walks 30117.3 Monte Carlo Circuit Simulation 30517.4 Symmetry, Superposition, and Resistor Circuits 313Chapter 18: The Big Noise 32118.1 An Interesting Textbook Problem 32118.2 The Polar Equations of the Big-Noise Flight 32218.3 The Acceleration on a Big-Noise Flight Path 328SOLUTIONS TO THE CHALLENGE PROBLEMS 333SPECIAL BONUS DISCUSSION 371Warning: Do Not Read before Reading Disscussion 17 373Chapter 19: Electricity in the Fourth Dimension 37319.1 The Tesseract 37319.2 Connecting a Tesseract Resistor Cube 376Acknowledgments 385Index 387