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.
|Publisher:||Princeton University Press|
|Product dimensions:||6.40(w) x 9.30(h) x 1.40(d)|
|Age Range:||18 Years|
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 xiPreface xiii
Chapter 1: Three Examples of the Mutual Embrace 11.1 Unphysical Laws 11.2 When Math Goes Wrong 61.3 Math from Physics 13
Chapter 2: Measuring Gravity 182.1 First, a Little Theory 182.2 Out in the Author's Garage 21
Chapter 3: Feynman's Infinite Circuit 243.1 An Infinity of Resistors 243.2 An Infinity of Reactances, andRecursion 273.3 Convergenceor Not? 323.4 Three More Infinite, All-ResistorNetworks 36
Chapter 4: Air DragA Mathematical View 444.1 Air Drag Treated Broadly 444.2 Air Drag Treated with Some Detail 51
Chapter 5: Air DragA Physical View 625.1 The Quadratic Force Law 625.2 Long Falls through a Real Atmosphere 70
Chapter 6: Really Long Falls 826.1 Falling into the Sun 826.2 Falling from Heaven to Hell 86
Chapter 7: The Zeta Functionand Physics 947.1 A Curious Double Integral 947.2 Fourier Series and the Zeta Function 957.3 The Zeta Function in Physics 100
Chapter 8: BallisticsWith 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 116
Chapter 9: BallisticsWith Air Drag 1209.1 Thin Air Cannot Be Ignored! 1209.2 Air Drag and Baseball 126
Chapter 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 157
Chapter 11: Gravity Far Above the Earth 17011.1 Kepler's Laws of Planetary Motion 17011.2 Weighing the Planets 175
Chapter 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 209
Chapter 13: Quilts & Electricity 21513.1 Recreational Mathematics 21513.2 Electric Quilts 22013.3 Three Impossibility Proofs 225
Chapter 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 245
Chapter 15: Two More Random Walks 26115.1 Brownian Motion 26115.2 Shrinking Walks 269
Chapter 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 296
Chapter 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 313
Chapter 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 328
SOLUTIONS TO THE CHALLENGE PROBLEMS 333SPECIAL BONUS DISCUSSION 371Warning: Do Not Read before Reading Disscussion 17 373
Chapter 19: Electricity in the Fourth Dimension 37319.1 The Tesseract 37319.2 Connecting a Tesseract Resistor Cube 376
Acknowledgments 385Index 387
What People are Saying About This
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
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
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"