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9781400833467

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

by
  • ISBN13:

    9781400833467

  • ISBN10:

    1400833469

  • Copyright: 2009-09-06
  • Publisher: Princeton Univ Pr

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Summary

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 Quiltwill 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.

Table of Contents

For the Readerp. xi
Prefacep. xiii
Three Examples of the Mutual Embracep. 1
Unphysical Lawsp. 1
When Math Goes Wrongp. 6
Math from Physicsp. 13
Measuring Gravityp. 18
First, a Little Theoryp. 18
Out in the Author's Garagep. 21
Feynman's Infinite Circuitp. 24
An Infinity of Resistorsp. 24
An Infinity of Reactances, and Recursionp. 27
Convergence--or Not?p. 32
Three More Infinite, All-Resistor Networksp. 36
Air Drag--A Mathematical Viewp. 44
Air Drag Treated Broadlyp. 44
Air Drag Treated with Some Detailp. 51
Air Drag--A Physical Viewp. 62
The Quadratic Force Lawp. 62
Long Falls through a Real Atmospherep. 70
Really Long Fallsp. 82
Falling into the Sunp. 82
Falling from Heaven to Hellp. 86
The Zeta Function--and Physicsp. 94
A Curious Double Integralp. 94
Fourier Series and the Zeta Functionp. 95
The Zeta Function in Physicsp. 100
Ballistics--With No Air Drag (Yet)p. 107
Shooting a Cannon in a Vacuump. 107
What Makes a Champion Shot-Putter?p. 112
Another Cannon Questionp. 116
Ballistics--With Air Dragp. 120
Thin Air Cannot Be Ignored!p. 120
Air Drag and Baseballp. 126
Gravity and Newtonp. 136
The Beginnings of Modern Gravityp. 136
Newton's Superb Theoremsp. 140
The Moon Test and Blowing-Up Planetsp. 148
A Surprising Gravity Calculationp. 152
Gravitational Contractionp. 157
Gravity Far Above the Earthp. 170
Kepler's Laws of Planetary Motionp. 170
Weighing the Planetsp. 175
Gravity Inside the Earthp. 186
Newton's Experimentp. 186
Gravity Inside the Earthp. 191
Pressure at the Center of the Earthp. 200
Travel Inside the Earthp. 203
Epiloguep. 209
Quilts & Electricityp. 215
Recreational Mathematicsp. 215
Electric Quiltsp. 220
Three Impossibility Proofsp. 225
Random Walksp. 233
Ronald Ross and the Flight of Mosquitoesp. 233
Karl Pearson Formulates a Famous Problemp. 236
Gambler's Ruinp. 241
The Monte Carlo Methodp. 245
Two More Random Walksp. 261
Brownian Motionp. 261
Shrinking Walksp. 269
Nearest Neighborsp. 285
Cannibals Can Be Fun!p. 285
Neighbors Beyond the Nearestp. 291
What Happens When We Have Lots of Cannibalsp. 294
Serious Physicsp. 296
One Last Random Walkp. 299
Resistor Mathematicsp. 299
Electric Walksp. 301
Monte Carlo Circuit Simulationp. 305
Symmetry, Superposition, and Resistor Circuitsp. 313
The Big Noisep. 321
An Interesting Textbook Problemp. 321
The Polar Equations of the Big-Noise Flightp. 322
The Acceleration on a Big-Noise Flight Pathp. 328
Solutions To The Challenge Problemsp. 333
Special Bonus Discussionp. 371
Warning: Do Not Read before Reading Disscussion 17p. 373
Electricity in the Fourth Dimensionp. 373
The Tesseractp. 373
Connecting a Tesseract Resistor Cubep. 376
Acknowledgmentsp. 385
Indexp. 387
Table of Contents provided by Publisher. All Rights Reserved.

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