How to Fall Slower Than Gravity: And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning

How to Fall Slower Than Gravity: And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning

by Paul J. Nahin

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Overview

An engaging collection of intriguing problems that shows you how to think like a mathematical physicist

Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar kind of glass called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world.

The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements.

More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

Product Details

ISBN-13: 9780691176918
Publisher: Princeton University Press
Publication date: 11/27/2018
Pages: 320
Sales rank: 1,192,263
Product dimensions: 6.30(w) x 9.40(h) x 1.20(d)

About the Author

Paul J. Nahin is the author of many popular math books, including In Praise of Simple Physics, Dr. Euler’s Fabulous Formula, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire. He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics.

Table of Contents

Preface xiii

Part I The Problems 1

Problem 1 A Military Question: Catapult Warfare 3

Problem 2 A Seemingly Impossible Question: A Shocking Snow Conundrum 4

Problem 3 Two Math Problems: Algebra and Differential Equations Save the Day 6

Problem 4 An Escape Problem: Dodge the Truck 8

Problem 5 The Catapult Again: Where Dead Cows Can't Go! 9

Problem 6 Another Math Problem: This One Requires Calculus 10

Problem 7 If Theory Fails: Monte Carlo Simulation 11

Problem 8 Monte Carlo and Theory: The Drunkard's One-Dimensional Random Walk 17

Problem 9 More Monte Carlo: A Two-Dimensional Random Walk in Paris 19

Problem 10 Flying with (and against) the Wind: Math for the Modern Traveler 21

Problem 11 A Combinatorial Problem with Physics Implications: Particles. Energy Levels, and Pauli Exclusion 22

Problem 12 Mathematical Analysis: By Physical Reasoning 29

Problem 13 When an Integral Blows Up: Can a Physical Quantity Really Be Infinite? 36

Problem 14 Is This Easier Than Falling Off a Log? Well, Maybe Not 39

Problem 15 When the Computer Fails: When Every Day Is a Birthday 47

Problem 16 When Intuition Fails: Sometimes What Feels Right, Just Isn't 55

Problem 17 Computer Simulation of the Physics of NASTYGLASS: Is This Serious? … Maybe 60

Problem 18 The Falling-Raindrop, Variable-Mass Problem: Falling Slower Than Gravity 72

Problem 19 Beyond the Quadratic: A Cubic Equation and Discontinuous Behavior in a Physical System 93

Problem 20 Another Cubic Equation: This One Inspired by Jules Verne 93

Problem 21 Beyond the Cubic: Quartic Equations, Crossed Ladders, Undersea Rocket Launches, and Quintic Equations 103

Problem 22 Escaping an Atomic Explosion: Why the Enola Gay Survived 114

Problem 23 "Impossible" Math Made Easy: Gauss's Congruence Arithmetic 122

Problem 24 Wizard Math: Fourier's Series, Dirac's Impulse, and Euler's Zeta Function 126

Problem 25 The Euclidean Algorithm: The Zeta Function and Computer Science 137

Problem 26 One Last Quadratic: Heaviside Locates an Underwater Fish Bite! 147

Part II The Solutions 155

Appendix 1 MATLAB, Primes, Irrationals, and Continued Fractions 225

Appendix 2 A Derivation of Brouncker's Continued Fraction for $$$ 247

Appendix 3 Landen's Calculus Solution to the Depressed Cubic Equation 251

Appendix 4 Solution to Lord Rayleigh's Rotating-Ring Problem of 1876 261

Acknowledgments 270

Index 273

Also Paul J. Nahin 281

What People are Saying About This

From the Publisher

“A fascinating tour de force of a variety of problems covering pure and applied mathematics, physics, and engineering that will keep your mind busy for days. You'll encounter lots of surprises, a healthy dose of challenging math, and many historical episodes told here for the first time. Highly recommended!”—Eli Maor, author of To Infinity and Beyond

“In this thrilling book, Paul Nahin captures the soul of mathematical physics in tall tales and delightful stories that invite the reader to relive the calculations that guided great inventors and pioneers throughout history.”—Christopher G. Tully, author of Elementary Particle Physics in a Nutshell

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