Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics

345 Pages·2013·25.66 MB·English

by  Robert B. Banks

Towing Icebergs,
Falling Dominoes,
and Other Adventures in
Applied Mathematics

ROBERT B. BANKS
Towing Icebergs,
Falling Dominoes,
and Other Adventures in
Applied Mathematics
Princeton University Press
Princeton and Oxford
Copyright © 1998 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire OX20 1TW
press.princeton.edu
Cover design by Kathleen Lynch/Black Kat Design.
Illustration by Lorenzo Petrantoni/Marlena Agency.
All Rights Reserved
First printing, 1998
Fifth printing, and first paperback printing, 2002
Paperback reissue, for the Princeton Puzzlers series, 2013
Library of Congress Control Number 2012949824
ISBN 978-0-691-15818-1
British Library Cataloging-in-Publication Data is available
This book has been composed in Times Roman and Helvetica
Printed on acid-free paper. ∞
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
To my mother,
Georgia Corley Banks,
sistCl~
and my brothers and
Barney, Dick, and Joan

Contents
ix
Preface
xiii
Acknowledgments
1 Units and Dimensions and Mach Numbers 3
Chapter
2 Alligator Eggs and the Federal Debt 15
Chapter
3 Controlling Growth and Perceiving Spread 24
Chapter
4 Little Things Falling from the Sky 31
Chapter
5 Big Things Falling from the Sky 42
Chapter
6 Towing and Melting Enormous Icebergs: Part I 54
Chapter
7 Towing and Melting Enormous Icebergs: Part II 68
Chapter
8 A Better Way to Score the Olympics 79
Chapter
9 How to Calculate the Economic Energy of a Nation 93
Chapter
How to Start Football Games, and Other Probably
Chapter 10
Good Ideas 109
Gigantic Numbers and Extreme Exponents 121
Chapter 11
Ups and Downs of Professional Football 133
Chapter 12
A Tower, a Bridge, and a Beautiful Arch 150
Chapter 13
Jumping Ropes and Wind Turbines 168
Chapter 14
The Crisis of the Deficit: Gompertz to the Rescue 179
Chapter 15
How to Reduce the Population with Differential
Chapter 16
Equations 189
viii CONTENTS
Shot Puts, Basketballs, and Water Fountains 201
Chapter 17
Balls and Strikes and Home Runs 219
Chapter 18
Hooks and Slices and Holes in One 234
Chapter 19
Happy Landings in the Snow 243
Chapter 20
Water Waves and Falling Dominoes 254
Chapter 21
Something Shocking about Highway Traffic 270
Chapter 22
23 How Tall Will I Grow? 283
Chapter
How Fast Can Runners Run? 300
Chapter 24
321
References
327
Index
Preface
Mathematics is a field of knowledge that has many remarkable
features. Perhaps the most remarkable feature of all is the one
that enables humans to describe, measure, and evaluate the many
aspects of endeavor that involve or affect human activity.
This book is a collection of topics that lend themselves to
relatively simple mathematical analysis. The most important as
pect of the book, however, is that all of these topics are con
cerned with phenomena, situations, events, and things that ap
pear in all our lives. Some of these are things-such as
familiar
throwing baseballs, saving money, and jumping rope. Others are
things-like icebergs being towed, federal debts being
imaginable
paid, and meteors crashing onto the earth.
These comments lead us to the following observation. It is
indeed remarkable that the language of mathematics provides the
mechanism we need to describe, accurately and concisely, the
almost endless list of phenomena and things around us. How in
the world would we be able to function without this beautiful
language?
This is where mathematical models come in. In the book,
simple models are developed to provide answers to questions.
Some of these questions are almost trivial in nature; others are
not. But all are questions that relate to human activity.
For example:
How far and how high do baseballs, golf balls and ski jumpers go and
what are their velocities and flight times?