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STREET-FIGHTING
MA THEMATICS
THE ART OF EDUCATED GUESSING AND
OPPORTUNISTIC PROBLEM SOLVING
SANJOY MAHAJAN
F OREWORD BY CARVER A. MEADStreet-Fighting MathematicsStreet-Fighting Mathematics
The Art of Educated Guessing and
Opportunistic Problem Solving
Sanjoy Mahajan
Foreword by Carver A. Mead
The MIT Press
Cambridge, Massachusetts
London, EnglandC 2010 by Sanjoy Mahajan
CForeword 2010 by Carver A. Mead
Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic
Problem Solving by Sanjoy Mahajan (author), Carver A. Mead (foreword),
and MIT Press (publisher) is licensed under the Creative Commons
Attribution–Noncommercial–Share Alike 3.0 United States License.
A copy of the license is available at
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
For information about special quantity discounts, please email
special_sales@mitpress.mit.edu
Typeset in Palatino and Euler by the author using ConT Xt and PDFT XE E
Library of Congress Cataloging-in-Publication Data
Mahajan, Sanjoy, 1969–
Street-fighting mathematics : the art of educated guessing and
opportunistic problem solving / Sanjoy Mahajan ; foreword by
Carver A. Mead.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-262-51429-3 (pbk. : alk. paper) 1. Problem solving.
2. Hypothesis. 3. Estimation theory. I. Title.
QA63.M34 2010
510—dc22
2009028867
Printed and bound in the United States of America
10987654321For JulietBrief contents
Foreword xi
Preface xiii
1 Dimensions 1
2 Easy cases 13
3 Lumping 31
4 Pictorial proofs 57
5 Taking out the big part 77
6 Analogy 99
Bibliography 123
Index 127Contents
Foreword xi
Preface xiii
1 Dimensions 1
1.1 Economics: The power of multinational corporations 1
1.2 Newtonian mechanics: Free fall 3
1.3 Guessing integrals 7
1.4 Summary and further problems 11
2 Easy cases 13
2.1 Gaussian integral revisited 13
2.2 Plane geometry: The area of an ellipse 16
2.3 Solid gy: The volume of a truncated pyramid 17
2.4 Fluid mechanics: Drag 21
2.5 Summary and further problems 29
3 Lumping 31
3.1 Estimating populations: How many babies? 32
3.2 Es integrals 33
3.3 Estimating derivatives 37
3.4 Analyzing differential equations: The spring–mass system 42
3.5 Predicting the period of a pendulum 46
3.6 Summary and further problems 54
4 Pictorial proofs 57
4.1 Adding odd numbers 58
4.2 Arithmetic and geometric means 60
4.3 Approximating the logarithm 66
4.4 Bisecting a triangle 70
4.5 Summing series 73
4.6 Summary and further problems 75