Sean Connolly - The Book of Perfectly Perilous Math: 24 Death-Defying Challenges for Young Mathematicians

THE BOOK OF

PERFECTLY

PERILOUS

MATH

by Sean Connolly

Workman Publishing New York

Copyright 2012 by Sean Connolly
Illustrations copyright by Allan Sanders

All rights reserved. No portion of this book may be
reproducedmechanically, electronically, or by any other means, including photocopyingwithout written permission of the publisher. Published simultaneously in Canada by
Thomas Allen & Son Limited.

Library of Congress Cataloging-in-Publication Data is available.

Design by Netta Rabin and Tae Won Yu
Cover and chapter opener illustrations by Allan Sanders
Method illustrations by Robb Allen
Math advisors: Kara Imm; George Hart, Museum of Mathematics

Workman Publishing Company, Inc.
225 Varick Street
New York, NY 10014-4381
www.workman.com

eISBN: 9780761163749

To Frederika, Jamie, Anna, Thomas, and Dafydd, who continue to help me sidestep perilsperfectly.

I am indebted to Raquel Jaramillo, Krestyna Lypen, and Netta Rabin of Workman Publishing as well as my agent, Jim Levine, for helping to solve the problems raised inand bythis book. We can all take pride in the result. In addition, the following individuals and organizations provided inspiration, patient advice, or willing ears at every stage:

AAAS, Camco International, Gregory Etter, Dr. Gary Hoffman, Hostelling International, Professor Stewart Johnson, Dr. Peter Lydon, Massachusetts Institute of Technology, Professor Frank Morgan, Dr. Sarah Morse, Professor Jay Pasachoff, Ian Phipps, Peter Rielly, Elizabeth Stell, Nora Walsh, and Williams College Department of Mathematics and Statistics.

The Book of Perfectly Perilous Math. Makes you think, doesnt it? Perilous has a dangerous ring to it. A perilous path probably snakes its way along a cliff top, with no guardrail and a river crashing its way through rapids hundreds of feet below you. Or maybe a perilous activity springs to mind, along the lines of sword-swallowing or free-fall skydiving.

Read through this book and youll find perils of all descriptionsscuba tanks running low at a sunken shipwreck, international spy games on a lightning-fast train, blood-sucking vampires threatening to take over an entire town, painful bites from a deadly spider. Two things draw them all together, apart from the fact that theyre all perilous. One is that a solution can be found using some basic math tools. And the other is that youre the one who has to find those tools and put them to use.

Thats the perilous explainedbut perfectly? Whats that doing anywhere near the word math? Its not so strange, really. Think of a complicated division problem where you do all the work and you get the answer, with no remainder. Perfect! And you can take this perfect idea even further into math territory. The star pitcher whos clocked up all those zeroesno runs, no hits, no bases on balls or errorshas just completed a perfect game. Those music standouts who can identify or exactly reproduce a particular note have perfect pitch. Remember: Each musical note has its own frequency (numbers again!).

The twenty-four challenges contained in The Book of Perfectly Perilous Math draw you into a world where all those math lessons meet real life. Sure, youve learned how much change to expect from a $5 bill if you buy two sodas and an ice-cream cone, but the challenges inside this book take you out of your comfort zone and into a world where life-threatening risks lie around every corner. You must summon your math skills just as you do whenever you pay for something or divide a pizza among friends... except this time the stakes are highermuch higher.

Each of the challenges in The Book of Perfectly Perilous Math puts you in the hot seat. Youre faced with a tough, maybe even do-or-die, problem that needs to be solved quickly. And that solution calls for all your math skills. Those same skills and concepts that you come across each day in math class take on a new meaningthey are now your survival skills.

Probability? It just might help you decide which door to choose if your life depended on it: the one that will lead you to freedom, or the one that will lead you to an executioners chambers.

Powers of ten? Use them to make a lifesaving medicine to save a scientist in the jungle.

The meaning of pi? It could make all the difference in creating a shield to save a planet from an asteroid hurtling through space.

Aligning with the Common Core Standards in mathematics for grades 5, 6, and 7, the problems are separated into three levels of difficulty, depending on your chances of survival: You Might Make It (grade 5), Slim to None (grade 6), and Youre Dead (grade 7). The Survival Strategies for each problem clue you in on the math tools youll need to use to make it through the danger.

Maybe you can jump in and find the right math tool to solve the problem. If not, then you can call on one of the greatest mathematicians of them all, Euclid. Each challenge includes a section called Euclids Advice, to help set you on the right track. You can think of Euclid as a helpful friend willing to whisper a hint in your ear.

Next comes The Solutionor at least our way of reaching the solution. Math problems can often be solved in different ways, and most require a series of steps, so think of this explanation as one road leading to the destination. Here is where youll see all those math ideas working together just as they do in the classroom, but in new and exciting surroundings.

Each challenge finishes with a Math Lab, a hands-on way of putting those math principles (the ones that led to the solution) into practice. The challenge that you just faced was perilous; with the Math Lab, its time for some fun. Dont get the idea that you need all sorts of special equipment just because you see the word lab. The Math Lab activities let you test and demonstrate those math principles using simple ingredients that you can find easilysuch as sand, ice cream, a beach ball, construction paper, pinecones, and cornflakes.

And those Brain Benders scattered throughout? Those are just fun ways to see the cool things you can do with math! But thats enough explanation. Its time for you to tackle those perilous problems. Start reading... now!

Chapter 1

CHANCES OF SURVIVAL: YOU MIGHT MAKE IT

SURVIVAL STRATEGIES: OPERATIONS AND ALGEBRAIC THINKING

DEATH BY: GIANT BLADE

The year is 1714. Youre in a dark Spanish prison. You wake up to find yourself tied to a table with ropes. In the darkness you hear a rhythmic swishing soundsomething going back and forth, back and forth. Eventually your eyes get accustomed to the dark and see that the source of the sound is a sharp blade at the end of a long pendulum thats swinging back and forth over your body. With each sweep it gets a little lowerand a little closer to your chest.

You note how long it takes between those swishes: exactly 7 seconds. And with each swish, the blade drops 1 inch lower. The last passing was only 15 inches above your chest. It wont be much longer before the blade slices right through you.