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# The Joy of x: A Guided Tour of Math, from One to Infinity

## bySteven Strogatz

### Paperback | October 1, 2013

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Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In

*The Joy of*x, Steven Strogatz expands on his hit*New York Times*series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you'd had, and*The Joy of*x*is the book you'll want to give to all your smart and curious friends.*### Details & Specs

Title:The Joy of x: A Guided Tour of Math, from One to InfinityFormat:PaperbackDimensions:336 pages, 8 × 5.31 × 0.84 inPublished:October 1, 2013Publisher:Houghton Mifflin HarcourtLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0544105850

ISBN - 13:9780544105850

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### Customer Reviews of The Joy of x: A Guided Tour of Math, from One to Infinity

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PREFACEI have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in psychology or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them.In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they mean when they say a proof is elegant. Sometimes we joke that I should just sit him down and teach him everything, starting with 1 + 1 = 2 and going as far as we can.Crazy as it sounds, that’s what I’ll be trying to do in this book. It’s a guided tour through the elements of math, from preschool to grad school, for anyone out there who’d like to have a second chance at the subject—but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.We’ll discover how Michael Jordan’s dunks can help explain the fundamentals of calculus. I’ll show you a simple—and mind-blowing—way to understand that staple of geometry, the Pythagorean theorem. We’ll try to get to the bottom of some of life’s mysteries, big and small: Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How many people should you date before settling down? And we’ll see why some infinities are bigger than others.Math is everywhere, if you know where to look. We’ll spot sine waves in zebra stripes, hear echoes of Euclid in the Declaration of Independence, and recognize signs of negative numbers in the run-up to World War I. And we’ll see how our lives today are being touched by new kinds of math, as we search for restaurants online and try to understand—not to mention survive—the frightening swings in the stock market.By a coincidence that seems only fitting for a book about numbers, this one was born on the day I turned fifty. David Shipley, who was then the editor of the op-ed page for the New York Times, had invited me to lunch on the big day (unaware of its semicentennial significance) and asked if I would ever consider writing a series about math for his readers. I loved the thought of sharing the pleasures of math with an audience beyond my inquisitive artist friend.“The Elements of Math” appeared online in late January 2010 and ran for fifteen weeks. In response, letters and comments poured in from readers of all ages. Many who wrote were students and teachers. Others were curious people who, for whatever reason, had fallen off the track somewhere in their math education but sensed they were missing something worthwhile and wanted to try again. Especially gratifying were the notes I received from parents thanking me for helping them explain math to their kids and, in the process, to themselves. Even my colleagues and fellow math aficionados seemed to enjoy the pieces—when they weren’t suggesting improvements (or perhaps especially then!).All in all, the experience convinced me that there’s a profound but little-recognized hunger for math among the general public. Despite everything we hear about math phobia, many people want to understand the subject a little better. And once they do, they find it addictive.The Joy of x is an introduction to math’s most compelling and far-reaching ideas. The chapters—some from the original Times series—are bite-size and largely independent, so feel free to snack wherever you like. If you want to wade deeper into anything, the notes at the end of the book provide additional details and suggestions for further reading.For the benefit of readers who prefer a step-by-step approach, I’ve arranged the material into six main parts, following the lines of the traditional curriculum.Part 1, “Numbers,” begins our journey with kindergarten and grade-school arithmetic, stressing how helpful numbers can be and how uncannily effective they are at describing the world.Part 2, “Relationships,” generalizes from working with numbers to working with relationships between numbers. These are the ideas at the heart of algebra. What makes them so crucial is that they provide the first tools for describing how one thing affects another, through cause and effect, supply and demand, dose and response, and so on—the kinds of relationships that make the world complicated and rich.Part 3, “Shapes,” turns from numbers and symbols to shapes and space—the province of geometry and trigonometry. Along with characterizing all things visual, these subjects raise math to new levels of rigor through logic and proof.In part 4, “Change,” we come to calculus, the most penetrating and fruitful branch of math. Calculus made it possible to predict the motions of the planets, the rhythm of the tides, and virtually every other form of continuous change in the universe and ourselves. A supporting theme in this part is the role of infinity. The domestication of infinity was the breakthrough that made calculus work. By harnessing the awesome power of the infinite, calculus could finally solve many long-standing problems that had defied the ancients, and that ultimately led to the scientific revolution and the modern world.Part 5, “Data,” deals with probability, statistics, networks, and data mining, all relatively young subjects inspired by the messy side of life: chance and luck, uncertainty, risk, volatility, randomness, interconnectivity. With the right kinds of math, and the right kinds of data, we’ll see how to pull meaning from the maelstrom.As we near the end of our journey in part 6, “Frontiers,” we approach the edge of mathematical knowledge, the borderland between what’s known and what remains elusive. The sequence of chapters follows the familiar structure we’ve used throughout—numbers, relationships, shapes, change, and infinity—but each of these topics is now revisited more deeply, and in its modern incarnation.I hope that all of the ideas ahead will provide joy—and a good number of Aha! moments. But any journey needs to begin at the beginning, so let’s start with the simple, magical act of counting.

Table of Contents

*Preface ix*

**Part One**

*From Fish to Infinity 3*

**Numbers**

An introduction to numbers, pointing out their upsides (they’re efficient) as well as their downsides (they’re ethereal)

Rock Groups 7

Treating numbers concretely—think rocks—can make calculations less baffling.

The Enemy of My Enemy 15

The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so . . . negative

Commuting 23

When you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before?

Division and Its Discontents 29

Helping Verizon grasp the difference between .002 dollars and .002 cents

Location, Location, Location 35

How the place-value system for writing numbers brought arithmetic to the masses

**Part Two**

**Relationships**

The Joy of

*x*45

Arithmetic becomes algebra when we begin working with unknowns and formulas.

Finding Your Roots 51

Complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems.

My Tub Runneth Over 59

Turning peril to pleasure in word problems

Working Your Quads 67

The quadratic formula may never win any beauty contests, but the ideas behind it are ravishing.

Power Tools 75

In math, the function of functions is to transform.

**Part Three**

**Square Dancing 85**

*Shapes*

Geometry, intuition, and the long road from Pythagoras to Einstein

Something from Nothing 93

Like any other creative act, constructing a proof begins with inspiration.

The Conic Conspiracy 101

The uncanny similarities between parabolas and ellipses suggest hidden forces at work.

Sine Qua Non 113

Sine waves everywhere, from Ferris wheels to zebra stripes

Take It to the Limit 121

Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus.

**Part Four**

**Change**

Change We Can Believe In 131

Differential calculus can show you the best path from A to B, and Michael Jordan’s dunks help explain why.

It Slices, It Dices 139

The lasting legacy of integral calculus is a Veg-O-Matic view of the universe.

All about

*e*147

How many people should you date before settling down? Your grandmother knows—and so does the number

*e*.

Loves Me, Loves Me Not 155

Differential equations made sense of planetary motion. But the course of true love? Now that’s confusing.

Step Into the Light 161

A light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer.

**Part Five**

*The New Normal 175*

**Data**

Bell curves are out. Fat tails are in.

Chances Are 183

The improbable thrills of probability theory

Untangling the Web 191

How Google solved the Zen riddle of Internet search using linear algebra

**Part Six**

*The Loneliest Numbers 201*

**Frontiers**

Prime numbers, solitary and inscrutable, space themselves apart in mysterious ways.

Group Think 211

Group theory, one of the most versatile parts of math, bridges art and science.

Twist and Shout 219

Playing with Möbius strips and music boxes, and a better way to cut a bagel

Think Globally 229

Differential geometry reveals the shortest route between two points on a globe or any other curved surface.

Analyze This! 237

Why calculus, once so smug and cocky, had to put itself on the couch

The Hilbert Hotel 249

An exploration of infinity as this book, not being infinite, comes to an end

*Acknowledgments 257*

Notes 261

Credits 307

Index 309

Notes 261

Credits 307

Index 309

Editorial Reviews

Amazon Best Books of 2012: Science and MathA delightful exploration of the beauty and fun of mathematics, in the best tradition of Lewis Carroll, George Gamow, and Martin Gardner. The Joy of x will entertain you, amaze you, and make you smarter."- Steven Pinker, Harvard College Professor of Psychology, Harvard University, and author of How the Mind Works and The Language Instinct"Steven Strogatz should do for math what Julia Child did for cookery. He shows that this stuff really matters, and he shows that it can nourish us."- James Gleick, author of The Information and Chaos"Steve Strogatz may be the only person alive with the skill to pied piper me into the murky abyss of set theory. I literally learned something on every page, despite my innumerate brain. This is a fantastic book, conveyed with clarity, technical mastery and infectious joy."- Jad Abumrad, host of Radiolab"This joyous book will remind you just how beautiful and mesmerizing math can be. Steve Strogatz is the teacher we all wish we had."- Joshua Foer, author of Moonwalking with Einstein"I loved this beautiful book from the first page. With his unique ingenuity and affable charm, Strogatz disassembles mathematics as a subject, both feared and revered, and reassembles it as a world, both accessible and magical. The Joy of x is, well, a joy."- Janna Levin, Professor of Physics and Astronomy, Barnard College, Columbia University, and author of How the Universe Got Its Spots and A Madman Dreams of Turing Machines"Amazingly, mathematicians can see patterns in the universe that the rest of us are usually blind to. With clarity and dry wit, The Joy of x opens a window onto this hidden world with its landscapes of beauty and wonder."- Alan Alda"This book is, simply put, fantastic. It introduces the reader to the underlying concepts of mathematics - presenting reasons for its unfamiliar language and explaining conceptual frameworks that do in fact make understanding complex problems easier. In a world where mathematics is essential but, largely, poorly understood, Steve Strogatz's teaching skills and deft writing style are an important contribution."- Lisa Randall, Frank B. Baird, Jr. Professor of Science, Harvard University, and author of Warped Passages and Knocking on Heaven's Door"Strogatz's graceful prose is perfectly pitched for a popular math book: authoritative without being patronizing, friendly without being whimsical, and always clear and accessible. His x marks the spot aÇô and hits it."- Alex Bellos, author of Here's Looking at Euclid"Strogatz has discovered a magical function that transforms aÇÿmath' into aÇÿjoy,' page after wonderful page. He takes everything that ever mystified you about math and makes it better than clear - he makes it wondrous, delicious, and amazing."- Daniel Gilbert, Professor of Psychology, Harvard University, and author of Stumbling on Happiness"