# The Magic of Maths

Solving for x and Figuring Out Why

*The Magic of Maths*is the maths book you wish you had in school. Using a delightful assortment of examples—from ice cream scoops and poker hands to measuring mountains and making magic squares—this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a maths genius!

A mathematician who is known throughout the world as the “mathemagician,” Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In

*The Magic of Maths*, Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate maths the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of maths.

If you are already someone who likes maths, this book will dazzle and amuse you. If you never particularly liked or understood maths, Benjamin will enlighten you and—with a wave of his magic wand—turn you into a maths lover.

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## Praise

"Arthur Benjamin shows you that numbers do more than just keep track of things and solve problems. He joyfully shows you how to make nature's numbers dance. Let his book be your partner for a lifetime of learning."

**-Bill Nye, science educator and CEO, The Planetary Society**

"Whether it's been decades since you last took algebra or you're currently dealing with the aches of solving for x,

*The Magic of Math*is a good read. Even though it includes, gasp, equations."**-Steve Mirsky,**

*Scientific American*"As soon as the reader has absorbed one 'trick', Benjamin is already moving on to the next one - and each is more dazzling than the last."

*-Physics World*"Arthur Benjamin's

*The Magic of Math*is a thoroughly engaging book for readers of many ages and mathematical backgrounds.... This is an absolute gem of a book. It contains something of interest for everyone, and the author's lively style and obvious affection for the subject makes this a book to keep, reread, and share."

*-Mathematical Reviews*"[A] fascinating book.... The writing style is inviting, and the book is filled with fun examples. Readers can easily jump around and choose from the wide variety of topics or read straight through."

*-Mathematics Teacher*"The book is a fast-paced tour of 12 broad topics ranging from simple arithmetic to the subtleties of infinite sums.... Benjamin approaches all of these subjects with the goal of emphasizing the wonder and magic inherent in them, while still giving the reader a sense of the mathematics hiding of the magicians sleeve.... The book offers a dizzying array of mathematical delights. But here, once the mathemagician has finished his sleight-of-hand, we have the luxury of peeking behind the curtain to understand how all those tricks are done."

*-Math Horizons*"This excellent book is filled with mathematical magic.... Benjamin's writing is very readable and entertaining: his numbers dance. "

*-Manhattan Book Review*"The book delivers on all the promise of both aspects of Benjamin's talent: teacher and performer. Like [Martin] Gardner, Benjamin telegraphs a joy in surprising mathematical stunts.... I recommend this book for the math enthusiast embarking on his or her university career, the high school adept in your life intrigued by math yet bored in class, or someone remembering fondly math as their favorite subject yet lacking time to enroll in courses now."

**-Tom Schulte,**

*MAA Reviews*"[Benjamin] use[s] some interesting trickery to draw the reader into the conversation about the importance of math in everyday life....

*The Magic of Math*is a good model for instructional material. It delivers material on a complex nature in a manner that most people will be able to understand, and you get some magic tricks and humor thrown in for the bargain. You will enjoy this book, you can count on that."

*-Roanoke Times*"[

*The Magic of Math*] would be perfect reading for the gifted and talented as a supplement to other course work. Of course, self-motivated individuals interested in mathematics will enjoy the book too. It would be a good resource for mathematics teachers seeking some additional spice for their presentations. The book is well written; graphics are particularly clear; physical format is excellent."

*-CHOICE*"[A] well-written, entertaining volume.... This solid reference for teachers seeking interesting classroom examples (and jokes) could easily lure a student into further studies in mathematics."

*-Library Journal*"An enthusiastic celebration of the beauty of mathematics.... Benjamin delivers a primer generously filled with insights and intuitions that make math approachable, interesting, and, yes, beautiful."

*-Kirkus Reviews*"[A] positively joyful exploration of mathematics. [Benjamin's] approach is simple and refreshingly practical.... Whether figuring out compound interest, using trigonometry to determine the height of a tree, or employing calculus to work out a shortest possible walking route, each topic is presented in the clearest, simplest way possible.... [I]ts energy and enthusiasm should charm even the most math-phobic readers."

**-**

*Publishers Weekly*, starred review"A look through Art's book shows there really is something magical about maths - and it can be cool too!"

*-The Weekly News (UK)*"With

*The Magic of Math*, Arthur Benjamin has emerged as the world's foremost math teacher and a national treasure. Parents should get this book for their children...and a second copy for themselves. It's that good. And important. Read it."**-Michael Shermer, publisher,**

*Skeptic*magazine, and author of*The Science of Good and Evil*"Prepare to be dazzled and delighted. This is a fun, fast-paced magic show of the greatest treasures of pre-college math, from poker hands to Pascal's triangle, all revealed with the flair of a showman and the clarity of a master teacher.

*The Magic of Math*will leave you smiling, awestruck, and begging for an encore."**-Steven Strogatz, professor of Mathematics, Cornell University, and author of**

*The Joy of x*"

*The Magic of Math*teaches you cool mathematical facts, theorems, puzzles, and problems from arithmetic to calculus. The book provides problems that are accessible to everyone. Teachers will find many ideas to motivate students and to provide an extra challenge for those who are already into math."**-Gail Burrill, president emeritus, National Council of Teachers of Mathematics, and Professor of Mathematics Education, Michigan State University**

"Conventional magic works because you can't understand how it works. The magic of mathematics comes from that exciting 'aha' moment when you suddenly get what's going on. Arthur Benjamin entertainingly provides readers with an all-access backstage pass to the magical world of mathematics."

**-Marcus du Sautoy, professor of Mathematics, University of Oxford, and author of**

*The Number Mysteries*"They say magicians should never reveal their secrets. Happily, Arthur Benjamin has ignored this silly adage-for in this small volume, Benjamin reveals to his audience the secrets of numbers and other mathematical illusions that have intrigued mathematicians for millennia."

**-Edward B. Burger, president, Southwestern University, and author of**

*The 5 Elements of Effective Thinking*"This book will be magical for my students, as it would have been for me throughout my school days. They'll be able to revisit the book frequently as they learn more math, finding deeper appreciation and discovering new areas to explore with each visit."

**-Richard Rusczyk, founder, Art of Problem Solving, and director, USA Mathematical Talent Search**

"In

*The Magic of Math*, Arthur Benjamin has pulled off a seemingly impossible trick. He has made higher mathematics appear so natural and engaging that you will wonder why you were ever bored and confused in math class. There are many books that attempt to popularize mathematics. This is one of the best. On virtually every page I found myself learning new things, or looking at familiar topics in novel ways."**-Jason Rosenhouse, professor of Mathematics, James Madison University, and author of**

*The Monty Hall Problem*"In

*The Magic of Math*, mathemagician Arthur Benjamin gives us an entertaining and enlightening tour of a wide swath of fundamental mathematical ideas, presented in a way that is accessible to a broad audience. A particularly appealing feature of the book is the frequent use of friendly, down-to-earth explanations of the concepts and connections between them."**-Ronald Graham, president emeritus, American Mathematical Society, and co-author of**

*Magical Mathematics*"This book is a whirlwind tour of mathematics from arithmetic and algebra all the way to calculus and infinity, and especially the number 9. Arthur Benjamin's enthusiastic and engaging writing style makes

*The Magic of Math*a great addition to any math enthusiast's bag of tricks."**-Laura Taalman, professor of Mathematics and Statistics, James Madison University**

"Mathematics is full of surprisingly beautiful patterns, which Arthur Benjamin's witty personality brings to life in

*The Magic of Math*. You will not only discover many wonderful ideas, but you will also find some fun mathematical magic tricks that you will want to try out on your friends and family. Be prepared to learn that math is more entertaining than you may have thought."**-George W. Hart, mathematical sculptor, research professor, Stony Brook University, and cofounder, The Museum of Mathematics**

"The Magic of Math is a delightful stroll through a garden filled with fascinating examples. Anyone with any interest in magic, puzzles, or math will have many hours of enjoyment in reading this book."

**-Maria M. Klawe, president, Harvey Mudd College**

"Arthur Benjamin has created an instant mathematical classic, by combining Isaac Asimov's clarity with Martin Gardner's taste and adding his own sense of fun and adventure. I wish he wrote this book when I was a kid."

**-Paul A. Zeitz, professor and chair of Mathematics, University of San Francisco, and author of**

*The Art and Craft of Problem Solving*"There's a playful joy to be found in this book, for readers at any level. Most magicians don't reveal their secrets, but in

*The Magic of Math*, Arthur Benjamin shows how uncovering the mystery behind beautiful mathematical truths makes math even more marvelous to behold."**-Francis Su, president, Mathematical Association of America**

"

*The Magic of Math*offers an expansive, unforgettable journey through mathematics where numbers dance and mathematical secrets are revealed. Just open the book and start reading; you'll be swept over by the magic of Benjamin's writing. Luckily, there is no magician's code to these secrets as you'll undoubtedly want to share and perform them with family and friends."**-Tim Chartier, professor of Mathematics, Davidson College, and author of Math Bytes**