Book Description

Science News publishes a weekly column devoted to 'cool stuff' from the world of mathematics. There have been over 250 articles under the title 'Ivars Peterson's Math Treks'. New developments and their applications, old puzzles revisited, famous problems and historic events have all featured. This column has been extremely popular for its brief, informal forays into some of the more unusual aspects of mathematics. Ivars Peterson has enhanced and updated a selection of articles for this book and further bibliographic details and web links are available online. The contents span a wide range of topics and there will be something here for anyone with an interest in mathematics. ... Read more

Book Description

A Mathematical Pandora's Box has been written in response to the success of Brian Bolt's earlier mathematical puzzle books. Through his own experience, the author has discovered a worldwide interest in these and similar puzzles. Not only do they stimulate creative thinking but they can also open up new areas of mathematics to the reader. This book contains 142 activities: in addition to puzzles, there are games, tricks, models and explanations of various phenomena. They range from number manipulation, through happy and amicable numbers, coin puzzles, picnicking bears and pentominoes, to building shapes with cubes. Some of the puzzles date from hundreds of years ago while many others are original, giving everyone something to think about. There is a detailed commentary at the end of the book, giving solutions and explanations, together with the occasional follow-up problem. ... Read more

Book Description

The fastest, easiest way to master precalculus . . . by doing it!

Do logarithmic functions throw you for a loop?Does the challenge of finding an inverse function leave you overwhelmed? Does the Law of Cosines make you feel clueless?With this helpful, easy-to-follow guide, you will gain total command of these precalc concepts–and many more–in no time at all.

Precalculus: A Self-Teaching Guide includes an algebra review and complete coverage of exponential functions, log functions, and trigonometry. Whether you are studying precalculus for the first time, want to refresh your memory, or need a little help for a course, this clear, interactive primer will provide you with the skills you need. Precalculus offers a proven self-teaching approach that lets you work at your own pace–and the frequent self-tests and exercises reinforce what you’ve learned. Turn to this one-of-a-kind teaching tool and, before you know it, you’ll be solving problems like a mathematician! ... Read more

Reviews (8)

Full of mistakes
I am only into Chapter 3 and have found numerous mistakes. Including mistakes in important formulas such as the Quadratic Formula. I do not recommend this book to anyone who already has problems with math!

Excellent
As a mathematician I give 5* to this publication. Everything is well explained, the series of chapters is very logical. I recomend it strongly. The exercises cover and target everything without being numerous.

publisher not responsive to error information
Like the other reviewers for this book, I found many errors. Fortunately for me, I am reviewing the material rather than learning for the first time.

I can't imagine how frustrated and inadequate new learners must feel as they try to identify and apply the rules of math with incorrect answers to both examples and self-test problems. I would recommend new learners look to another book to learn Precalculus.

While I have found other Wiley Self Teaching Guides to be accurate and very helpful, Wiley Publishing didn't respond to my suggestion to add a correction paper to every copy of this edition (the minimum ethical response).

I would also that any one considering a Wiley Publishing purchase to check with online reviews before purchasing.

Too many errors to be useful, too few sample problems
The presentation of the subject matter is very adroit, but the problem with the book is two fold:

1) there are numerous errors. For instance, on page 150 problem 1 can only be solved using one measure of the triangle, yet the other measure of the triangle is incorrect for the degree measure provided. In the same set of sample problems, the 7th problem is entirely inconsistent with errors in both the problem statement, the solution statement, and the diagram of the solution statement. This is only a single example, but I marked each problem I found wrong in the book and found that there is a high (~10%) error rate . As another reviewer pointed out, there are even errors in the discussion of identities and axioms, which is horrendous for the students. Errors in problems sets only confuse people, but errors in the lesson is catastrophic, especially in a section you're supposed to memorize.

2) There simply are not enough problem sets to do in order to gain a mastery of the subject matter. There are usually 6 or 7 problems per section, and no additional problems which conclude a chapter. The standard textbook provides this sort of exhaustive problem sets, and this is quite useful for a mastery of the subject. You may be intimately familiar with the assertions of the text, but you will have a hard time applying them without practice.

Full of errors
Although the authors have very clear ways of explaining mathematical processes and procedures, the book contains plenty of errors, some minor, some major.

For example, when explaining the relationships between trig expressions (p. 153), it is stated that sin u = 1/cos u; in fact, a sine is the inverse of a cosecant, not a cosine. A simple but important typographical error.

On page 131, it is clearly stated that 9pi/4 radians is a coterminal of 7pi/4 radians; they are at righta angles to each other. The authors arrived at this solution using incorrect math, which does not lead me to believe that they are checking their work very well.

I have found many more such errors, and I am disappointed with the book. I didn't buy it from Amazon, and I'm taking it back to the store for a refund. ... Read more

Book Description

70 Quick-and-Easy Games to Build Math Skills
Hands-on games to help you reinforce key math skills including addition, subtraction, multiplication, division, fractions, probability, and factors. All games are easy to make and play. Includes reproducibles. ... Read more

Book Description

Going beyond folding instructions, Origami3 takes a unique and scholarly look at the implications and applications of this art. This collection of essays from The Third International Meeting of Origami Science, Math, and Education demonstrates the diversity of interests that origami inspires, discussing the theoretical and mathematical foundations of paper folding, applicable origami design techniques, and the use of origami as a teaching tool for mathematics and language. Teachers, mathematicians, engineers, and origami hobbyists will find this title to be both interesting and practical. ... Read more

Book Description

A melancholy Dr. Broth, professor emeritus of non-Euclidean, paleolinguistic astrohistoriography, strolls the topiary gardens of a campus arboretum. He has just returned from a conference on the Hyde-body problem, and his luggage -- one bulging attaché case -- did not appear at the baggage claim. Unfortunately, it contained the only copy of his just-finished manuscript, his life's work...lost!

Now join the delightful, puzzling, and hilarious adventures of Dr. Broth, the humble gardener Ollie, and their more-or-less trusted companion McGuffin (a time-traveling alpaca), as they hurtle through time and space in search of Dr. Broth's treasured manuscript. Visit postapocalyptic Chicago, Mercury, ancient Greece, revolutionary France, New York a few years ago, the Peru of the Incas, and a Scotland about to be overrun by clones, among many other places neither you nor any reasonably sane person would look for lost luggage. Of course, McGuffin is never too sure where, or rather when, his time traveling will land him -- and you won't be either as these marvelous characters dash off into the mind-boggling unknown.

With 80 original puzzles varying wildly and unpredictably in difficulty and format, everyone from brain-teased veterans to young intrepid detectives will find a treasure trove of worthy challenges in these pages. Quite simply, as Dr. Broth would agree, there's never been a puzzle adventure like it. Let the search begin! ... Read more

Reviews (7)

A Puzzle Book with a Twist...
This is the first puzzle book I've come across with a storyline running through the complete book.There are 80 good puzzles which need to be solved along the way.From what I've said ,it might sound like this is a mystery book--not so this is definately a book of puzzles.The puzzles are all quite different,but of the types that puzzle lovers are familiar with.The storyline is quite funny.The conversation along the way is fun:

"'Grand small talk? What's that?"asked Ted.
"That's an oxymoron," said Dr.Broth.
"And that,"said Mel nodding toward a peasant woman in a short skirt,"is one foxy moron.If they've got to be stupid,might as well make 'em foxy.That's what Uncle Sal used to say,anyway."
Not your typical puzzle book ;but different and a lot of fun to be enjoyed by anyone who likes puzzles.

FIRST RATE WINNER FOR MICHAEL ABRAMS
Michael Abrams has an excellent puzzle book for lovers of puzzles of all ages. Along with a very pleasing and amusing story line, Michael offers up puzzles from easy to difficult, and always fun.Being the puzzle editor for DISCOVER magazine's BRAINBOGGLERS column has served Michael well in capturing the right puzzle at the right time to make the reader fully engaged . . . and then realizing the answer in one of those AHA! moments. Thank you, Michael, and I hope there are more adventures on the way.

brain-boggling is right!
although the puzzles really drive me nuts...i love this book! the quirky illustrations match the clever, playful storyline. a friend left the book at my house and i won't let him have it back until i'm done reading it! my mom just lOves puzzles... guess what she's getting for Christmas!

Bran Boggling while Tummy Joggling
Dr. Broth, Ollie and a host of other really odd characters not only succeeded in boggling my mind(I have solved about half the puzzles over the past three weeks), they also provoked some amusement and out loud laughter. If I found myself stumped on any of the harder puzzles, my clenched jaw soon loosened at what I think is a really delightful and amusing story. My ten year old daughter is now begging for an Alpaca doll for Christmas! (anyone know where to get one?) So, I definitely recommend this new puzzle and story book to anyone who enjoys challenging their brains and having a good laugh at some cleverly imagined, nutty adventures though space and time.

A "Must Have" for Puzzle Lovers
Our two teen-age sons, my husband and I made a game out of reading this delightful book. When we discovered "Dr. Broth and Ollie's Brain-Boggling Search for the Lost Luggage, we began to play 'puzzle-a-day', fashioned after public radio's "chapter-a-day". Each evening after dinner, we read another section of the charming story and challenged one another to be the first to solve the puzzle. The puzzles spanned the difficulty continuum. Some we solved so quickly, we had to do another right away. Many were quite challenging to our tired 'end-of-the-day' minds. There were even a few we had to 'sleep-on'. Thanks to Michael Abrams and Jeffrey Winters for many hours of family fun. And 'hats-off' to Marc Rosenthal for his wonderful illustrations! ... Read more

Book Description

Rich selection of 100 practice problems—with hints and solutions—for students preparing for the William Lowell Putnam and other undergraduate-level mathematical competitions. Real numbers, differential equations, integrals, polynomials, sets, other topics. Hours of stimulating challenge for math buffs at varying degrees of proficiency. References.
... Read more

Reviews (3)

100 of'em!!!!!
this book is directed towards high school students preparing to take mathematics competetion such as the CMC and IPO. the book contains 100 thinking skills math question with solutions. Being a high school student (with a huge intrest for math) i was able to solve 71 problems, but i must admit that i really did face ALOT of problems solving some of them.(wait till you see the solution for question #5, #8, #41 and 46 Recomended to any high school student prepared to sit any exam or have an intrest for pure thinking skills math qestions, but if you are looking for something REALLY hard then you best look somewhere else...

Good book to buy
The Green book of Mathematical Problems is definitely a great book. It contains challenging brainteasers that will be of interest to anyone interested in undergraduate-level mathematical problems dealing with real numbers, differential equations, integrals, polynomials, sets and other mathematical topics. This book offers a selection of 100 problems with hints and solutions. The hints are very helpful and the solutions are easy to follow. The book isn't expensive. So it's a good choice.

100 of em!!!!!!!!!!
This weird titled book contains 100 mathematical problems. Most of the problems in the book require high school level mathematics.... Personally I - a high school student- found no difficulty solving 71 problems in the book. Unfortunately a good number of the problems in the book, I have seen in other mathematical problem books. Nevertheless, I really enjoyed the problems in the book. The book is targeted to those students preparing to take math competition such as ILO and the CMC. The solution of the problem are clearly outlined and I had no difficulty following them...wait till you see the solution for problems #21, #41, #42 and #90... I strongly recommend this to high school student interested in mathematics, if you are looking for something REALLY REALLY hard you could well steer away from this book and find something harder... ... Read more

Book Description

Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens?

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.

Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

... Read more

Reviews (1)

no breadth
The book should have been subtitled
'knight's tours' (=hamiltonian paths).
It includes endless variations on this
theme (and little else) e.g. tours on
nonplanar surfaces - even ones that only
exist in theory! The book really amounts
to little more than a monograph on hamiltonian
paths - a subject for specialists only since
there are no useful general theorems in this
notoriously difficult topic. ... Read more

Book Description

Math, history, art, and world cultures come together in this delightful book for kids, even for those who find traditional math lessons boring. More than 70 games, puzzles, and projects encourage kids to hone their math skills as they calculate, measure, and solve problems. The games span the globe, and many have been played for thousands of years, such as three-in-a-row games like Achi from Ghana or the forbidden game of Jirig from Mongolia. Also included are imaginative board games like Lambs and Tigers from India and the Little Goat Game from Sudan, or bead and string puzzles from China, and Möbius strip puzzles from Germany. Through compelling math play, children will gain confidence and have fun as they learn about the different ways people around the world measure, count, and use patterns and symmetry in their everyday lives. ... Read more

Book Description

Featuring games, stories, brainteasers, and fascinating graphics, this popular calendar stimulates curiosity, opens up the imagination, and provides entertainment for every day of the year. The box for each date contains a problem whose solution is the date itself - the challenge lies in figuring out how to arrive there, and possibly discovering more than one method. In addition, every month offers a treasure trove of information: how random numbers shape the landscape, Zeno's zany paradoxes, the Möbius strip, prime twins, mathematical connections between codes, new technologies, the workings of lighthouses, and much more. ... Read more

Book Description

Here is another collection drawn from Martin Gardner's 'Mathematical Games' column in Scientific American. Each chapter explores a different theme, for example fractals, surreal numbers, the sculptures of Berrocal, tiling the plane, Ramsey theory and code breaking, all combining to create a rich diet of recreational mathematics. Most chapters can be readily understood by the uninitiated: at each turn there are challenges for the reader and a wealth of references for further reading. Gardner's clarity of style and ability systematically to simplify the complex make this an excellent vehicle in which to start or continue an interest in recreational mathematics. ... Read more

Book Description

Grab a pencil. Relax. Then take off on a mind-boggling journey to the ultimate frontier of math, mind, and meaning as acclaimed author Clifford Pickover, Dorothy, and Dr. Oz explore some of the oddest and quirkiest highways and byways of the numerically obsessed. The thought-provoking mysteries, puzzles, and problems range from zebra numbers and circular primes to Legion's number--a number so big that it makes a trillion pale in comparison. The strange mazes, bizarre consequences, and dizzying arrays of logic problems entertain readers at all levels of mathematical sophistication. The tests devised by enigmatic Dr. Oz to assess human intelligence will tease the brain of even the most avid puzzle fan. They feature a host of mathematical topics: geometry and mazes, sequences, series, sets, arrangements, probability and misdirection, number theory, arithmetic, and even several problems dealing with the physical world. With numerous illustrations, this is an original, fun-filled, and unusual introduction to numbers and their role in creativity, computers, games, practical research, and absurd adventures that teeter on the edge of logic and insanity. Clifford A. Pickover is the author of over twenty highly acclaimed books on such topics as computers and creativity, art, mathematics, black holes, human behavior and intelligence, time travel, alien life, and science fiction. Among his books are Computers, Pattern, Chaos, and Beauty (St. Martin's Press, 1990), Wonders of Numbers (Oxford University Press, 2000), Dreaming the Future (Prometheus, 2001), The Zen of Magic Squares, Circles, and Stars (Princeton University Press, 2001), The Stars of Heaven (Oxford University Press, 2001), The Paradox of God and the Science of Omniscience (Palgrave, 2002). A Ph.D. graduate of Yale University, he is a prolific inventor with dozens of patents, the associate editor for several journals, the author of colorful puzzle calendars, and puzzle contributor to adult and children's magazines. Pickover's computer graphics have been featured on the cover of many popular magazines and on T.V. shows. ... Read more

Reviews (3)

What is interesting and what solvable?
I prefer mathematical puzzles that have two features:
- they are interesting (i.e. they have that difficulty that make them worth trying to solve);
- they are solvable without developing a whole new theory and without writing program code.
In this book most problems that are interesting (very interesting and intriguing, I must admit) are not solvable in the foresaid sense, and most solvable ones are not interestin. Of course, a few are both. The picture sequences to be completed are very original, and sometimes difficult, examples of QI tests.
However, in spite of that slight flaw, I have really enjoyed reading it. It may depends on my appreciation of Oz novels and movie, and even if this book is not likely to mark the history of mathematical entertainment, it remains a worthy reading.

A true mathematical wonderland
This wonderful mathematical puzzle book has over 100 puzzles sure to delight readers -- from kids to adults. The problems include: mazes, sequences, probability, and more. Most puzzles are very clever and fun. I liked considering the yellow-brick road that crosses America. How many bricks would it take? I also liked the zebra numbers and circular primes. Legion's number is a number so big that it makes a a billion look puny.

Anyone who has pondered the vastness of our mathematical universe will love this book.

Math Puzzles from another Universe!
I found the puzzles and problems in this book to be original and varied, and with a wide range of difficulty levels. I enjoyed the fact that some puzzles might actually have more than one answer, which leaves room for healthy debate and for better understanding the way different people think. I think this book can be enjoyed by readers of different levels of mathematical sophistication. For example, a freshman in high school could skip the more difficult problems, like the one on Ramanujan Congruences, although this is one of the most interesting chapters. My favorite chapter is one that poses a statistics-like question, dealing with bones thrown into a pit. You have to figure out the ratio of the long piece to the short piece. Here's a sample of other chapters that I really enjoyed:

1. The Yellow-brick Road
2. An Experiment with Kansas
8. The Problem of the Bones
16. Omega Sphere
28. Legions' Number
29. The Problem of the Tombs
35. Prime-poor Equations
36. Number Satellite
43. Ramanujan Congruences and the Quest for Transcendence
49. The Jellyfish of Europa
99. A Connection Between Pi and e
103. The Scarecrow Formula
107. The Omega Crystal
108. Attack of the Undulating Undecamorphs

I've already spent hours reading and rereading the book, and showing it to friends, and I know I'll spend many hours more! ... Read more

Book Description

If you enjoy beautiful geometry and relish the challenge and excitement of something new, the mathematical art of hinged dissections is for you. Using this book, you can explore ways to create hinged collections of pieces that swing together to form a figure.Swing them another way and then, like magic, they form another figure! The profuse illustrations and lively text will show you how to find a wealth of hinged dissections for all kinds of polygons, stars and crosses, curved and even three-dimensional figures. The author includes careful explanation of ingenious new techniques, as well as puzzles and solutions for readers of all mathematical levels. These novel and original dissections will be a gold mine for math puzzle enthusiasts, for math educators in search of enrichment topics, and for anyone who loves to see beautiful objects in motion. ... Read more

Book Description

A unique and utterly charming guide to the history of mathematics.

The secret of constellations, the enigma of the golden mean, and the brilliance of a proof-these are just some of the wonders Clawson explores with unbridled delight in this recreational math book. Throughout the book he divulges the wisdom of the ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations still have deep meaning today.

Transporting us beyond mere appreciation, Clawson urges us to tackle functions, tangents, and the concept of infinity. He helps us intuitively comprehend these and other building blocks of mathematics through explaining their discovery and uses. By accompanying him on his journey, we taste the fruit of knowledge that has eluded us until now. ... Read more

Reviews (1)

A Great Book
I bougth the spanish version of this book, And now I can say that this is one on the greatest bokks I ever read. The author explains the origins of Mathematics and some of the great matehmatical thems such Series, Calculus, Fibonacci Numbers, Cryptography and so on... If you want to know new mathematical terms and you enjoy this science, this is your best chance. ... Read more

Book Description

Many of the most important mathematical concepts were developed from recreational problems. This book uses problems, puzzles, and games to teach students how to think critically. It emphasizes active participation in problem solving, with emphasis on logic, number and graph theory, games of strategy, and much more. Answers to Selected Problems. Index. 1980 ed.
... Read more

Reviews (2)

Recreational mathematics as course work
This book is the heavyweight champion of problems in recreational mathematics, containing a large number of very detailed problems in many areas. The presentation strategy is to develop the topic by using problems followed by an explanation followed by a detailed solution. The style is largely that of a textbook, which in fact is what it is designed to be. The authors developed the material as the main text for a course they teach in applied problem solving.
The chapters are largely independent, so it is possible to pick and chose the topics for a course. Do not let the word recreational in the title lead you to believe that these problems are bunnies. I am a co-editor of Journal of Recreational Mathematics and I found myself thinking long and hard about some of these problems. Granted, many are straightforward, but there are enough of the head-scratching variety to satisfy every taste. The general topics are logic, basic number theory, graph theory and games, with a few other topics interspersed.
With hundreds of problems, detailed solutions to the demonstrations and hints for most included, this is a resource unlike all others. If you teach a course in mathematical problem solving or beginning computer programming, you cannot help finding a problem in here that you can use to illustrate a topic or as a test question. I have already used a couple as the seeds for some programming exercises. Better yet, consider it as a textbook for your course in mathematical problem solving.

Published in Journal of Recreational Mathematics, reprinted with permission.

Problem Solving Through Recreational Mathematics
I first became acquainted with this book about twenty years ago when it first appeared. Since it didn't fit into a standard niche in college mathematics curricula, it never really caught on and, before the Dover edition, was out of print for a number of years.

This was a shame, as this is both a wonderful and remarkable book. It has a broad appeal; amateur mathematicians, professional mathematicians, and puzzle buffs should all find something in it to interest them. It is both fun and rewarding at the same time. One can learn a great deal of mathematics from it. It also contains a method for solving linear Diophantine equations that I have never seen anywhere else.

The authors have added a chapter on probability which should further enhance this highly original work. ... Read more

Book Description

Reviews (1)

A good mind trainning book
It brings a collection of several puzzles that involves logic and mathematics to solve them, althought much more of good sence is necessary ... Read more

Book Description

Reviews (4)

Simply excellent
This book is worth getting if only to find out how to make a hexaflexagon. The problems in it are truly absorbing.

Reeks of Awesomeness!
After a long afternoon of studying ordinary differential equations, computer science, and japanese, it is great to find a book like this that sucks you right in, absorbs your brain for a couple of hours, and then inspires you to cut, paste, & fold paper. What you see absolutely reeks of awesomeness. I love Martin Gardner! (Last month's reading, Knotted Doughnuts, was equally fun!)

A delight for young and old
Martin Gardners column "Mathematical Games" was in the magazine "Scientific American" for so long that he was more than an institution. This was the first of his books to take some of the ideas from the many columns and present them in volume format.

I first came across it in a British edition titled "Mathematical Puzzles and Diversions" in my early teens. From memory it took me around three weeks and two rolls of adding machine tape to finish with the hexaflexagons (don't ask, just buy the book) in the first chapter.

Mr Gardner deserves his reputation as a writer who can simplify complex subjects without talking down to the audience and this is well demonstrated in this volume. Some of the later chapters deal with parts of probability and game theory that skirt around some complex maths while someone with little mathematical ability (such as myself) finds it easy to follow along. The prose is light and easily read while the subject matter is entertaining.

I would recommend this book for someone mathematically inclined in their early teens or anyone in their mid teens or later. If you have a child capable of mathematical and/or logical thought who is getting turned off mathematics by the rigors and dullness of school then this volume may well turn the trick - I know it was influential in convincing me that it was my schooling and not my mind that had ruined my maths ability. I give it only four stars as it is now starting to show its age, otherwise it would have five.

Hexaflexagons and Mathematical diversions
This book is an amazing one and it is definetly recommended to the people who like math puzzles, games, or thought challenges. Also it is a great book to distract yourself. It is a book that you would like to keep in your shelf. Martin Gardner is a great writer and has other great books on many other different mathematical puzzles. ... Read more

Reviews (1)

I have never read a book so quickly
I received this book for Christmas 2003, by the 26th I only had 40 pages left. If you are looking for a book to improve your mathematical ability, this is not for you. If you like to think and wonder why things are the way they are, then this is the book for you. I found myself reading one section after another, chapter after chapter. From the reasons why pyramid schemes are destined to fail, what is the best way to pack boxes of belongings when moving house, when do you take the money and leave 'Who wants to be a Millionaire' and many more fascinating and thought provoking ideas and concepts. I liked the book so much, I bought the previous book 'Why do buses come in threes?' the same day I finished this one - and I have already read one third of that one and it is not even New Year yet. This book would make the perfect gift for anyone who likes to think! So if you think they think, I think you should get it! ... Read more

Book Description

Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ''Yu'' square, went on to a life of courtly comfort and fame.

Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization?

Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

Reviews (8)

No Math, but pretty anyway
This is a book about mathematical artifacts, but it has practically no mathematical content of its own. A casual reader who wants to gaze at these beautiful objects and come away impressed but with little understanding will find this a marvellous book.However, a mathematically inclined reader is not satisfied with someone declaring that an object has such-and-such a property, he wants to know WHY.

Chapter 1 of this book gives dozens of fascinating constructions, but for most of them not a shred of proof is offered that the arrays produced are the magic squares Pickover claims.It leaves me wondering whether or not Pickover could produce such proofs himself, even for the more simple constructions in the book.

Pickover describes some interesting computer experiments at the end of the chapter but seems completely stymied as to why they work.The demonstration is a lovely, but simple, piece of matrix theory that I would expect my first or second year Linear Algebra students to be able to perform.
He shows two "brute-force" proofs for the order 3 case, one by Hendricks and "another" by Johnson (at least here is an attempt at including a proof), but annoyingly seems unaware that the second is just a minor variation on the first.I wonder if Pickover actually tried to follow these proofs himself or if he just copied them for his book.

Mathematics is not a collection of statements that the hearer must accept on "authority", it is a systematic development of theory in which every statement can be, at least in principle, demonstrated by a logical argument.The mathematics is in understanding "why", not in the acceptance of fact.Without demonstration of the claims, all that is left is the shell with no life.Beautiful, like other shells we find along the shore, but not the genuine article itself.

I am reminded somewhat of Stephen Hawking's popularizations of physics in which the reader is deeply impressed with the beauty of the subject, but comes away knowing practically no actual physics to speak of, for the author carefully sealsthe machinery of physics from his reader and presents only the glamorous face.In the case of Hawking, however, the author's authority is unquestionable; I'm sure he could, if pressed, demonstrate every claim in his books from first principles.I suspect that Pickover could not.

Aside from a few excusable errors of fact, the book shares a serious omission with almost every book on magic squares that I have seen, in that it does not present what is surely the most elementary construction known for magic squares of any odd order, as the sum of a circulant and a back-circulant matrix.Even Pickover would be able to prove that this construction works, since the reason it works is extremely obvious.Given the connection of this construction to the very important subject of orthogonal Latin Squares, you would think a serious writer would devote some space to it.

Aside from all of the above, the material in the book is comprehensive and fascinating, drawing on a number of sources, displaying many artifacts that have titillated dabblers for millennia. As a museum piece I'd have to give the book an "A", but as a piece of mathematics, only a "D".

What fun!
OK, there were a couple of typos -- keeps you on your toes.Lots and lots of examples of different variations on the magic square theme -- and puzzles for the reader to solve.Some of those puzzles are quite easy and some are quite difficult and have yet to be solved by anyone.You can't be a mathphobe to read this book, but you don't need to be a math whiz either.Anybody who likes the challenge of a good crossword or crossnumber puzzle should like this.

Diverse collection
A magic square is an array of numbers in which the sums of numbers in rows, columns, and diagonals are equal. A magic square uses consecutive numbers from 1 to N.Here's an example,


4 9 2
3 5 7
8 1 6


This book is different from all others I've seen on the subject, and I don't know any other books that present the large range of patterns that you'll find here.The book also focuses on discoveries in the last few years. As Pickover says, the book is essentially an exhibit of magnificent forms discovered through the centuries. All sorts of historical and quirky-human aspects are also described.Centuries ago, people believed that magic squares to had special, magical powers....

an editor please
This book contains print and mathematical errors. A cute book but because of the math misprints [I refuse to believe the author cannot add]a shoddy publication very uncharacteristic of Princeton

Great book on pure mathematical fun
While I am writing this in late February, it is still a safe bet to conjecture that this is the best recreational mathematics book that will be published this year. Magic squares are a fascinating area of mathematics, and Pickover covers a great deal of ground in bringing the field up to date. A magic square is a square grid of numbers where the row and column sums are the same. They appear throughout history and the most famous person to create them was the immensely talented Benjamin Franklin.
Magic squares can be created using many different formulas, including the moves of a knight on a board, using operations other than addition, and the embedding of magic squares inside magic squares. If you have not followed the development of the field, you will be amazed at how many different ways they can be constructed.
Magic squares have also been extended to include magic cubes of three and four dimensions. The star of the book is John Hendrick, an incredible person who seems blessed with some form of magic as he creates ever more complicated magic structures. Hendrick uses only a programmable calculator in his searches for larger and more complex magic figures, which makes his work all the more remarkable. Additional magic structures are the star and circle, where the points of intersection are marked with numbers and the sums of the points along lines are equal.
Pickover writes with his usual style and straightforward simplicity in this book. The material is presented well and can be understood by anyone with a basic middle school mathematics background. This is a cool book! ... Read more

Book Description

Ross Honsberger has compiled another collection of miscellaneous gems from elementary mathematics, this time from sources the world over, and ranging from the latest International Olympiads all the way back to Euclid. Each one casts light on a striking result or a brilliant device and any reader with only a modest mathematical background will appreciate the ingenious solutions that are also presented. ... Read more