Math--the application of reasonable logic to reasonable assumptions--usually produces reasonable results. But sometimes math generates astonishing paradoxes--conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true: Conclusions that, for example, tell us that a losing sports team can become a winning one by adding worse players than its opponents. Or that the thirteenth of the month is more likely to be a Friday than any other day. Or that cones can roll unaided uphill. In Nonplussed!--a delightfully eclectic collection of paradoxes from many different areas of math--popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas.Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs. Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.
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Book Description
Editorial Reviews
Review
Nonplussed! is a collection of lovely paradoxes: facts that are provable logically but are nevertheless seriously counterintuitive...It is an exciting book. It should be in every...college library. It would even be the right gift for mathematicians and anyone who uses mathematics--economists, business analysts and many others--and indeed for anyone who would claim to be educated. -- Peter M. Neumann, Times Higher Education Supplement
This is a splendid collection of articles, inspired by Martin Gardner's writings. Old conundrums are given new twists and applications, newer perplexing ideas are described with panache. The forthcoming companion book has a high standard to maintain. -- John Haigh, London Mathematical Society Newsletter
It is therefore recommended that Julian Havil's headmaster award him further sabbatical leave for the purpose of producing a sequel to this welcome addition to the mathematical literature. -- Peter Ruane, MAA Review
A review of a book as good as this must either repeat the positive adjectives other reviewers have used, or require a very large thesaurus. Since I find myself in complete agreement with all of the following words from other reviews, I will repeat them immediately: marvelous, crystal-clear, great, amazing, stimulating, delightful, fascinating, strong, surprising, classic, interesting, eclectic, insightful, magnificent. That one book could encourage such gushing praise seems as unlikely as one book being able to cram in a great variety and depth of mathematical problems, colourful historical anecdotes, significant nods to ethno-mathematics, difficult but well-explained proofs, clear and engaging prose and beautiful diagrams. Yet Havil?s book succeeds on all accounts...The brilliant writing, the wonderful problems, the weaving together of past and future, games and discovery, and world number cultures will have you returning to this ageless book time and again. -- Phil Wilson, Plus Magazine
This fascinating expedition by Havil through some engaging and often surprising mathematical and statistical oddities is more demanding than the usual 'popular math book' it is billed...All topics are covered by an always carefully crafted mathematical exposition, not leaving out necessary preliminaries and providing rigorous proofs. -- J. Mayer, Choice
Even many high school students without a calculus background will benefit from the problems contained in the book. . . . The book contains a little algebra, some geometry, and a great deal of probability. It could serve as recreational reading for teachers as well as for student use in a probability course or courses following algebra 2. Mathematics clubs and teams would also find Nonplussed! useful. -- Paul Kelley, Mathematics Teacher
This is a fun book containing many diverse problems that I had not seen before but it also stimulates some genuinely interesting mathematical thought. Above all, this book highlights the 'frailty of the intuition we routinely use to guide us through our everyday lives' and that, in my mind, is no bad thing. -- Nathan Green, Mathematics Today
I recommend the book to everyone interested in entertaining mathematics. -- Christina Birkenhake, Mathematical Intelligencer
This book discusses such problems in a generally accessible way, but it does not shy away from using rigorous mathematical arguments to explain them. . . . Some of these topics are quite familiar, but even so I found the discussions clear and often learned some new and quite surprising tidbits. -- Stan Wagon, Mathematical Reviews
Those that spend their working lives avoiding mathematics by approaching their problems in all sorts of different ways will benefit from looking at this text, even if it involves following through but one single problem and its mathematical solution. -- C.J.H. Mann, Kybernetes
The book is perfect for independent or group study for students in advanced high school mathematics classes or university-level undergraduate mathematics classes. Selected chapters are suitable for discussion during professional development sessions aimed at engaging mathematics teachers in rigorous mathematics investigations and discussions. -- Anne Papakonstantinou, Mathematics Teacher
This lovely book will attract the attention of readers who are interested in recreational mathematics like mathematical puzzles and paradoxes. -- Yuri V. Rogovchenko, Zentralblatt MATH
Havil has an excellent mix of an interesting history of each topic and clear and lucid solutions to the problems. . . . Havil's strength is the historical background he gives to each topic and his style of writing which is so easy to read. . . . An interesting and challenging book well worth reading. -- John Sykes, Mathematics in School
This is a splendid collection of articles, inspired by Martin Gardner's writings. Old conundrums are given new twists and applications, newer perplexing ideas are described with panache. The forthcoming companion book has a high standard to maintain. -- John Haigh, London Mathematical Society Newsletter
It is therefore recommended that Julian Havil's headmaster award him further sabbatical leave for the purpose of producing a sequel to this welcome addition to the mathematical literature. -- Peter Ruane, MAA Review
A review of a book as good as this must either repeat the positive adjectives other reviewers have used, or require a very large thesaurus. Since I find myself in complete agreement with all of the following words from other reviews, I will repeat them immediately: marvelous, crystal-clear, great, amazing, stimulating, delightful, fascinating, strong, surprising, classic, interesting, eclectic, insightful, magnificent. That one book could encourage such gushing praise seems as unlikely as one book being able to cram in a great variety and depth of mathematical problems, colourful historical anecdotes, significant nods to ethno-mathematics, difficult but well-explained proofs, clear and engaging prose and beautiful diagrams. Yet Havil?s book succeeds on all accounts...The brilliant writing, the wonderful problems, the weaving together of past and future, games and discovery, and world number cultures will have you returning to this ageless book time and again. -- Phil Wilson, Plus Magazine
This fascinating expedition by Havil through some engaging and often surprising mathematical and statistical oddities is more demanding than the usual 'popular math book' it is billed...All topics are covered by an always carefully crafted mathematical exposition, not leaving out necessary preliminaries and providing rigorous proofs. -- J. Mayer, Choice
Even many high school students without a calculus background will benefit from the problems contained in the book. . . . The book contains a little algebra, some geometry, and a great deal of probability. It could serve as recreational reading for teachers as well as for student use in a probability course or courses following algebra 2. Mathematics clubs and teams would also find Nonplussed! useful. -- Paul Kelley, Mathematics Teacher
This is a fun book containing many diverse problems that I had not seen before but it also stimulates some genuinely interesting mathematical thought. Above all, this book highlights the 'frailty of the intuition we routinely use to guide us through our everyday lives' and that, in my mind, is no bad thing. -- Nathan Green, Mathematics Today
I recommend the book to everyone interested in entertaining mathematics. -- Christina Birkenhake, Mathematical Intelligencer
This book discusses such problems in a generally accessible way, but it does not shy away from using rigorous mathematical arguments to explain them. . . . Some of these topics are quite familiar, but even so I found the discussions clear and often learned some new and quite surprising tidbits. -- Stan Wagon, Mathematical Reviews
Those that spend their working lives avoiding mathematics by approaching their problems in all sorts of different ways will benefit from looking at this text, even if it involves following through but one single problem and its mathematical solution. -- C.J.H. Mann, Kybernetes
The book is perfect for independent or group study for students in advanced high school mathematics classes or university-level undergraduate mathematics classes. Selected chapters are suitable for discussion during professional development sessions aimed at engaging mathematics teachers in rigorous mathematics investigations and discussions. -- Anne Papakonstantinou, Mathematics Teacher
This lovely book will attract the attention of readers who are interested in recreational mathematics like mathematical puzzles and paradoxes. -- Yuri V. Rogovchenko, Zentralblatt MATH
Havil has an excellent mix of an interesting history of each topic and clear and lucid solutions to the problems. . . . Havil's strength is the historical background he gives to each topic and his style of writing which is so easy to read. . . . An interesting and challenging book well worth reading. -- John Sykes, Mathematics in School
From the Inside Flap
"Nonplussed!, as the title suggests, is a marvelous study of some two dozen choice mathematical problems that boggle the mind. Unlike so many books on recreational math, Havil doesn't hesitate to give crystal-clear proofs and their necessary equations. John Conway's great checker-jumping puzzle is here, along with amazing nontransitive betting paradoxes and other confounding results almost impossible to believe. No one interested in recreational mathematics on an intermediate advanced level should pass up this stimulating, delightful volume."--Martin Gardner"In Nonplussed!, his new book of fascinating discussions of mathematical questions, Julian Havil's literary signature is evident even without seeing his name on the cover. The presentation always displays his strong ability to weave together the historical with what is often a surprising mathematical twist, even for those problems that have been around long enough to be called classic. Nonplussed! will be a classic, too."--Paul J. Nahin, author of Dr. Euler's Fabulous Formula"Nonplussed!! is a very interesting and eclectic mix of paradoxes that has the potential to be a very useful and lasting contribution to popular mathematics."--Christopher J. Sangwin, author of Mathematics Galore"I greatly enjoyed this book and I imagine that anyone who liked high school math will too. Nonplussed! certainly succeeds in surprising-and in giving insightful proofs of the mathematical results discussed. It is a magnificent demonstration of how far even rather straightforward mathematics can take you. And by describing many of the historical characters involved and the problems that motivated them, it makes mathematics seem like an adventure."--Nick Huggett, author of Space from Zeno to Einstein
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Finally I have decided to 'get a web page' and, thanks to Amazon,the procedure is very easy. I will try to add to it as time passes. Apparently, in profile I resemble Vladimir Putin; hence the choice of the lead photo!
Customer Reviews
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Most Helpful Customer Reviews
23 of 25 people found the following review helpful
Format:Hardcover|Amazon Verified Purchase
This book will delight readers who like to get their hands into their math. Havil sticks to mostly elementary concepts, avoiding highly abstract fields that would lose most readers. When a subject could go too far afield, Havil warns about it and presents only the part the reader needs to know, citing original source references for the interested reader. He gives complete, understandable proofs of some startling statements--proofs that leave you understanding exactly how you got there. The great thing is that you can choose to work through these problems for yourself, verifying each step, or you can just follow along with his proofs and take on faith any simple algebraic rearrangements that he may have skipped over. Compared to Havil's earlier classic on Euler's Gamma Function, this one's a bit easier to read, with numerous short sections on a variety of topics.
One minor complaint is that I found some typesetting errors. One, ironically, occurs on page 49 where he uses the notation "!n" (the number of derangements of n objects) when actually he meant "n!" (the number of permutations of n objects). It's ironic because only two paragraphs later Havil warns that !n can be easily confused with n!, whereupon he adopts a new notation for !n. In the delightfully bizarre but challenging chapter on John Conway's Fractran, there are a few typos that might confuse that minority of readers who will actually try to go line-by-line through the explanation of the Fractran machine (p. 172), but if you're one of those people, discovering the errors will anyway prove your mastery.
One minor complaint is that I found some typesetting errors. One, ironically, occurs on page 49 where he uses the notation "!n" (the number of derangements of n objects) when actually he meant "n!" (the number of permutations of n objects). It's ironic because only two paragraphs later Havil warns that !n can be easily confused with n!, whereupon he adopts a new notation for !n. In the delightfully bizarre but challenging chapter on John Conway's Fractran, there are a few typos that might confuse that minority of readers who will actually try to go line-by-line through the explanation of the Fractran machine (p. 172), but if you're one of those people, discovering the errors will anyway prove your mastery.
25 of 30 people found the following review helpful
By O. De Vries
Format:Hardcover
The book of Julian Havil is certainly not easy reading. Perhaps I am a dummy, but at several pages I had to read over a paragraph several times before understanding its real meaning, but the result was always worth the trouble. The calculations itself are explained thoroughly and his way of highlighting different sidesteps are often eye-openers.
People loving Martin Gardner's articles in Scientific American, will certainly appreciate this book.
People loving Martin Gardner's articles in Scientific American, will certainly appreciate this book.
8 of 11 people found the following review helpful
Format:Hardcover|Amazon Verified Purchase
I read Impossibles first and really enjoyed it a lot. This was also enjoyable, but I found myself skimming over the proofs much of the time. I did not do that with Impossibles (but I don't remember there being as much). The problems discussed were ineresting, but I did not find myself telling my other geek friends about very many.
By Gary Sawyer
Format:Paperback
This was a good read, although the writing style could have been more precise at times. The choice of
topics was varied, and most of the chapters presented interesting topics, especially the Banach-Tarski paradox.
Through no fault of the author, several of the topics would not be very accessible to those without fairly extensive
math backgrounds. There were a couple of blatant errors of fact, which I cannot fathom not being caught by even a cursory proofreading. For example, in Chapter 7, he states, "if Q [the rationals] is countable and R [the reals]not so, then what has been added - the transcendental numbers - must not be countable." What you add to the rationals to get the set of real numbers is the irrational numbers (of which the transcendental numbers are but a subset). For a mathematical piece, even a light exposition, that was sloppy - and inaccurate. Picky? Perhaps, but there were a couple of those, and frankly, in a math book, even popular interest, that is inexcusable.
topics was varied, and most of the chapters presented interesting topics, especially the Banach-Tarski paradox.
Through no fault of the author, several of the topics would not be very accessible to those without fairly extensive
math backgrounds. There were a couple of blatant errors of fact, which I cannot fathom not being caught by even a cursory proofreading. For example, in Chapter 7, he states, "if Q [the rationals] is countable and R [the reals]not so, then what has been added - the transcendental numbers - must not be countable." What you add to the rationals to get the set of real numbers is the irrational numbers (of which the transcendental numbers are but a subset). For a mathematical piece, even a light exposition, that was sloppy - and inaccurate. Picky? Perhaps, but there were a couple of those, and frankly, in a math book, even popular interest, that is inexcusable.
0 of 1 people found the following review helpful
Format:Kindle Edition
Reproduction of the equations was so poor as to be difficult to read or follow them - at least in the version I purchased. I imagine they were reproduced as figures, rather than as type, which seems a serious mistake for a book of this sort.
0 of 1 people found the following review helpful
By G. Poirier
Format:Paperback
I have read a number of books of this type over the years. Some are a model of clarity and are truly a pleasure to read. At the other end of the spectrum, there are those that are seriously lacking in this regard and are a chore to go through. In the case of this book, I would place it closer to the latter end of the range. Consequently, I would agree with the prior reviewers who have expressed similar sentiments. More specifically, I often found myself bewildered at how some of the initial equations were set up since very little in the way of explanation was given. Much more space was devoted to going through calculations line by line - something which, in my view, is of much less importance. On the positive side, the author has addressed more than a dozen problems of different types, thus potentially appealing to readers with different interests. I my case, I found a few of these problems to be quite fascinating while in the case of several others, I had no interest whatsoever - the lack of clarity causing me to skim over the material, as in the case of a prior reviewer. Finally, I do agree with the author that the mathematics level for most of the problems is up to about the senior high school level; however, in a few cases, the mathematics is well beyond that.
Overall, I was rather disappointed with this book. Although clearly not ideal for the general reader, this book may appeal to serious math buffs with a very broad range of interests and perhaps a refined intuition to enhance their understanding of what the author is trying to convey.
Overall, I was rather disappointed with this book. Although clearly not ideal for the general reader, this book may appeal to serious math buffs with a very broad range of interests and perhaps a refined intuition to enhance their understanding of what the author is trying to convey.
Most Recent Customer Reviews
1.0 out of 5 stars
complete bewilderment
Another one of these books written by someone who feels that he does not have to express himself clearly, just "cleverly. Read more
Published on January 14, 2010 by Robert Allen
3.0 out of 5 stars
Mathematically Impeccable--Real World Flawed
This book is a valuable addition to a math-puzzler's library, but contains some flaws on real-world data. Read more
Published on July 8, 2007 by Charles Kluepfel
