Impossible?: Surprising Solutions to Counterintuitive Conundrums by Julian Havil (PDF)

Description

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable—and all of it mathematically irrefutable.Whenever Forty-second Street in New York is temporarily closed, traffic doesn’t gridlock but flows more smoothly—why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion—how is this possible? What does the game show Let’s Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐i warn the potential purchaser that this may not be quite what you expect. There is a demand for substantial mathematical sophistication – which was a little beyond my level (i do have a doctorate, but not in math, and had to stop taking math courses after my sophomore year in college because matrix algebra was about all i could handle). i don’t doubt that the book is delightful for those strong in math and i probably would give it 5 stars except that the title strikes me as a bit misleading. probably your average college graduate would not know enough to find these conundrums counterintuitive, and the solutions, likewise, are probably not much more surprising than that the conundrums are supposedly common-sensical. not a criticism of the material, more of the packaging.james h waters phd

⭐I am a math teacher searching for interesting examples to share with my students and fellow teachers. I recently purchased seven books on the topics of interesting math problems and puzzles, and, having skimmed them all and carefully read several of them, this is by far my favorite. I am very glad I purchased this book, which is the reason for the five star review. I have to agree with some of the other reviewers, however, that there are several typos that make the text much more difficult to read than it would otherwise be. I wanted to post an error here that I didn’t see mentioned in other reviews, in case it helps someone. In Ch 6, the Seven-Hat Problem, the list of 16 codewords (binary vectors of length 7) has two pairs of duplicates. If you read the chapter, you realize this is not possible. The codewords 0101110 and 1011010 are both listed twice; I believe a correction is the to replace the duplicates with 0110010 and 1100011.

⭐As expected from this author, the topics are well chosen and the counter-intuitive results intriguing.However,contrary to my experience with Havil’s earlier books, “Impossible” seems to reflect hasty preparation and/or careless editing, hence the lower rating. An earlier review referred to the error in the proof of the irrationality of log2. To this can be added a number of others. For example: wrong signs in the Taylor expansions of sinx and cosx (p.226);numerous P(n-k,k)instead of P(n-k-1)in the coin toss discussion (p.97); log n – 2/3 instead of log n -3/2 (p.101);over-counting by a factor 3! in the mathematical expression for the number of ways of picking one pair(not two pairs as stated)in a poker hand, and the omission of -40 and -1098240 in the last line of the odd card discussion (p.106). While It should be emphasized that this is not a book for the casual reader,even the reader with some measure of mathematical sophistication will be frustrated by such errors and misprints;certainly, an unnecessary impediment to what could be a enjoyable journey for one seriously interested in mathematical conundrums.

⭐fun book. well written, well organized, interesting selection of topics. if you enjoy recreational mathematics and logic puzzles, buy and enjoy.

⭐I am a mathematician, so my opinion is probably biased. This is the kindof popular book on mathematics that would have appealed to me in my young ageand seems still very enjoyable and instructive (I have only skimmed it so far).The main reason for my review is that, the book not giving an email address for theauthor, this place seemed the easiest one to point out a computation errorthat invalidates the proof of irrationality of log 2 in the appendix.The correct computation will lead to a correct proof, but a different one, whichas expected, must use the uniqueness of prime factorization.

⭐This is an interesting and thought-provoking book that presents a series of mathematical problems and puzzles, the answers to which are often surprising. It is a book from which most people (who read it thoroughly) would learn about some interesting areas of mathematics, and discover new ways to look at some perhaps already-familiar topics.Understanding much of what the author is saying requires some background in math, but definitely not a degree in the subject. An introductory course in calculus would be helpful, because the book does use lots of simple calculus, and some familiarity with basic probability ideas would also be good to have. (I should admit, however, that I didn’t fully understand either of the last two short chapters, so there are some areas that are more advanced.) Someone with less of a math background would still be able to understand some of the problems, at least partly (for instance, anyone who has played poker would be able to understand the gist of what he shows about the effect of wild cards) and get something out of the book, but would have a hard time following many of the series of equations – which are used to demonstrate what the author is saying and which help to explain the reason behind a surprising result.There are, unfortunately, a number of errors in some of the mathematical expressions and equations, which made the book more difficult and frustrating to read: sometimes, I thought I was misunderstanding something, when the problem was that the algebra was wrong. There are also some places where the author’s explanation is too short, isn’t clear, or where an equation doesn’t reflect what is said in the text. This seems like it would be more confusing to a reader with a less-advanced background.Despite these reservations, I still found the book to be worth reading. Mostly, it isn’t fast or easy reading, but it’s a book that taught me a few things, often stimulated my thinking, and I still find myself pondering the implications of some of the chapters.

⭐There are errors everywhere and many things are obscure. You simply can’t read this book all the way through. You can pick some pieces here and there though.

⭐Il secondo libro di “finti paradossi matematici” di Julian Havil, dopo

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⭐Nonplussed!

⭐, ha l’allitterativo sottotitolo “Surprising Solution to Counterintuitive Conundrums”. Anche qui i vari capitoli presentano fatti matematici più o meno noti che a prima vista lasciano perplesso il lettore, anche se non digiuno di matematica, ma che sono assolutamente veri. Il livello tecnico dei vari capitoli varia molto: temi come il teorema di Goodstein e il paradosso di Banach-Tarski sono a livello universitario, mentre la differenza tra conoscenza mutua e conoscenza comune, la legge di Benford, il paradosso di Simpson oppure il paradosso degli ascensori che vanno sempre in direzione opposta sono alla portata di chi abbia una formazione matematica a livello della scuola superiore.Come sempre, Havil trova il giusto equilibrio tra la parte matematica “seria”, quella che in genere viene sempre sottintesa nei libri classici di divulgazione matematica, e la parte per così dire più ricreativa, dove i risultati vengono presentati per stupire con gli effetti speciali. In questo modo il lettore può scegliere fino a che livello approfondire, cosa che non succede certo molto spesso.In definitiva, un ottimo libro sia per la didattica che per i curiosi della matematica!

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