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.
Impossible?
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Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem ... Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment. -- J.T. Noonan Choice This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! ... This is another excellent book by Havil, following in the Martin Gardner tradition. -- Alan Stevens Mathematics Today Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers. -- John J. Watkins Mathematical Intelligencer Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer. -- Ray Bert Civil Engineering I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor. -- Blair Madore MAA Reviews
Synopsis
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.
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39 von 44 Kunden fanden die folgende Rezension hilfreich
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you may be a little too surprised by these surprises to be surprised
21. Oktober 2008
Von James H. Waters
- Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
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
james h waters phd
6 von 6 Kunden fanden die folgende Rezension hilfreich
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Intriguing Topics, Careless Editing
30. Mai 2011
Von Henry S. Valk
- Veröffentlicht auf Amazon.com
Format:Taschenbuch|Von Amazon bestätigter Kauf
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.
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.
12 von 15 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen
I liked what I saw so far.
30. September 2009
Von Peter Gacs
- Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
I am a mathematician, so my opinion is probably biased. This is the kind
of popular book on mathematics that would have appealed to me in my young age
and 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 the
author, this place seemed the easiest one to point out a computation error
that invalidates the proof of irrationality of log 2 in the appendix.
The correct computation will lead to a correct proof, but a different one, which
as expected, must use the uniqueness of prime factorization.
of popular book on mathematics that would have appealed to me in my young age
and 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 the
author, this place seemed the easiest one to point out a computation error
that invalidates the proof of irrationality of log 2 in the appendix.
The correct computation will lead to a correct proof, but a different one, which
as expected, must use the uniqueness of prime factorization.
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