Nonplussed!: Mathematical Proof of Implausible Ideas by Julian Havil (PDF)

Description

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. Did you know 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.

User’s Reviews

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

⭐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.

⭐Another one of these books written by someone who feels that he does not have to express himself clearly, just “cleverly.” I, for one, resent having to figure out what an author is trying to say–clarity is everything!!!!. Mr. Havil needs to be informed that the rigor demanded in a textbook is not the same as that in a volume for the public at large.From the first chapter on the two coin problem, I knew I was in trouble when I could not figure out from the exposition what the correct answer is. After being put off by the notation on the tennis problems which I could not understand and which the author did not disdain to explain and daunted by the complex mathematics involved (despite the author’s assurance that some high school mathematics is all that is needed) I gave up.This type of conceited garbage writing about one of the greatest discplines is what has given mathematics the bad name it has. Perhaps, Mr. Havil should have beta-tested the book rather than rushing inconsiderately into print.In short, I looked foward to an entertaining and informative discussion of counterintuitiveness and I ended up regretting my purchase of the booik and my knowledge of its existence.Robert Allen

⭐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.

⭐Pretty good. I can’t totally follow all the math any more, but I can follow the logic and explanations. Fun book.

⭐Great book!

⭐This book is a valuable addition to a math-puzzler’s library, but contains some flaws on real-world data.For example, Havil shows, with impeccable mathematics, that if a given player has over 91.9643…% probability of winning any given point on his or her serve, that he or she has a higher likelihood of winning at the start of the game than when the score is 30-15 or 40-30. He uses this fact to back up a claim that “a high quality tennis player serving at 40-30 or 30-15 to an equal opponent has less chance of winning the game than at its start.” Again, this is predicated on that 92% or better percentage of winning any given point. But in real life, high quality tennis players, even when serving, against an equal opponent does not have this high a percentage of the points gained. Take 92% as the percentage. That would mean that over 70% of the time, the non-server would not even get one point (score of 15) during a given game. If anyone watches Wimbledon or the U.S. Open, one sees that such occurrences are rare, not common. As even Havil points out, it also implies that the server will win at least 99.9% of the games. But in high-level play, set scores of 6-3, 6-4, etc. are common. With 99.9% of the games being won by the server, 99.4% of sets would go into tie-break. That’s clearly not the case in the real world. But this discrepancy is needed in order to make the “paradox” that creates the “nonplussed” reaction.In the chapter on the calendar, Havil explains why the Christian feast commemorating Jesus’ ascension into Heaven never falls on a Sunday by claiming that that feast is also called Holy Thursday. It’s not. It’s Ascension Thursday. Holy Thursday, 42 days (six weeks) before Ascension Thursday, is the day before Good Friday, and commemorates the Last Supper.

⭐This was a good read, although the writing style could have been more precise at times. The choice oftopics 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 extensivemath 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.

⭐Julian Havil hat mich mit seinem Zweitwerk, “Impossible” schwer beeindruckt. Dass Mathematik von Paradoxien strotz, wusste ich schon, aber Havil hat sich besonders eklatante Beispiel ausgesucht, die einen total verblüffen. So auch in diesem Werk. Dass 2 x 2 glich 4 ist, wissen wir, aber Havil findet sogar hier verblüffende Ausnahmen. Allerdings ist es für einen Nicht-Mathematiker nicht immer ganz leicht, seinen Argumenten zu folgen. Einfach drüberlesen geht nicht. Wer sich aber die Mühe macht, seine Lieblingskapitel durchzuarbeiten, der wird reich belohnt. Und kann auch noch interessierte Bekannte mit Havils Erkenntnissen verblüffen.

⭐

⭐The book would be a perl. However, it cannot be read in kindle format. Formulas are unreadable and figures require to be enlarged every

⭐Failed copy with pages 48-49, 52-53, 56-57, 60-61, 64-65, 68-69 simply not printed.Hope Julian Havil will read this someday.

⭐Ce livre est très intéressant. A quand une traduction en français ? Les démonstrations ne sont pas toujours d’une grande clarté.

⭐

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