Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs. Many mathematical results are very counterintuitive , so they seem paradoxical.
ISBN 13: 9780691120560
Here, Havil presents some of the simpler ones, and goes through the maths to show that they are true. About half of them are probability or statistical paradoxes, the rest range over geometric and numerical cases. I would have preferred, especially in the probability cases, a bit more on getting an intuitive feel for why these results are true, in addition to the mathematical demonstrations that they are true.
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But that aside, there is much here to amuse and inform. In The Irrationals , the first popular and comprehensive work on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them.
Fascinating and illuminating, this is a book for everyone who loves math and the history behind it. Please click the button below to reload the page. If the problem persists, please try again in a little while.
Mathematical Proof of Implausible No cover image. Read preview. Synopsis Math--the application of reasonable logic to reasonable assumptions--usually produces reasonable results. Read preview Overview. Watkins Princeton University Press, If we move from theoretical intelligence levels to real-world matters of the state of health of individuals, we approach the medical concept of stage migration and a realistic example of the Will Rogers phenomenon.
In medical stage migration, improved detection of illness leads to the fast reclassification of people from those who are healthy to those who are unhealthy. When they are reclassified as not healthy, the average lifespan of those who remain classified as healthy increases, as does that of those who are classified as unhealthy some of whose health has been poor for longer. In short, the phenomenon could cause an imaginary improvement in survival rates between two different groups. Recent examples of this have been recorded for example in the detection of prostate cancer I.
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Summary Math—the application of reasonable logic to reasonable assumptions—usually produces reasonable results. Read on the Scribd mobile app Download the free Scribd mobile app to read anytime, anywhere.
Book Preview Nonplussed! Is the rotated coin now head up or head down? Figure 1. A coin rolling around another fixed coin. Figure 2. The situation simplified.
Nonplussed!: Mathematical Proof of Implausible Ideas - Julian Havil - Google книги
When it is first seen, the result is indeed surprising — and the solution clever. Roger Bacon In this first chapter we will look at three examples of sport-related counterintuitive phenomena: the first two couched in terms of tennis, the third intrinsically connected with it.
Winning a Tournament The late Leo Moser posed this first problem during his long association with the University of Alberta. The situation if the new member plays his friend twice.
This gives a total probability of winning the prize of Now suppose that M chooses the seemingly worse alternative of playing T twice, then table 1.
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