Nonplussed!: Mathematical Proof of Implausible Ideas

Első borító
Princeton University Press, 2007 - 196 oldal

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.


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Real proofs of a selection of nonintuitive, college-level, recreational math results, half of them involving probability. Not a fat book, but digesting every equation would make for a long reading time. Teljes értékelés elolvasása


Three Tennis Paradoxes
The Uphill Roller
The Birthday Paradox
The Spin of a Table
Conways Chequerboard Army
The Toss of a Needle
Torricellis Trumpet
Parrondos Games
Friday the 13th
The InclusionExclusion Principle
The Binomial Inversion Formula
Surface Area and Arc Length

Nontransitive Effects
A Pursuit Problem

Más kiadások - Összes megtekintése

Gyakori szavak és kifejezések

Népszerű szakaszok

1. oldal - I daresay you haven't had much practice," said the Queen. "When I was your age I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.
vii. oldal - Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.) I concentrate toward them that are nigh, I wait on the doorslab.
xi. oldal - He that hawks at larks and sparrows has no less sport, though a much less considerable quarry, than he that flies at nobler game: and he is little acquainted with the subject of this treatise— the UNDERSTANDING— who does not know that, as it is the most elevated faculty of the soul, so it is employed with a greater and more constant delight than any of the other.
xi. oldal - Mistake not this for a commendation of my work; nor conclude, because I was pleased with the doing of it, that therefore I am fondly taken with it now it is done. He that hawks at larks and sparrows, has no less sport, though a much less considerable quarry, than he that flies at nobler game: and he is little acquainted with the subject of this treatise, the Understanding, who does not know, that as it is the most 'elevated faculty of the soul, so it is employed with a greater and mere constant delight...
vii. oldal - Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. — WS ANGLIN, "Mathematics and History" 00 An old couple like that, the man thought, acting like kids.

A szerzőről (2007)

Julian Havil is a former Master at Winchester College, England, where he taught mathematics for more than thirty years. He is the author of Gamma: Exploring Euler's Constant and Impossible?: Surprising Solutions to Counterintuitive Conundrums (both Princeton).

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