The Moment of Proof

Mathematical Epiphanies

Donald C. Benson

331 pages, parution le 01/05/2001

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Résumé

In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka - the joy of discoverythat mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. The book is packed with intriguing conundrums - Loyd's Fifteen Puzzle, the Petersburg Paradox, the Chaos Game, the Monty Hall Problem, the Prisoners' Dilemma - as well as many mathematical curiosities. We learn how to perform the arithmetical calculation called "casting out nines" and are introduced to Russian peasant multiplication, a bizarre way to multiply numbers that actually works. The book shows us how to calculate the number of ways a chef can combine ten or fewer spices to flavor his soup (1,024) and how many people we would have to gather in a room to have a 50-50 chance of two having the same birthday (23 people). But most important, Benson takes us step by step through these many mathematical wonders, so that we arrive at the solution much the way a working scientist would - and with much the same feeling of surprise.

Contents

Acknowledgments
Introduction 1

I Recalling

1 Reflections 5
2 Hand in Hand 13
3 Further Progression 23

II Counting

4 Interesting Numbers 41
5 Tenpins, and Counting 57
6 Order and Reorder 71
7 Outcast 89
8 The Power of Two 101
9 Divide and Conquer 123
10 Set and Match 137
11 Chance Encounter 149

III Balancing

12 Cutouts 167
13 Seesaw, Marjorie Daw 185
14 Two Pearls 197

IV Numbering

15 New Numbers for Old 209
16 Prime News 227
17 The Unknown Division 237
18 Secret Messages 259

V Winning

19 Be Wise, Optimize 277
20 The Play's the Thing 293

Notes 311
References 319
Index

L'auteur - Donald C. Benson

Donald Benson - Professeur émérite de mathématiques à l'Université de Californie

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Donald C. Benson
Parution	01/05/2001
Nb. de pages	331
Format	18,5 x 23,3
Couverture	Broché
Poids	705g
Intérieur	Noir et Blanc
EAN13	9780195139198
ISBN13	978-0-19-513919-8