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When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka-the joy of discovery-that 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. And indeed the delights of this book are many and varied. 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 proof 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. Every fan of mathematical puzzles will be enthralled by The Moment of Proof. Indeed, anyone interested in mathematics or in scientific discovery in general will want to own this book.
I. RECALLING; 1. Reflections; 2. Hand in Hand; 3. Further Progression; II. COUNTING; 4. Interesting Numbers; 5. Tenpins, and Counting; 6. Outcast; 7. The Power of Two; 8. Divide and Conquer; 9. Set and Match; 10. Chance Encounter; III. BALANCING; 12. Cutouts; 13. Two Pearls; IV. NUMBERING; 14. New Numbers for Old; 15. Prime News; 16. The Unknown Division; 17. Secret Messages; V. WINNING; 18. Be Wise, Optimize; 19. The Play's the Thing
I recommend it to teachers and lecturers and as an inexpensive addition to libraries in schools, colleges and teacher training institutions. The Mathematical Gazette