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Playing with Infinity: Mathematical Explorations and Excursions Paperback – July 22, 2010
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You and a bunch of friends are points on the plane. Under what conditions can you take a small step that will simultaneously bring you closer to all your friends? (From the introduction)
What is it that makes the axiom about parallel lines different from all the others? (From Chapter 18)
Although the author is not concerned here with politics or history, occasional references to the fate of her pupils and their parents remind us that this masterpiece was created in occupied Hungary during the Second World War. In an understated way, it is a tribute to the human spirit.
My general impression of this book is that of a mathematical counterpart to Gamow's, "One, Two, Three ... Infinity" -- but not quite as good. Of course Gamow's work is such a masterpiece that "not quite as good" still leaves lots of room. And that is why this book is a gem in its own right. I recommend this book especially to high school students with a strong interest in mathematics.
So, why is the book not quite as good as Gamow's? For one thing it does not quite have the breathtaking sweep of Gamow. The other is that in the process of making things simple, Rozsa overdoes it at times. Concepts that great minds struggled with for centuries appear as child's play. The image of little ten-year-old Eva rediscovering the irrationality of the square-root-of-two all by herself seems a little strained. But then again -- maybe she did do it!
Have pen and paper handy because to really enjoy the book I found myself doing some of the "the reader can solve for himself..." stuff. Another point is that you can more or less read the chapters independently and in no particular order and still reap huge benefits from the material.
Thank God for Dover which still publishes this book. My copy is a 1976 edition. If you are interested in getting back in touch with things you may have long forgotten get this book.