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Rating: 
Summary: Good intentions, poorly done
Review: About me: I helped edit Arthur Engel's Exploring Mathematics With Your Computer and other math books. I looked forward to seeing a book presenting to the very young simple math ideas which are outside the school curriculum. I leave it to librarians and teachers to say how children react to this book; what I wish to point out are two instances where the mathematical knowledge conveyed by the author, not to mention of the editors and translators, is below par. On p. 16-17 we see perspective views of two walls of a house which have on them pictures whose true shapes are squares. One needs no expertise to see that something about these views is wrong. The laws of perspective enable one to say what it is. If you hold a camera straight and take a picture of a vertical square on a wall, the images of the horizontal sides can not be longer than the longer vertical side image. In the book they are much longer! A written discussion of pespective is in fact too difficult for early elementary grades. The proper way to discuss images with young children is by producing images of objects with a camera obscura, a box with a pinhole or lens in the middle of one side and frosted glass on the other. The LCD screen of a digital camera could also be used, except that it is too small and delicate. ------------ A later section of the book is devoted to the following kind of puzzle. Can we walk in one stretch along every block of every street of a village exactly once? Leonhard Euler pointed out, first, that this is impossible if there are more than 2 junctions where an odd number of streets come together, and second, that it is otherwise possible. The first statement can be derived in a way which even a third grader can understand. Every time we pass through a junction, two more of the blocks which meet at the junction become traversed. Thus, at a junction other than where we start or end our walk, we can finish off all the blocks only if the number meeting at the junction is even. The author devotes a number of pages to this puzzle but misses the opportunity to present Euler's simple but ingenious argument. Worse than that, he misquotes Euler by saying the walk is impossible if there are more than 3 odd junctions. This is true but does not imply that the walk is impossible on Euler's original example, the figure on the left of p. 66, which has 3 odd junctions.
Rating:
Summary: Good intentions, poorly done
Review: About me: I helped edit Arthur Engel's Exploring Mathematics With Your Computer and other math books. I looked forward to seeing a book presenting to the very young simple math ideas which are outside the school curriculum. I leave it to librarians and teachers to say how children react to this book; what I wish to point out are two instances where the mathematical knowledge conveyed by the author, not to mention of the editors and translators, is below par. On p. 16-17 we see perspective views of two walls of a house which have on them pictures whose true shapes are squares. One needs no expertise to see that something about these views is wrong. The laws of perspective enable one to say what it is. If you hold a camera straight and take a picture of a vertical square on a wall, the images of the horizontal sides can not be longer than the longer vertical side image. In the book they are much longer! A written discussion of pespective is in fact too difficult for early elementary grades. The proper way to discuss images with young children is by producing images of objects with a camera obscura, a box with a pinhole or lens in the middle of one side and frosted glass on the other. The LCD screen of a digital camera could also be used, except that it is too small and delicate. ------------ A later section of the book is devoted to the following kind of puzzle. Can we walk in one stretch along every block of every street of a village exactly once? Leonhard Euler pointed out, first, that this is impossible if there are more than 2 junctions where an odd number of streets come together, and second, that it is otherwise possible. The first statement can be derived in a way which even a third grader can understand. Every time we pass through a junction, two more of the blocks which meet at the junction become traversed. Thus, at a junction other than where we start or end our walk, we can finish off all the blocks only if the number meeting at the junction is even. The author devotes a number of pages to this puzzle but misses the opportunity to present Euler's simple but ingenious argument. Worse than that, he misquotes Euler by saying the walk is impossible if there are more than 3 odd junctions. This is true but does not imply that the walk is impossible on Euler's original example, the figure on the left of p. 66, which has 3 odd junctions.
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