Theoni Pappas
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Customer Reviews:
Total reviews: 9
Average rating: 3.5 of 5
A pathetic little book that could have been good 1 out of 5 stars.
56 of 64 people found this review helpful.
This book could have been good if the author had done a careful job of writing the text, and perhaps if the illustrations were original, and above all if the author had understood the material she was writing about. Sadly these are often not the case with this book.Rather, this book gives every sign of being essentially copied from bits of many dozens of other books. All the illustrations appear to be low-quality xerographic copies from other books (clearly used without any permissions).
But worst of all, the book is chock full of misstatements, misconceptions, and sentences that don't convey any meaning.
This book gives the non-expert reader the impression that he or she is learning something, but a great deal of the time this is just the illusion of learning.
I will list a few of the errors and illusory learning that I can readily find:
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p. 6: The illustration of the cycloid curve should show it to be in a vertical direction where one arch meets another; instead it is at 45 degrees to the vertical.
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p. 7: It is stated that when marbles are released in a cycloid-shaped container, they will reach the bottom at the same time. This phenomenon occurs for a bowl whose cross-section is an *inverted* cycloid, but that is omitted.
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p. 13: Both the "impossible tribar" and "Hyzer's optical illusion" are NOT mathematically impossible, contrary to what is written. (They can be constructed in 3 dimensions.) Twistors are mentioned but not defined, even in a rough, metaphoric way -- just not at all.
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p. 18: It is mentioned that pi cannot be the solution of an algebraic equation with integral coefficients, but there is no discussion in the book of what such an equation is.
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p. 19: Also, it is stated that the probability of two randomly chosen integers' being relatively prime is 6/pi. Not only should the correct number be 6/(pi * pi), but the idea of randomly choosing an integer is left completely undiscussed, although there is no known way to do this.
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p. 38: The Platonic solids (aka regular polyhedra) are discussed here, but although they are defined twice, neither definition is correct. (The author neglects to mention that the faces of such a solid must be *regular* polygons.)
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p. 45: The Klein bottle is discussed and illustrated here, but there is no mention that a genuine Klein bottle cannot be constructed in ordinary 3-dimensional space. (The familiar model of a Klein bottle depicted here is a self-intersecting version of the real Klein bottle, which does not intersect itself. This is much like the fact that a picture of a knot drawn in the plane must appear as if the knot intersects itself, though it does not do so in space.)
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p. 46: The illustration at bottom purports to show what the model of the Klein bottle would look like if it were sliced in half. The halves are erroneously shown as identical, but they should be mirror images of each other.
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p. 78: The title of this page is "Fractals -- real or imaginary?"
This is an entirely misguided question that will only confuse the reader. All mathematical concepts are real within mathematics, and do not exist (except as approximations) in the real world.
It's a worthwhile topic in the philosophy of mathematics, and could well have been introduced in this book, but it has nothing whatsoever to do with fractals per se.
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p. 91: Here the author attempts to describe a model of hyperbolic geometry (in a circular disk) devised by Henri Poincaré. However, she gets it exactly backwards, saying that objects get smaller as they approach the boundary of the disk.
(She may have been well-aware of how this model works, but her prose is at best completely ambiguous.)
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p. 96: Here it is stated that it has been proved that knots cannot exist in more than 3 dimensions. Apparently the author is unfamiliar with an extensive and thriving field of higher-dimensional knots. (For example, a sphere can be knotted in 4-dimensional space.)
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There are many, many more such gaffes, but I fear I have gone on too long. I just wanted to make it crystal-clear that this book is riddled with erroneous and vacuous statements.
