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Penrose Tiles To Trapdoor Ciphers, and the Return of Dr. Matrix

Martin Gardner
Mathematical Association of America
Publication Date: 
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Richard Vinson
, on

This revised reprint of a 1989 book is typical Martin Gardner. It is well written, has excellent references, is up-to-date, and is varied enough for almost anyone to find something that will hold their interest.

As the title suggests, the book contains a variety of topics, among which are: Penrose Tilings, Fractals, Surreal Numbers, The Oulipo, Induction, Trapdoor Ciphers, Ramsey Theory, Curiosities of various sorts, and the return of Dr. Matrix with a new puzzle. There are enough references given so that anyone interested in a particular topic can find sufficient additional materials to pursue that topic in detail.

The illustrations are well done, although I had trouble with two of the color plates (the colors were not distinct). As usual, the author presents problems that range from the not-quite-trivial to some that require the reader to pause and reach for the pencil and paper that we all know to keep handy.

The book is written at a level that will enable a good high school student to understand enough of the material to keep up her interest. On the other hand, it has enough depth to interest a professional mathematician, particularly when it discusses topics that go beyond one's particular research interests.

This book should be recommended for inclusion in high school and college libraries. It provides an easily accessible source of enjoyable materials that can be used for extra/supplemental reading for students. Like many of Gardner's book, it should be a part of the educational experience of prospective teachers of mathematics. The MAA is doing the mathematical community a real service by keeping these books in print.

Richard Vinson ( is a professor of mathematics at the University of South Alabama in Mobile, AL.