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Mathematical Recreations: A Collection in Honor of Martin Gardner

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Recreational mathematics is a broad subject, and the definition of what is recreational is open to interpretation. In this book, Klarner made some excellent choices of material to include. The main topics are:

* Games
* Geometry
* Two-Dimensional Tiling
* Three-Dimensional Tiling
* Fun and Problems
* Numbers and Coding Theory

The list of contributors includes some of the biggest names in mathematics. Richard K. Guy in mathematical games, Adi Shamir, Ronald L. Rivest and Leonard M. Adleman in secure messaging; Solomon W. Golomb and Howard Eves in geometry; Ronald Graham, Branko Grunbaum, G. C. Shephard, Raphael Robinson and H. M. S. Coxeter in tiling; Donald Knuth and Ross Honsberger in fun problems and Donald Knuth and Neil Sloane in numbers and coding theory. The level of difficulty is on the higher end of the spectrum, yet most of the papers can be understood if read carefully.
Martin Gardner has earned many accolades. This book demonstrates one of the highest, as it is a consequence of a quiet call for papers for a book to be published in his honor. The fact that so many high caliber mathematicians wrote so many high quality papers is a tribute that very few people could even hope for.

Published in Journal of Recreational Mathematics, reprinted with permission.

First, a small correction. This collection of mathematical essays was assembled as a tribute to Martin Gardner, on the occasion (20 years ago!) of his retirement. This book was not edited by Gardner, but it is in the same spirit (and the same size) as his "Mathematical Games" books of his Scientific American columns, so it does make a nice companion volume.

There are lots of good things in this book, but the best is Doris Schattschneider's essay "In Praise of Amateurs," on the ways of tiling the plane with convex pentagons. Does this sound like an incredibly arcane, useless subject? Well, I suppose it is, but it's also a delicious story, and this volume is the only place where I have seen it told in full. There are 13 essentially different ways to tile the plane with convex pentagons. Many of these beautiful patterns were discovered by Marjorie Rice, a San Diego housewife with only a high school education. Furthermore, she discovered these designs years after it was "proved" that there were only eight ways. If you thought the aperiodic Penrose tiling of the plane was a fascinating discovery, you will want to read this essay, admire these 13 patterns, and ideally find a fourteenth.

This essay alone is worth the price of the book. While the rest of the book is not quite up to its standard, it too is quite worthwhile. There are essays by Scott Kim, Donald E. Knuth, H.S.M. Coxeter, Solomon W. Golomb, and many others, all clearly illustrated. The section on 3-dimensional tiling is also quite cool.