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Half a Century of Pythagoras Magazine

Alex van den Brandhof, Jan Guichelaar, and Arnout Jaspers, editors
MAA Press
Publication Date: 
Number of Pages: 
MAA Press Spectrum
[Reviewed by
Tricia Muldoon Brown
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Half a Century of Pythagoras Magazine is a compilation of problems and articles found in the Dutch magazine established in 1960. The first version of this book was published in 2011 and the current is the English translation. Pythagoras is intended for a high school audience, but the cleverness of the puzzles and the historical details give a somewhat broader appeal for this book.

The book is divided into seven chapters, including a solution set in Chapter 7. The first and sixth chapters contain brainteasers and so-called “Dionigmas”, named after the Dutch mathematician who created these puzzles, Dion Gijswijt. The brainteasers found in Chapter 1 are short puzzles, explained quickly with two to three sentences and often with small illustrations. These puzzles are quite good for exercising creativity, as they are designed to have simple, elegant solutions that do not require advanced mathematics. The level of difficulty varies, but for most experienced mathematicians the puzzle would provide only a short diversion.

Similar to the brainteasers, Dionigmas are mathematical puzzles meant to be solved using basic techniques and ingenuity. The puzzles and their solutions tend to be slightly longer than those in the first chapter and can often feel paradoxical at first. For example, in the tradition of classical dissection problems, the third Dionigma, called Cut and Paste, directs the reader to “Cut both figures into two pieces and rearrange the four pieces to form a square.”

A first strategy would be to separate the figures preserving each interior square. However, the reader can quickly see that a square with integer side lengths is impossible, so another strategy must be used.

Between these two chapters of puzzles are found four chapters of articles, entitled “Puzzles, Games, and Strategy,” “Mathematics and Art,” “Geometry,” and “Numbers”. Each chapter contains articles on its title subject interspersed with related problems for the reader. The articles are very diverse, covering mathematical concepts from topology, discrete mathematics, number theory, and analysis, among others.

One appeal of the book for a student or novice mathematician is that the reader to start directly into these articles with very little mathematical background. But the articles have other strengths. The historical details provide a wonderful frame of reference for the reader and give a depth of human interest to the mathematics. Numerous mathematicians, artists, and craftsmen are discussed in conjunction with their mathematical interests. An index cataloging these people would be a welcome addition in future versions of this text.

Overall, Half a Century of Pythagoras Magazine is very readable and appropriate for students and recreational puzzlers as well as for teachers looking for interesting historical examples for the classroom. The English translation is well done and just enough background is provided to allow readers to understand the problems without referring to external sources.

The real weakness of the book is the lack of transition between articles in Chapters 2 through Chapter 6. There is no transitional language from one article to another, which can be quite jarring if a reader tries to read straight through a chapter. Headings are also misleading, as some articles contain several parts, each with their own heading. One must look for a small symbol to identify a switch from one article to another. Further, while provided in the bibliography, authors of articles are not associated with their work within the text. The readability would have been much improved if these were placed within the text to demonstrate the progression from one article to another.

Tricia Muldoon Brown ( is an Associate Professor at Armstrong State University with an interest in commutative algebra, combinatorics, and recreational mathematics.

1. Brainteasers
2. Puzzles, Games, and Strategies
3. Mathematics and Art
4. Geometry
5. Numbers
6. Dionigmas
7. Solutions
About the Editors