Serious Fun with Flexagons: A Compedium and Guide

Les Pook
Publisher:
Springer
Publication Date:
2009
Number of Pages:
329
Format:
Hardcover
Series:
Solid Mechanics and Its Applications 164
Price:
129.00
ISBN:
9789048125029
Category:
Monograph
[Reviewed by
Collin Carbno
, on
12/30/2009
]

This book comes across as a sort of encyclopedia or a classification of flexagons. As such, the one real strength of the book is that numerous kinds of flexagons that are covered.

While mathematically I found the flexagon information exciting, the descriptions somehow failed to capture my imagination. For a start, I often found it difficult to grasp the significance of much of what the author was stating. For example, “The first two topological invariants for an ideal vertex ring of regular polygons are the same as those for an ideal edge ring of identical regular polygons but the third is different” is an interesting statement, but surrounding discussion wasn’t really enough to fully convince. Pook gives a lot of mathematical information on the flexagons in question, but he does not give the supporting arguments and proofs so that one can actually believe and understand. Thus, I was left wondering whether he determined these statements experimentally by building models, by finding proofs, or from the work of others.

The book claims to have more than 100 designs for constructions of various flexagons, many of them new to the world. Although I didn’t count them, it is true that the book is filled with various flexagon designs. It took me over an hour, however, to figure out how to get the first simple flexagon made, as the instructions and notation for creating the flexagons did not seem that well explained. No doubt, an experienced flexagon builder, more familiar with the notation, would have no problem following this sort of construction, and I found building the second and third ones easier. Thus, if you are a novice flexagon builder, looking for designs, you would be better off just grabbing flexagon information from the internet. The more serious researcher, however, will find this book an amazing resource for various kinds of flexagons.

I found the diagrams in the book adequate but too small and the 3-dimensional photographs of the finished flexagons were of surprisingly poor quality and shading resolution. If this was a \$9.99 book this might be acceptable, but given the actual price, it is not.

In all fairness to the book, it has a wonderful index, and the author has put intense amount of thought into how to classify and organize the various categories and properties of the flexagons. I’m sure this book will remain a reference book of choice in the subject of flexagons for a long time. But if you looking for a book to have some fun with some interesting constructions, and hope to learn a little mathematics on the side, I’m think you find this book disappointing. If you are looking for some sort of “Encyclopedia of Flexagons” this flexagon book appears to be the best on the market.

Collin Carbno is a specialist in process improvement and methodology. He holds a Master’s of Science Degree in theoretical physics and completed course work for Ph.D. in theoretical physics (relativistic rotating stars) in 1979 at the University of Regina. He has been employed for nearly 30 years in various IT and process work at Saskatchewan Telecommunications and currently holds a Professional Physics Designation from the Canadian Association of Physicists, and the Information System Professional designation from the Canadian Information Process Society.