Skip to main content

The Secret World of Flexagons - Scott Sherman, Yossi Elran and Ann Schwartz ***

A great book for the right audience. When I was a teenager I loved Martin Gardner's Mathematical Puzzles and Diversions books. They combined mathematical oddities, such as there being more than one size of infinity, with numerical tricks and some physical maths-based objects, most notably flexagons. As someone who is physically inept, I never got much beyond a basic hexaflexagon, but these paper-based three dimensional structures that could change shape when manipulated, a bit like more sophisticated versions of paper fortune tellers, were fascinating.

Now we have a chunky, large format title exploring flexagons in far more depth. The first part of the book takes us into different flexagon structures and the range of possibilities enabling flexing. Some of these require quite sophisticated manipulation of the paper structure (which I did struggle with somewhat, being clumsy). Each flexagon type comes with a flat template to reproduce. These are sometimes quite small and for me benefited from blowing up a bit to make them more practical to manipulate, though many are reproduced larger later in the book.

Having got past the basics, the authors introduce more and more complex flexes (who is for a Möbius flip flex?), before exploring the culture that has built up around flexagons, such as naming conventions and 'pinch state diagrams', which use network diagrams to show how the different transformations are linked. We also get an exploration of the relationship between flexagons and group theory, some maths theory specifically built around flexagons, and the links between flexagons and topology. The final section, 'fun with flexagons' looks at combining flexagon structures with art work to give a more impressive visual impact.

This book will be hugely appealing if this is your thing. I'm giving it three stars, which my rating system describes as 'good solid book, worth reading if you are interested in the topic', not to say that it's a mid-ranking book, but rather that I suspect there are many popular science/maths readers it won't appeal to. I confess I did lose my interest in much of recreational maths as I got older, but if you find the concepts here get you excited, you absolutely need this book.

Paperback:   
Kindle:  
Using these links earns us commission at no cost to you
These articles will always be free - but if you'd like to support our online work, consider buying a virtual coffee or taking out a membership:
Buy me a coffee
Review by Brian Clegg - See all reviews and Brian's online articles or subscribe free here

Labels

Labels:

Comments

Post a Comment

Popular posts from this blog

Target Earth – Govert Schilling *****

I was biased in favour of this great little book even before I started to read it, simply because it’s so short. I’m sure that a lot of people who buy popular science books just want an overview and taster of a subject that’s brand new to them – and that’s likely to work best if the author keeps it short and to the point. Of course, you may want to dig deeper in areas that really interest you, but that’s what Google is for. That basic principle aside, I’m still in awe at how much substance Govert Schilling has managed to cram into this tiny book. It’s essentially about all the things (natural things, I mean, not UFOs or space junk) that can end up on Earth after coming down from outer space. That ranges from the microscopically small particles of cosmic dust that accumulate in our gutters, all the way up to the ten kilometre wide asteroid that wiped out the dinosaurs. Between these extremes are two topics that we’ve reviewed entire books about recently: meteorites ( The Meteorite Hunt...
Post a Comment
Read more

The Decline and Fall of the Human Empire - Henry Gee ****

In his last book, Henry Gee impressed with his A (Very) Short History of Life on Earth - this time he zooms in on one very specific aspect of life on Earth - humans - and gives us not just a history, but a prediction of the future - our extinction. The book starts with an entertaining prologue, to an extent bemoaning our obsession with dinosaurs, a story that leads, inexorably towards extinction. This is a fate, Gee points out, that will occur for every species, including our own. We then cover three potential stages of the rise and fall of humanity (the book's title is purposely modelled on Gibbon) - Rise, Fall and Escape. Gee's speciality is palaeontology and in the first section he takes us back to explore as much as we can know from the extremely patchy fossil record of the origins of the human family, the genus Homo and the eventual dominance of Homo sapiens , pushing out any remaining members of other closely related species. As we move onto the Fall section, Gee gives ...
Post a Comment
Read more

The Language of Mathematics - Raúl Rojas ***

One of the biggest developments in the history of maths was moving from describing relationships and functions with words to using symbols. This interesting little book traces the origins of a whole range of symbols from those familiar to all, to the more obscure squiggles used in logic and elsewhere. On the whole Raúl Rojas does a good job of filling in some historical detail, if in what is generally a fairly dry fashion. We get to trace what was often a bumpy path as different symbols were employed (particularly, for example, for division and multiplication, where several still remain in use), but usually, gradually, standards were adopted. This feels better as a reference, to dip into if you want to find out about a specific symbol, rather than an interesting end to end read. Rojas tells us the sections are designed to be read in any order, which means that there is some overlap of text - it feels more like a collection of short essays or blog posts that he couldn't be bothered ...
Post a Comment
Read more