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:
Review by Brian Clegg - See all reviews and Brian's online articles or subscribe free here

Comments

Beyond Belief - Helen Pearson *****

Apparently it comes as a surprise to many that medicine was not particularly scientific until the end of the twentieth century (to be honest, it's no surprise to me - we had a GP who used homeopathy in the 90s). Instead it was based on anecdotal guidance - the kind of thing that appeared to work. Evidence-based medicine has since improved the field, trying where possible to base decisions on evidence, ideally based on randomised controlled trials. The first part of Helen Pearson's book covers this well - though I think it's by far the least interesting part of what we discover. Instead what's truly fascinating is the rest of it, looking at a wide range of other fields where evidence was rarely properly used and that are only now starting to dip a toe in the water. These include social policy, policing, conservation, business and education. The main part of the book gives us examples of how bad these areas have been in terms of basing decisions on what's always been ...

The Infinite Book – John D. Barrow ****

Authors are often asked to review books on a topic they’ve written on themselves. The reasoning is sensible – they ought to know something about the subject – but there’s always that uneasy suspicion that there’s going to be a bit of bias creeping in. So I think it’s only fair to admit up front that I have written a book on infinity (of which more later). Infinity is a wonderful subject, because it’s intimately mind-bending (if the combination sounds paradoxical, that’s what infinity is all about) and gives you the chance to pull in all sorts of different concepts and assocations along the way, something Barrow does with great gusto. There’s a surprisingly large amount of coverage here for God, and for the universe, and the book jumps around from Aristotle to Hilbert’s Infinite Hotel (explained at great length), from the paradoxes of infinite sets to the paradoxes of time travel. Overall it’s an enjoyable journey that gives plenty of opportunity to be amazed and surprised. The...

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...

Search This Blog