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A topologist, a physicist, a data scientist, and a statistician walk into a room…
No this, is not the beginning of a joke, although it sounds like a good one! This is the beginning of a true story about the creation of a particularly interesting mathematical object called a hexaflexagon, which is something almost anyone can make and play with. Here’s an example of one:
The story of the flexagon is a remarkable story. It’s about creativity, collaboration, and the kinds of amazing things that happen when people work together across disciplines. It’s also particularly interesting to me because it starts – quite literally – with a throwaway idea: What can I do with this strip of paper?
In 1939 Arthur Harold Stone, an English mathematician, finished his studies at Trinity College Cambridge and went to Princeton, USA, to work on a PhD. Annoyingly, American notebook sheets did not fit exactly into his UK standard folder – and so he had a problem. His solution – trimming off an inch of paper from the bottom – led to a surplus of these regularly-sized paper strips, and so he began to play with them, folding them in various ways.
Stone found that by folding the paper into equilateral triangles and sticking, he could make an object called a flexagon – a paper model that folded flat but also had more faces that folded out. He found that he could make a trihexaflexagon (so called because it has six sides and three faces) and a hexahexaflexagon (six sides, six faces) – but naming flexagons is a very interesting question and not a completely consistent phenomenon even now (for example, some people use N-flexagons, and others hexa/tetra/octaflexagons).
Stone showed his models to his friends Bryant Tuckerman, Richard Feynman and John W. Tukey, some of whom you may have heard of! They formed the Flexagon Committee and began to investigate these intriguing new creatures. The excitement of flexagons lay in their hidden features; while they looked like flat polygons with just two sides, when “flexed” you could reveal more sides that folded out.
Fast forward more than 70 years, and people are still investigating the different types and features of flexagons today. Their flexibility and ability to reveal a surprise side or two, along with their accessibility, makes them attractive to anyone interested or curious about mathematics. We like them too – and have used one in a particularly punny way in our new book, The Primary Teacher’s Maths Journeybook. Throughout the book, teachers look in detail at model of maths teacher knowledge that happens to be hexagon shaped – and so we thought it would be a lovely visual pun to have a template for building a hexaflexagon at the back of the book with the model on it, too: a model-building activity of a more concrete nature.
Below you can download the template to our hexaflexagon design to try making one.
Download Hexaflexagon template
If you'd like to try building a hexaflexagon, then download the template of the design found in The Primary Teacher’s Maths Journeybook.
Join the conversation: You can tweet us @CambridgeMaths or comment below.