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What are flexagons?

Learn about the history of flexagons, the most important skill to enjoy flexagons, and how they have developed over time.
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It all started in 1939. Arthur Stone, a graduate student from England, packed his bag with math books and binders and left for Princeton University in America. During the evenings at Princeton, he went through the course material, but he had to trim his American letter size sheets to fit them to his A4 size English binder. Now, letter size sheets are slightly wider and slightly shorter than A4 sheets, so his trimming left him with quite a lot of strips of paper. Experimenting with these strips of paper and folding them in different ways, Arthur created paper toys. One hexagon shaped paper toy, when manipulated by a series of what is now called “flexes”, revealed some rather unusual and unexpected properties.
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Arthur called the collection of paper-toys flexagons
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and shared his discovery with his friends at Princeton: Bryant Tuckermann, Richard Feynman and John Tukey. Together they founded a “flexagon committee” to study the largely growing family of flexagons. Tuckerman was a graduate math student, Tukey a young mathematics instructor and Feynman a physics graduate student who would become a Nobel prize winner, famous for his contributions to particle physics, in particular for a series of so-called Feynman diagrams. Flexagon diagrams, used and invented by the Flexagon committee were Feynman’s inspiration for his particle physics diagrams. Our friends did not publish their fundamental work about flexagons. Creative laymen and excited mathematicians contribute pieces to the puzzle of discovering flexagons You are invited to join us!

A brief introduction to flexagons

What are flexagons? That’s quite a difficult question to answer as there are so many different kinds.

I suppose the best way to describe it is by its construction. A flat, paper template is folded into a model that supports more than two distinguishable faces. Even the Wikipedia description does not take into account many of the flexagons that have been discovered in the past years.

Skills you need to have to enjoy flexagons

The most important skill you have to learn in order to enjoy flexagons is how to flex the flexagon once it has been constructed. Flexing means exposing the different faces of the flexagon by some manual manipulation of the paper.

There can be many different flexes on a flexagon, each exposing new faces, patterns or structures.

The first flexagon discovery

The video above presents the first flexagon discovery. Watch the video to see how they were invented by the British mathematician Arthur Stone, while he was still a graduate student in math, and then studied by a group of students who all became notable mathematicians and physicists: John Tukey, Bryant Tuckerman and Richard Feynman.

Flexagons over time

Flexagons have come a long way since their invention and we are now in the position to look at them with perspective. When we do this, we can come to the conclusion that learning about flexagons from a historical perspective can be misleading, and can make it more difficult to understand some of the properties of new flexagons that are being studied today.

If you’d like to learn more about flexagons, check out the full online course, from the Davidson Institute of Science Education, below.