Skip main navigation

The history of flexagons

Learn about the history of flexagons and how chance can promote scientific research.
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.
Arthur called the collection of paper-toys flexagons
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!

So, you know now that flexagons were invented by the British mathematician Arthur Stone, while he was still a graduate student in math. Together with other notable mathematicians and physicists, John Tukey, Bryant Tuckerman and Richard Feynman they studied flexagons and the math behind them, and we’re going to follow in their footsteps.


As you saw, flexagons were discovered by chance. Do you know of other discoveries that were made by chance?

This article is from the free online

Flexagons and the Math Behind Twisted Paper

Created by
FutureLearn - Learning For Life

Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now