What is a Flexagon used for?

Flexagons are interesting puzzles made from folding strips of paper. You can make them from a wide variety of polygons: various triangles, quadrilaterals, pentagons, and so on. Once assembled, you flex them, i.e. fold them in different ways, in order to find new sides and rearrange the polygons.

What does the word Flexagon mean?

: a folded paper figure that can be flexed along its folds to expose various arrangements of its faces.

When were Hexaflexagons invented?

It all began in the fall of 1939. Arthur H. Stone, a 23- year-old graduate student from England, in residence at Princeton University on a mathematics fellowship, had just trimmed an inch from his American notebook sheets to make them fit his English binder.

How many types of Flexagons are there?

There are 18 such possible configurations for triangles with different colors, and they can be seen by flexing the hexahexaflexagon in all possible ways in theory, but only 15 can be flexed by the ordinary hexahexaflexagon.

How many sides does a Trihexaflexagon have?

Step 1: A Brief (Or Not So Brief) History on Flexagons Arthur Stone is credited with the discovery of the first flexagon: the trihexaflexagon. As denoted by the prefix, it has three sides. He had bought his binders in the United States and his paper in the United States.

Is Flexagon a word?

This shows grade level based on the word’s complexity. a three-dimensional figure having polygonal faces that is constructed from a folded sheet of paper in such a way that different faces are exposed when the figure is flexed along its folds.

Who invented Hexaflexagons?

Arthur H. Stone invented the Hexaflexagon and started a flexagon committee with his friends Tuckerman, Feynman, and Tukey (who all later became well-known in their respective fields).

How is a Trihexaflexagon created?

1. Pinch two triangles together so the fold between them points towards you. Push the other two triangles in from the other side, then open the flexagon out from the point nearest you. If it does not open, try a different pair of triangles.

How do you make a 2x Hexaflexagon?

Start by pinching two triangles together along one of the edges. Do the same on the opposite side and push the corners toward each other. Open opposite triangles. Take the center of these triangles and open them to reveal the face of your hexaflexagon.

Who are the members of the Princeton Flexagon Committee?

Stone’s colleagues Bryant Tuckerman, Richard Feynman, and John Tukey became interested in the idea and formed the Princeton Flexagon Committee. Tuckerman worked out a topological method, called the Tuckerman traverse, for revealing all the faces of a flexagon.

When was the flexagon introduced to the public?

Flexagons were introduced to the general public by Martin Gardner in the December 1956 issue of Scientific American in an article so well-received that it launched Gardner’s “Mathematical Games” column which then ran in that magazine for the next twenty-five years.

Why are there 3 extra configurations in flexagon?

The 3 extra configurations are impossible due to the arrangement of the 4, 5, and 6 tiles at the back flap. (The 60-degree angles in the rhombi formed by the adjacent 4, 5, or 6 tiles will only appear on the sides and never will appear at the center because it would require one to cut the strip, which is topologically forbidden.)

How are the faces of the hexaflexagon exposed?

Photos 7 and 8 show the process of everting the hexaflexagon to show the formerly hidden red triangles. By further manipulations, all six colors can be exposed. Once folded, faces 1, 2, and 3 are easier to find than faces 4, 5, and 6. An easy way to expose all six faces is using the Tuckerman traverse.