Have you ever made a tetraflexagon or hexaflexagon? [The animation above shows a hexahexaflexagon, being flexed to reveal its six faces.] The original flexagons were discovered about the year of my birth (1939), but became famous when Martin Gardner wrote them up in his Scientific American column on mathematical recreations. [They're best known from a collection of his columns published in hardback and paperback in 1959.] The most common types of flexagons are the tetraflexagon, which appears to be a square of paper that has been folded twice and then opened out, and the hexaflexagon, which appears to be a hexagonal sheet of paper which has been folded three times along diagonals and then opened out. Appearances are deceiving. As the animation above illustrates, the hexahexaflexagon can be pinched between the fingers and "flexed," to reveal six different sides! That's right, six different sides.

There are a number of on-line sources that will tell you all about them, how to make them, and how to flex them. For example, flexagons 1, flexagons 2, flexagons 3, flexagons 4, flexagons 5, and tetraflexagons. A flash animation of the flexing of a hexahexaflexagon can be found here. A movie of a hexahexaflexagon being flexed can be found here.

After making some hexahexaflexagons, are you ready for a real challenge, the incredible HeptaHexaFlexagon?

If you passively read some of these links, and then pass on, you will come away with nothing. Particularly if you have kids, print out one of these pages (almost all have instructions) and make a tetraflexagon or hexaflexagon. And then play with it! It's precisely in such play that learning begins and continues. Play is the origin of all science, the origin of all man's understanding of the world around us, an understanding that has reached breathtaking levels in 2008, and that the fundamentalists are so utterly terrified of.

Flxagons combine both art and science, because once you have made some tetraflexagons and hexaflexagons you will want to go beyond a simple marking of each new face as you find it with a penciled numeral, you will find yourself itching to decorate each new face in a distinctive and artistically pleasing way. Have at it... all you need is some sheets of paper you can cut into long strips, the scissors for the cutting, and a glue stick to hold the flexagon together once you get it folded. Go play....

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