Sangaku Flexagon

(Sangaku, from

In the course of writing my chapter synopses of the Martin Gardner Colossal Book of Mathematics, I decided that I wanted to make some flexagons. My net search turned up, which has some very nice free artwork for downloading. What I found most interesting, though, was that one of the patterns was for a sangaku flexagon. Sangaku was the Japanese equivalent of western calculus, discovered about 10 years before calculus appeared in Europe. It was practiced by the upper educated class strictly for its own sake, using wooden Chinese blocks of fixed area to solve advanced math problems. The thing is, the Japanese never found an application for these solutions, instead painting them on wooden planks to be hung up inside of Shinto shrines, dedicated to one of the local gods. I first learned about sangaku while reading volume 38 of the Q.E.D. manga. I’ve been interested in it ever since. Unfortunately, it seems that the sangaku craze never made it down to the southern end of Kyushu, because none of the big shrines down here have ever located sangaku planks in their inventory.

So, this flexagon may be the closest I’ll get to it.

As a quick note, flexagons are folded strips of paper in a hexagonal shape. If you pinch one corner and pull the opposite one, you can turn it inside out to reveal a third face.

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