When I was in college I tutored a high school student in mathematics for three years. I took it as a personal challenge to create widely varied methods of explanation and practice to get the material not just to stick, but to be understood and retained in a flexible way. When we were doing geometry, one of my attempts was physical instantiations of triangles and quadrilaterals with dowels and rubber tubing. All the individual pieces plus measurements are after the cut!
Time for that middle-school-era “flexagon” I talked about. Because I recently learned how to make them, I present it in animated GIF form.
To flex from one face to the next, you fold the long edges away from you and open down the middle. When 1 and 2 are showing, 1 will not open but 2 will reveal 3. When 2 and 3 are showing, 2 will open to 1 and 3 will open to 4. Finally, as you would expect, when 3 and 4 are showing 3 opens to 2 and 4 does not open.
Of course, after making lovely schematics for you, I remembered to do a search to try to find this. It’s a tetra-tetraflexagon, known since at least 1961. I think my instructions still add something, but I’ll put them under a cut.
Meanwhile, I made a new one without numbers. Unfolded it looked as follows:
And here’s another animation!
At the Sew-Op, we have a lot of fabric that is too small to sew with, unless you are extremely dedicated. In looking for things that can be done with very small scraps, I found many projects that use Mod Podge to glue fabric to a number of different surfaces. With the idea that, project in hand, we might be able to donate our fabric to a good home (a local art gallery that holds classes and after school programs), I decided to test this Mod Podge theory.
I used ordinary cotton calico, the kind sold for quilting. I have some doubts that Mod Podge would work terrifically well to glue anything very heavy or thick. I cut pieces to wrap around two binder clips and cover a promotional magnet, brushed Podge on the surface of the item, pressed the fabric onto it (this required trimming to fit in all cases, more so for the binder clips), and brushed more Podge onto the surface of the fabric.
As you can see, it worked beautifully, with the caveat that the color of the base shows through the fabric a bit. On the other hand, the glue made the fabric sparkle a bit, which was an unexpected bonus.
If you are disappointed in the post so far, never fear, there’s more. Recently a video was going around about flexagons. It made me think of the old fortune tellers we made in grade school (I’ve also heard them called cootie catchers) and I decided to make one. I was ambitious and cut out pieces for a dodecahexaflexagon (twelve faces, each a hexagon, two of which show at any given time), but came to my senses and made a trihexaflexagon first. I cut six equilateral triangles of each of three decorative papers, two inches on a side, and a bunch of half inch squares of plain paper for the hinges. I glued them together using rubber cement, following the instructions on the Flexagon Portal, with only a front side on one end. After folding the whole thing up I glued the back on.
Changing from the second face to the third…
And back to the first…
Even more recently I discovered an old flexagon I made in middle school (I think). I’m not sure whether it officially counts as a flexagon, but it has more than two faces. In fact, it has four, and each consists of six squares in a two by three rectangle. With Thanksgiving I did not have time to explore it for this post, but it will appear at some point in the future!