I tried making the curvilinear origami buds that I mentioned in my post Origami II. Here is the result:

They were a bit harder than I thought. These were my first two tries. I hope to get better as I practice. Some of my creases cracked on these.

My 7-year-old decided to design his own origami mountain. It’s actually kirigami since he did some cutting. Here is the finished product:

I thought it was wonderful. I told him at the outset that I thought such a project would be too hard, but fortunately he didn’t listen to me.

The kids and I also made some tetraflexagons:

These were easy to make and fun to play with. I later found out that these are more specifically hexatetraflexagons, since they have 6 (hexa-) faces each made up of 4 (tetra-) panels. There is a whole zoo of flexagons (tritetraflexagons, hexahexaflexagons, tridodecaflexagons, . . .), and probably more to be discovered. This is a young field of recreational mathematics and one that is ideal for non-mathematicians to participate in. Who knows, maybe one day there will be important applications of flexagon theory. Try making some that are found on one of these sites: flexagon portal, wikipedia flexagon article, and then experiment, genralize and think about how you can bend or break the rules to make new mathematical objects that no one has envisaged before.

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The buds and the mountain are both great.