Mini 2

Well, I managed the more symmetric tail. And maybe the legs? But the head, despite the more careful folding at the beginning, got almost completely lost when I had to reverse-fold it at the end and couldn’t find the middle. Oh, well. Too bad I don’t really like gum. Anyway, Elisabeth asked for a better gauge of how big the dragon is, so here’s the second attempt guarding its treasure and the pair trying to fend off a larger relative (one of my favorites, made from 9″ square paper).

Autumn Leaves at Albany Airport

I was walking through the Albany airport a couple of weeks ago, when I looked up and saw one of the most brilliant artistic concepts I’ve seen in a while.

The artist cut maple leaves out of gold foil and suspended them from a skylight by transparent threads. Since each leaf was only attached to the ceiling by a single thread at its center of balance, the leaves rotated in the slight breeze generated by the airport’s air currents.

The effect of autumn leaves slowly fluttering down from the sky was altogether convincing (and all the more striking for occurring in the middle of a sterile modern airport). But it’s the simplicity of the technique that I find the most striking. No virtuosic skills would be required to make something like this–any of us might easily replicate it with scissors, nylon thread and gold paper. The genius of the artist rests almost entirely in his having seen that easily acquirable materials might so easily be combined to create this evocative natural effect.

Here are a couple of pictures, courtesy of the Albany Airport website

So…does anyone have a suggestion of another exquisite application for these effects?


As a dragon, it’s hard to be awe-inspiring when you’re only an inch long. For instance, unless your folder was really, really careful, you probably won’t have any legs. Or eyes, for that matter. But on the whole, I think I did pretty well with this one. Of course, it doesn’t have any legs or eyes, really, but it’s almost too small to be able to tell that they’re not there. It’s made from a 1.75″ square piece of gum wrapper, and, except for the head, it’s probably about as precisely folded as my first attempts at this model (on 9″ square paper). I admit, I used a pin to help with some of the smaller folds (especially having just cut my fingernails, my fingers just don’t get that precise), and the foil backing helps tremendously.


I ate another piece of gum today, so maybe I’ll try again. Maybe this time I’ll be manage eyes and legs, and perhaps I’ll even try for a more symmetric tail.



I wanted to make tangrams for my school, and I discovered that lined 3”x5” index cards are perfect for making tangrams! This is because the distance from the top line to the bottom line is exactly 2.5” and the lines are 1/4” apart, so the middle line is marked.

To make tangrams out of an index card:
0. You could cut off the top and bottom outside the lines if you want, to give yourself straightedges and not get confused. Or you can do that at the end, and use another index card for a straightedge and perpendicular.
1. Fold the index card in half, to make two squares, and trace the resulting line. Draw the diagonal in one square to make the two big triangles. Make sure to check that the two diagonals meet at the center card-line, thus:

It's hard to see, but the topmost index card is showing the diagonal on the bottom, which meets the pencilled line in the middle.

It's hard to see, but the topmost index card is showing the diagonal on the bottom, which meets the pencilled line in the middle.

2. Start the diagonals in the other square, but only to the center point of that square (which, again, you can find using the index card’s middle line). Now you have the medium-size triangle.

3. Using the other index card to make a perpendicular line, draw a vertical line halfway up in the middle of the second square. Mark the same line at the top. Now you should have the square and one small triangle.

4. Draw the last diagonal from the side of the card to the midpoint of the top line, so that you have the parallelogram and the other small triangle.

I am in the Madrid Café at 45th and Sansom, Philadelphia.  The owner was happy to try tangrams.

I am in the Madrid Café at 45th and Sansom, Philadelphia. The owner was happy to try tangrams.

I also discovered a tangram alphabet, whence the title picture.

Finally, I made my own “paradox.” I’m sure this has been done and googling will reveal it; nevertheless, I invented it myself. 🙂 Having gone back to tangrams with a much more mathematically trained mind than I had as a child, I always consider the lengths of sides and parallel positions and so on, so it’s much easier to solve tangrams and to puzzle out things like that.

Wait, one of the squares has a hole in it...

Wait, one of the squares has a hole in it...

Wet-folding Origami

In my last (and first) post I said I’d try wet-folding, because some of these models seem to require either thinner or more malleable paper. So I decided that the African Elephant would be a good place to start, partly because the pattern (although tricky) doesn’t have very many folds overall (and doesn’t require any particularly precise folding), and partly because the instructions suggested it. So first I folded it in the usual way (i.e. with dry, normal paper):

Elephant (dry)

It worked, more or less. The hand-drawn instructions failed me when they tried to describe the fold for the tusks, but I made something up, which seemed to work. The model, however, only gives the general 3D shape of an elephant, requires a certain amount of paper-sculpting at the end, which is hard to do with normal paper.

So I took the advice of Wikipedia and wet both sides of a piece of paper using a damp kleenex, to ready it for wet-folding (using, of course, the same type and size of paper as before, albeit of a different color). As I tried to manipulate the paper I  noticed a couple of things:

  1. The paper I’ve been using has a grain–most of the fibers run in the same direction. If it’s wet equally on both sides it doesn’t wrinkle much out of the plane, but in the plane it expands different amounts along different axes when wet. So to start off, my paper wasn’t square. Like, really not square, with a difference of maybe a third of an inch (out of seven inches) between the two directions. But I was afraid it would dry out if I wasted time trying to trim it, so I just ignored it, and did all of my folds to within a 1/6 inch error. Good thing the pattern didn’t require much precision.
  2. The color on the paper is water-soluble. I could swear I ended up with almost as much color on the tissue I was using to wet the paper as on the paper itself.
  3. My (unvarnished) wooden table-top is much dirtier than I had thought. It turns out that wet paper picks up a lot of dirt. Of course, the more I tried to wipe off the dirt, the more color I lost…
  4. In this condition, I started folding the elephant, completely botching the folds leading up to the tusks, which in turn made even my makeshift tusk-fold impossible (I sort of skipped that part, just twisting the tusks into existence, which seemed to work, more or less). And I noticed some more things:

  5. Wet origami paper does hold creases (I’d been rather suspicious that it wouldn’t at all), but they become very hard to see after a while.
  6. The paper dries quite quickly. That is, too quickly to finish folding a (simple) elephant. And furthermore, re-dampening a semi-3D elephant with a wet kleenex is hard.

Anyway, here’s how it came out:

Elephant (wet)I suppose the non-crease folds tend to be somewhat smoother, and the model holds its shape better, but if I was hoping to use wet-folding to facilitate folding through thick sections in complex models, I am bound to be disappointed unless I can significantly improve my technique.

Conclusion:  Next time I should try using a spray bottle, a ruler and exacto knife, and a clean, non-absorbent hard surface, and maybe I’ll be able to make a better elephant.

This is what happens…

…when Caltech doesn’t give me any work for the first two weeks:


Of course, since I took that picture, several more models have been added to the collection. I’ve been going through the nicer-looking models on Most of the ones I’ve been doing are listed under ‘complex,’ with a few under ‘intermediate,’ but I can for the most part place them into categories as follows:

  1. Straightforward and elegant. Which is not to say easy to fold with little prior experience; it merely means that I could understand the instructions, didn’t run into any problems in the folding, etc. These tend to make nice, simple-looking, and furthermore, recognizable models the first time around. (This category includes the eagle, caterpillar-on-a-leaf, and chameleon near the front of the picture, and probably the shark, as well.)
  2. Hard, but elegant. Similar to the first category, but requires either a long period of staring at the diagrams from oblique angles in an attempt to make sense of them or else going to outside help, such as youtube videos of the folding process. Of course, this category depends on prior experience, but there are definitely some folds out there which just can’t be portrayed in a 2D diagram. (This category includes the dragon, pegasus, horse, and perhaps the wasp in the back, although that might fall under category 4, below)
  3. I’m stuck. Of course, anyday now these models might move to category 2, but as it is, these are the models I’ve tried and altogether failed to make. For instance, there’s a sea-turtle pattern that looks nice, but halfway through, having apparently understood all of the instructions hitherto, my model inexplicably no longer looks like the diagram (Sea turtle not pictured… maybe someday I’ll put up a picture of its current state… I think I threw away the blue crab.)
  4. Straightforward in theory, but impractical. That is, I understood what I was supposed to do, but couldn’t do it. You know how they say you can’t fold a piece of paper in half 7 times? This category includes all of those models which want you to make clean creases through 30 layers of paper (not as many as 2^6, but still impractical). (This would include such nigh-unrecognizable models as Dr. Octopus, an alien as from AVP, and the grasshopper, as well as an unrecognizable unfinished model on my desk, whose instructions started asking me to pull out almost non-existent flaps I couldn’t reach.) Many of these, though, might benefit from the art of wet-folding, which I have yet to try. I’ll post more when I get around to it.
  5. I suppose there’s also Technically Interesting but not particularly pretty, which includes the hedgehog and maybe the armadillo (and to some extent the shark, though it actually looks pretty nice if you squint at it). These tend to take a long time, but end up pretty angular and not so lifelike. On the other hand, if you need something to do with your hands while you talk to your friends, try folding 200 hedgehog spines (not on the hedgehog pictured here, but the more complicated model, which I foolishly gave away–so of course I had to make another. But I wasn’t foolish enough to make the complex version twice).

If people want, I can post pictures of individual models with little blurbs about what I did and didn’t like about them, the things I changed/ignored, etc.