Tag 'Harvard'

With 45 more swords, this pattern could be extended into a full icosadodecahedron-type shape, where the sword blades make the triangles and the handles make the pentagons. With rigid swords, the shape would even hold itself together with no wire or glue. As it is, it makes a very nice hat:

And then it was time to go. I had a wonderful time, met many wonderful people, and had a big wonderful space to play in. Here's what it looked like as of yesterday morning:

I want to emphasize the improvisatory and collaborative nature of the week. Most of the time, I had some sort of vague plan/inspiration, and it was really through the help and input of other people that things ended up being awesome.

I'd say "Hey, I got these things. Let's try connecting them like this and see what happens. Then maybe we can hang it somewhere or something." We'd try it out, see what potential problems were, and do some bugfixing. The result was an amazing week and a big room full of fun stuff.

I'm interested in finding a longer residency of this sort. And looking forward to hopefully returning to Pfoho next year!

It's made of 32 baskets arranged like the faces of a truncated icosahedron (that's the shape of a soccer ball). The 20 "hexagons" are in shades of blue and green in a 5-color pattern. The 12 red baskets are like the black pentagons on a standard soccer ball. It's a little imposing to sit under. Here's how the dining hall looks, as of last night:

There were clothes hangers, dolls, clipboards, and protractors.

Here's some vertically-oriented photos.

There were also sponges, plastic containers, crayons, and wooden spoons.

The people at the crayon table were extra diligent, staying longer to figure out how to make a crayon-tip polyhedron and how to use the wrappers to fold intersecting tetrahedra.

Inspired by the three-fold symmetry clothes-hanger arrangement someone had made, I later grabbed some help and made this:

Then it was umbrella time! I made the residents start unpacking the umbrellas, and went to get some materials. I know that my mathemusician-in-residenceship has had some effect, because when I got back, this is what greeted me:

Awesome. Then we got started on connecting the umbrellas into a hyperbolic plane. Between us all, we figured out a good way to build and display it. Then something magical happened. Some students had the idea of writing poetry on the umbrellas, so we got out some white-board markers and turned the hyperbolic umbrella surface into a big collaborative writing/drawing space.

I love collaborative sculpture! I'm thrilled with the result. It would have never happened without the creative input of many people.

I decided they should be a giant dodecahedron. I guess I'm at that point in my Mathemusician-In-Residenceship that I can gesture vaguely and people will know what I'm talking about, because after explaining just a little, I was able to sit back and drink juice while everyone else did the work (I didn't even have to take the photos! These are by the lovely Janice He).

The dining hall is beginning to shape up rather nicely.

The Harvard Crimson also put out this nice video covering the events from the balloon workshop the night before:

Various groups of people wandered in and out of the dining hall throughout the evening, and we made a bunch of different things, including some snub pfolyhedra in Pfoho colours.

It came together nicely! Thank you to everyone who helped, whether it was by constructing, hanging, or cheering us on.

There's also a photo of me demonstrating some balloon techniques on the front page of the Harvard Crimson. I also just bought a ton of supplies for the workshop I'm giving on Friday, which should be pretty crazy, so don't forget to come by if you're around.

For some residents, being trapped wasn't all bad.

If you take your paper cross (which you can cut from a square in a single straight cut, if you fold it in half three times) and put a mobius twist in each of the loops, the result is quite different! I first heard of this trick from Mike Caputo (who has an article about it in the Jan/Feb 1990 issue of TOMT), and there's a nice YouTube video by Daniel Keogh demonstrating the process.

Soon we moved on to exploring new shapes to cut in half. I especially like this variation, by Anne Goetz: start with an eight pointed asterisk, and connect opposite ends with a twist (be sure to twist them all the same way). The result was very surprising to me. We explored more, and it seems to generalize to all Mobius asterisks with 6 or more points. I'll let you try it for yourself, rather than ruining the surprise.

Another student, Carlos Rodriguez-Russo, found a variation that when cut in half yields a trefoil knot. And if that's not enough to keep you entertained all night, here's one last puzzle. What asterisk shape, twisted how, gives the result below when cut in half?

I'm quite excited by all the cool cut-in-half things we discovered last night. It's going to be a fun week.