in which I ‘fold’ cubes with others

A while back I posted some dice ‘folding’ I did that was inspired by Eric Aberg. While I was working on it, the thought crossed my brain that it would be extra fun to do this with teachers at PCMI. I figured I could probably get a small group together some evening and have some fun.

picture of the group that showed up to fold cubes.

See? Just a small group for an evening of math art shenanigans. If you look closely you can spot @crstn85, @zaduma, and @matienda.

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fun with folding dice

I posted the video below on my facebook back in March when I made it and as I ponder topics for #MTBoS30 I thought I would post it here as well.

Inspired by Erik Aberg’s Ghostcube video, I ordered some reject casino dice and went to town with them and some packing tape (after discovering scotch tap is useless with sharp-edged dice). I highly recommend giving it a go if you want a fun project.


Thinking about folding

Ever want to give each kid in a class a piece of patty paper and have them measure out a line of length l somewhere on it and then tell them that’s the hypotenuse of a right triangle and then ask them to drawn in that right triangle (but it has to fit on the paper they have)? Then take all the papers and line up all the l‘s?

Because I do. Though I’d probably also throw in that isosceles right triangles are boring and that I expect more interesting angles from them.

These are the semi-random musings that interrupt my reading. Bonus points for anyone that has a class do this and send me pictures  [:


in which I recommend classroom origami

My old classroom held relics from the students I taught each year. The day before winter break was one that I always took to talk about origami, show some clips from an awesome documentary, and teach the kids a few basic things. Recently on twitter some folding pictures happened which spawned me to fold which lead to classroom origami talk. I’ve shared this a bit before over at Global Math, but thought I would document a bit here.

PHiZZ 105 torus

Exhibit A

Every piece in this was done by a student of mine. Not all the kiddos signed their pieces, but many did. There are 5 of these in my old classroom–one for every year I taught at the school except for the first one due to a storm canceling school the day before winter break (I know, right?). I did, however, put it together. I’ve found few kids have the manual dexterity + patience needed to assemble a large one of these so I do that myself over the break. Here’s what it looked like before I started:

box of PHiZZ pieces

box of PHiZZ pieces

If this project looks huge (100+ pieces?!), never fear. Part of the beauty of the PHiZZ model is that there are various sizes you can make with the same module. Kiddos who get into origami often like to start with the 12-unit (cube!). You can also do 30-unit or 90-unit versions. And yes, you can go higher then those.

where to learn
I learned how to make the PHiZZ Units from this website back in college. Now we have the benefit of Tom Hull himself instructing how to make the unit in a youtube video.  I don’t show videos on how to fold in class since I like to go at the pace the class needs (and the pace a precalc class needs is much different than the pace of an algebra 1 class) and use the document camera. Now, the above torus is a variation on the typical balls people make.

Many of the books I have are well out of print and inherited from my grandmother who taught me how to fold when I was very young. I mostly do modular origami and I like pretty much anything by Tomoko Fuse. There are lots of rubbish websites, but OrigamiUSA has some free patterns and links to local origami organizations.

One of my favorite things about the PHiZZ model beyond the lovely creation at the end is that you can use paper from Staples Memo Cubes to make them. I actually don’t like PHiZZ models made with origami paper as most origami paper is either too slick, to thin, or both. Good washi paper would work, but it’s not worth the cost. I would typically purchase 2-3 of these cubes at the start of the school year and use them to teach some basic origami as well as using them for student reminders (they are bright).

other thoughts
As i was working on this last night30 pieces

I started wondering how do you teach this type of patience? In college I thought nothing of spending the 2-3 hours focus and make a 90 piece PHiZZ model. I find the process completely absorbing and satisfying in the way working a big math problem and coming up with an elegant solution is. How much of the origami side of my nature has influenced the math? How much more accepting am I that good things (beautiful things!) take patience, trial-and-error, puzzling over directions (sometimes in Japanese, which I do not read even a little bit), struggling and putting them down for a breather lest I rip them in half so I can come back later with fresh eyes.

More importantly, how much can teaching students origami help them build up those traits? Listening carefully. Immediate feedback. Attend to precision.

Start with the figures that only take a dozen folds. Do the ones that move or jump because those are so satisfying. Then do harder ones. Make origami a warm up one day a week. Smile with thanks at the kids leaning over to help their neighbors. Congratulate the ones that struggled last week but get this weeks’ figure. Encourage the ones growling in frustration to keep trying and slip them an extra sheet before they leave in case they want to try again later on their own without peer eyes on them.

Tonight I’ll be working on this module pattern. Happy folding :]

in which I plot in origami with friends #TMC13

Hey all! Heading to TMC13? Like art? How about origami? Have some time on the plane/train to do some folding? Awesome. Let’s begin!

The Inspiration: Madamoiselle Maurice and an image to honor our hosts

Colors: blues and yellows (Drexel colors–don’t stress about the shade as some variety will be nice). Shoot for a 4:1 ratio of blue to yellow.

Figures: Birds (in blue, because it’s Twitter Math Camp) and pinwheels (in yellow)

Sizes: Try to keep the paper under 7″. Like shade variations, size variations will also be cool.

I’ll be working with some inside sources to find a good spot for the final project. The goal here is a group art project that’s mathy, a homage to our hosts and something to visually capture what I feel is one of the themes of the Mathtwitterblogosphere: that together we create an awesome, giving community.

Q & A:

But, Ashli, I really love to make this other type of bird. Could I fold those blue birds instead of the design you suggest?
Of course. Like cranes? Fold cranes. Just keep in mind that you want a design that lays relatively flat to make it easy to affix to the wall.

What about butterflies? can I make blue butterflies?
Just make sure it has wings, people. We need some cohesion with this design.

Can the yellow ones be other shapes? Like hats or little tshirts?
If the power of Gauss compels you, then you go for it. But try to stick to un-organic things for the yellow.

I don’t have any paper, but I’d be into folding when I arrive at TMC13. Will there be any paper I can use there?
Currently working on acquiring some to have in stacks for people who want to help out with this. I’ll also have some boxes to put finished projects in. If anyone has spare paper and wants to bring it along, that would also be cool.
[Update: Thanks to a speedy Amazon order, a bunch of 6″ origami paper is getting delivered to The Math Forum offices on Wednesday, July 24th. I’ll have it out somewhere obvious during the opener so you can grab some and fold while you listen.]

Is this something that I’ll be able to take an epic nerd-photo in front of?
Yes, yes it is. Not that I would ever get 100+ people to fold paper in order to assemble an epic backdrop for math-nerd photos *cough*

Thanks for reading! Super excited to meet you all at TMC13!

in which 3d graphing is explored

While I’m not sure about all school districts, in mine there is this awkward time after the seniors have graduated but before the rest of the school gets out. In classes where all the kiddos are in the same grade, this isn’t a problem. I have never taught a math class where every kid was in the same grade. Since I taught some (technically) 4th year classes, however, I do my finals during the ‘senior’ finals time and that leaves me a week or so with the students who remain. Typically I like to spend time covering a special topic.  I chose to explore 3d graphing and had them make these in 2011:
y = sin(x)*cos(z)
And this in 2012: