Had a great time with our half group theory, half Zometool project last night:

Just after I finished writing it up I saw these two posts on Twitter from Fawn Nguyen:

and

These two posts made me really happy. First off, we both spent our night figuring out how to put a Zome cube inside a larger geometric structure. Amazing!!

Even more exciting, though, the specific shape in Fawn’s pictures reminded me of a fun story from this summer.

Every year we head to Cape Cod with a bunch of friends from college – this year we had something like 10 adults and 10 kids in the house. We knew ahead of time that one of the days was going to be rained out by the remnants of a hurricane and we needed to bring lots of extra indoor activities. I brought our Zometool set as well as our 3D printer to have some math fun with the kids.

Some of the kids told me that they don’t like math, but since they’ve been on vacation with me lots of times they know that there will be math and fun together. The 3D printer was a big hit, not surprisingly, and the Zometool set was even more of a hit. We did a couple of activities out of this Zome Geometry book,

but mostly the kids just played. One of the 11 year old girls who really does not seem to enjoy school math at all was particularly enthralled by the Zometool set. She build some wonderful creations on her own including this one:

If you look at the 2nd picture posted by Fawn Nguyen above you’ll see a cube inside a shape known as a “rhombic dodecahedron.” When you embed the cube inside of this shape you get to see 6 little yellow square pyramids on top of every cube face. Definitely hard to see that a cube fits inside the rhombic dodecahedron at first, but as I talked about in yesterday’s blog post, the Zometool set is such a great aid because solving these problems is so much better when you can hold the shape in your hand.

Now look at the shape built this summer by the girl who doesn’t like her school math classes. The important difference here is that the yellow pyramids are inside of the cube instead of on the outside. Actually she’s divided up the top and bottom of the cube in a clever way so that the inside pyramid equivalent to the outside pyramid in Fawn’s example is built out of several smaller pyramids, but that is a minor detail for purposes of this blog post. The really neat thing about her shape is that it shows you how to chop up a cube into 6 congruent pyramids, and that observation solves the problem posed in Fawn Nguyen’s first twitter post above! The volume of the rhombic dodecahedron is exactly the volume of two cubes – the one on the inside plus the one formed by the 6 square pyramids on the outside. That important second step comes courtesy of an 11 year old kid who doesn’t like math playing around with a Zometool set on a rainy summer morning. Yay!!

So one shape comes from math teachers’ circle group in California, and the other from a kid just free building, for lack of a better phrase. One shape from a group dedicated to teaching math, one from a kid who tells me that she doesn’t like math at all. Funny how fuzzy the boundaries can be sometimes, and amazing how useful the Zometool sets are in helping people see math in a different, and probably more useful, way 🙂