## Saturday, May 12, 2012

### Big Math: Kid Sized Geometric Structures

Oh my gosh, look what we built!   This was not a small moment of math, no indeed.  This was a BIG math moment, one that took nearly all day (mostly because we had to figure it out for ourselves from start to finish).  And, it cost next to nothing and yet we gained so much.  In these next two pictures it's only about a third of the way done, but isn't it wonderful?

You can run around the outside of it, of course...

Or you can hang out inside it but, at this point, it's still not all that stable and there's a LOT more building to do.  But I'm getting ahead of myself -- here's how it all started...

Having just finished the entire Hunger Games series in one week I was left with nothing to read while the kid fell asleep except this.  It's a catalog that came in the mail and I was flipping through it when there it was!  Some kind of structure involving tubes of newspaper, making some kind of geometric form...hey, I could make that!  What's this?  \$40.00 for some connectors?  I don't need those connectors -- I'll figure out some other way!

That evening I figured out how to make those paper tubes and found out it's much easier and faster if you roll a section of newspaper around a dowel rod.  After it's rolled I tape down the long edge to the roll with clear tape and then slide the dowel out.

After making four or five of them I left it there for the night.  As I often do, I left the tubes lying around to be 'discovered'.  It didn't take long.  At about 8:30am the next morning the questions started coming in from the girl.  All I had to do was show her the catalog picture and we were ON!

So, we got started building.  I couldn't tell all that much from the catalog picture, but I figured it was at least a hexagonal base, and those triangles were reminiscent of the dodecahedron and icosahedron I made from straws and pipe cleaners this winter.  I figured this was pretty much the same process, just bigger.  This was our first big lesson -- the issue of scale.  Turns out, the bigger your structure is, the more effort it takes to make sure it doesn't fall down.

Anyhow, at least I had the tube figured out.  My rolling method leaves a pretty sturdy paper tube but it is somewhat time consuming to make a bunch and pretty much for the mama to do and the six year old to watch.  Luckily, my kid likes hanging around, soaking in the process, while making things like this are happening.  You can learn a lot by listening to your parents mutter to themselves!

But what to do for the connector?  Now that was the perfect opportunity to do some brainstorming with the kid.  After some experimentation we settled on a small amount of folded newspaper that made a nice connector, but only when two empty tubes meet.

For a connector that attaches to an empty tube on one end and an already-connected tube on the other, the kid and I finally figured out that a combination of paper and folded pipe cleaner would do the trick.  And it did, sort of.

It turns out that the points where five tubes meet need much more reinforcement.  In that case, use lots and lots of tape.  But I'm getting ahead of myself.

After finishing the hexagonal base and the first level of triangles we needed a break and luckily it was time for lunch.  How did it get to be lunch time so fast?!  We left it there for an hour or two but eventually both of us felt compelled to return to the project.  During our break I took a minute to look at the catalog picture and description more closely and discovered the following:

It was \$40 for connectors and 120 tubes around which to roll your newspaper...???  Why did they even mention newspaper in the first place?  With all those tubes, no wonder that structure in the catalog looked so sturdy!

I was pretty much clueless as to how to proceed past the first level.  I experimented with adding triangles to make a second layer, but it didn't seem stable or look right.  I said to my girl, "Hey, I think we need to make a model so we can figure out what we're going to do next.  I'll need help with that."

We pulled out the straws, I cut up some pipe cleaners, she connected the straws to make triangles, folded angles and helped me build the model.  Turns out this was a very helpful process.  What we figured out was that the second row of triangles needed to be connected by shorter edges (half of a straw length) if it was to have any chance of being useful.

Isn't it pretty?  Not sure what to call it, but at this angle it has the look of an icosahedron about it.

We applied what we had learned  in the model making process to the big structure and...it was still really hard.  Completely unwieldy.  Things falling, sagging, coming apart.  If those connectors had been close by for purchase, I  might have caved in and bought the things.  Since this was not the case, I had no other choice but to persevere.  I noticed the connectors had started failing and so I brought in the big guns -- tape.

It was actually an incredible lesson in physics.  When even one side of one triangle lost its connection to the structure, the whole thing would start to tumble.  The kid was in the center helping to hold everything up so that it wouldn't completely collapse.  I'll spare you the gory details but, short story, I was quite liberal with the tape and we did eventually get it to the point where it felt fairly sturdy.

At some point in the middle of this circus act I said to the child, "It's a good thing we're doing this ourselves.  If we had bought the connectors I don't think we would be learning as much as we are."

I wanted to leave it there, but the girl wanted the pointy thing on top, so we persevered.  And, what do you know?  Finally, finally, the thing felt whole, strong, sound.  Plus, the girl can stand up inside it!

"Mama, look!  A pattern!!  Up triangle, down triangle, up triangle.  Rhombuses!  Big triangle, narrow triangle.  And, uh, what do you call it? [running over to get the Cuisenaire rods to make the shape] A trapezoid!"

We even called over to our next door neighbors so they could come and admire our accomplishment, which they did and which is precisely why we like them so much.

"Mama," she said, "It's beautiful on the outside, but it's even more beautiful when you're inside it.  There's a flower up there."

Ah, the magic of math.  Structure, symmetry, order, strength, beauty.  Ours.

[Linking to Saturday's Artist at Ordinary Life Magic.  :-]