A Work in Progress: Paper Quilts & Hexagonal Rotation Designs

I am in the process of developing a paper quilt project for kids using a hexagonal design built from triangles.  Here's a picture of what my kid and I have done with paper quilts in the past:

The design incorporates lots of little triangles, but the end result is pretty square.  Not that there's anything wrong with that, but wouldn't it be cool if a beginner paper quilter could create something more circular using triangles? 

Yes!

Here's the book that was the inspiration for my hexagon-based project, as detailed in a recent post:

It turns out snowflakes are hexagonal!  But they look so different from what we usually think of as a hexagon...

source

There are endless tessellating design possibilities here which would be fun to explore with paper in the future, but I've got something else on my mind at the moment....

In her snowflake book, Paula Nadelstern shows how to design snowflakes using a "60˚ triangle" unit.  She doesn't say equilateral, but I think that's what she means. I read through her book and tried to get the gist of how she makes these beautiful fabric images; it appears the whole thing revolves around one single, accurate triangle template. 

Here's what happened when I thought I could get away with a random black-line triangle pulled of a google search, one that had every appearance of being an accurate equilateral triangle:

Not good!  Seems to be missing a few degrees.  So, I tried again.  In her book, Paula gives a formula that was helpful for constructing an accurate triangle.  The smallest one had a vertical length along the center axis of 2 3/8" and a horizontal length, to both the right and the left of the center axis of 1 3/8".  It worked!  Here's a picture of how I marked it out.  I cut out the triangle template using an exacto knife.

I made the template out of cardstock because it was all I had on hand.  I made it what I'll call the 'reverse' of a traditional-type template so I could easily see where I was putting the triangle on the patterned paper. 

As you can see, below, I was pretty successful at getting the same part of the repeating design in the same place on each triangle using this 'see through' template. 

Here it is, starting to come together:

And here is what it looked like when all six triangles had found their places:

Yay! I thought it looked really good at this point, but I wanted to see if I could give it just a little more shape.  

What I noticed in Paula's designs is that the snowflakes get their form by focusing the design at the edges where the triangles meet; one edge has half the design, the adjacent edge has the reflection.  Focusing on the 'spokes' (for lack of a better term) that are created where the edges meet (and create lines that radiate out of the center of the hexagon and through each vertex) ultimately creates the snowflake's design.  I think!

I had just enough time to try a small experiment to see if I could highlight the 'spoke' portion of the hexagon. After making a couple more measurements and lines I cut a new template out of the leftover 'insides' of the triangle template.

I think the final design looks more like a flower or a star, but I'm still pretty pleased.   

I think I'll try stripes next time and see what happens! 

While I was in the process of cutting out and placing triangles, my daughter got really excited about the intermediate shapes I was creating.  For the K- 2 set I think a great start to the project would be to give them some patterned paper triangles and some glue sticks and let them explore what kinds of designs they can make, observe others' work, and help them find ways to describe what they see.  Later, you could bring in some inspiring hexagonal designs (both your own and others') to serve as models for the rotational design element.  Once you spend some time deconstructing the examples it would be time to give the kids more materials and start the design/observation/reflection process all over again. 

I believe that, even with the younger elementary kids, the experience of putting six duplicate, congruently patterned triangles together to make a hexagon has the potential to reveal the complexity of this shape in a new and inspiring way.  I, for one, am seeing hexagons in a whole new light.

For middle and high school students the challenge of building the perfect template for such a project could easily catapult this whole investigation into some really cool mathematical inquiry.  (Plus, I like the idea of giving them a choice, at first, about whether to use a 'pretty good' black-line template or the measuring method and let them compare the results!) 

Finally, to make this a viable project for multiple children I really need to find a easier way to prep a large amount of paper triangles.  Does anyone out there know what kind of cutting tool might be able to do this?   I'm planning to play around with this some more, so stay tuned!