## Tuesday, September 11, 2012

### Weaving Fibonacci

I'm still exploring how to use paper weaving specifically to engage elementary students in mathematical inquiry.

So far I've found that paper weaving has the potential to open up discussions of different kinds of symmetries, encourage exploration of inverse operations, and support inquiry into how number multiples can influence design.  That's what I have at the moment, but I'm sure there's more.

The other night I asked myself, "How could I weave Fibonacci numbers?"  I picked three colors for a warp (vertical strips).  Green=2, Blue=3, and Purple=5.  That gave me a warp of ten.  I had already played around with weaving multiples of five...

...but this was a completely different process.  I wove with a weft (horizontal strips) using a simple over-under weave, but used the same color/number pattern as the warp.

Holy cow!  Do you see what happened?  I got square numbers!  Green=4, Blue=9, and Purple=25!

It was late but I decided to try one more Fibonacci warp.  Instead of weaving 2, 3, 5 for the weft as well, I played around with a basic over-under weave with red, orange, yellow, orange, red... as the color pattern.  I love the little orange boxes with alternating red and yellow centers that resulted.

Looking at these two pieces again I have a bunch more ideas for playing around with warp, weft and weaving pattern in relation to 2, 3, 5.  But, I so love when artistic inquiry and mathematical inquiry merge like this, to such beautiful and interesting results.  It's what we do in Math in Your Feet and it's clear to me that a design approach is perfect for integrating math with other mediums as well.

p.s.  The Math in Your Feet Facebook page is developing into a fun place for me to share interesting bits of mathematical art and design.  I'd love to have your company over in that space as well!