Found Math

It's been over five months since I pretended I was Tana Hoban, the photographer who found math everywhere with her camera and turned the pictures into wonderful books for children.  Since then our eyes have been WIDE open, finding math just about everywhere we look. The more math we see, the better we become at finding it; the more math we find, the better we are at understanding it.

As my six (now seven) year old and I traveled around town this spring we found lots of shapes and patterns, parallel and intersecting lines, even spirals.  It's been your basic geometry kind of math, but we've had some incredible conversations about what we see and find. 

Lately, though, our math eyes have become remarkably more advanced.  For example, my daughter saw a tetrahedron in ropes staked into the ground, steadying a young tree.   I started the spiral inquiry, but she's the one that started seeing them everywhere we went, even places we go to regularly.  She still notices spirals all the time.  Recently, she found math in the most prosaic of circumstances...a moment of recursion in the restroom mirrors (one on each wall) at a local grocery store.   I guess math is everywhere!

As for me, my eyes have very recently been opened to stars.  I would have never recognized this particular star for what it is without the last week of exploration and inquiry under my belt.  There are actually at least four different kinds of stars in this picture.

And, here's an 8 star I also found today.

The stars and the rest of the photos are from our trip to the zoo and botanical gardens.  My daughter found some flowers that had dropped to the ground and shouted over to me, "Mama, look!  These have five petals!  A Fibonacci number!"

These circles were near the carousel at the zoo.  I love it!  And, that reminds me that, although it was impossible to get a picture of it, the carousel platform was round on the outside, but actually created out of twelve trapezoidal sections leaving an interesting hole in the middle -- a dodecagon!  Geez, I was really impressed with myself for seeing that one.

Channeling Tana Hoban: Juxtaposition Edition

When my kid was a preschooler, I used to stare wistfully at the Tana Hoban books at the library.  Because my kid rarely liked any stories outside of a narrative context, I knew there was no way she'd sit down with me to take a closer look.  Turns out, the thing I love more than looking at Tana Hoban's work is pretending to be Tana Hoban.

It sort of just happened, but the best things are like that, I think.  The plan was to do 'cheetah training' at the Y and then explore campus on an extraordinary morning full of sun and blue.   We completed the first part of the plan and started the second.  We really had no agenda but then things started catching our eyes.  The first one was the building with the intricately carved limestone decorations and the round tower four stories high.  What would it be like inside?  Should we go explore?  Yes!

Here's something we saw on the outside of the building:




















Turns out that if it's round on the outside, it's round on the inside, too.  How do you lay square tiles in a curve?




















And the view from the round tower was just as round.




















After a full exploration of Maxwell Hall (including an incredible ten foot limestone fireplace and a very mysterious and steep spiral staircase) we decided to continue our explorations outside.  The funny thing was that, even though we've spent a lot of time on this part of campus, we kept seeing things we'd never seen before...

Like hexagons!  Gorgeous ones!

Teeny tiny squares in a grid, inside a circle!

Hexagons in circle, around a pentagon!

A basket weave of parallel lines, in a circle!

A drain with wavy, curvy lines!

My personal favorite, a tessellation of rhombuses!  You don't see too many rhombuses out in the wild like this. 

Then it was time to got back to our car and go home for lunch.  On the way, we found even more designs, especially ones that expanded from a center point into a circle.

Flowers, too.

Concentric circles.  "And stars!"

A curve through the squares. 

And more.

So much wonderful design in this modest drain.

Trash can.

"Look Mama! More circles!"  Notice, more curves.  So lovely.

My favorite thing was finding shapes within shapes and especially so many different kinds of patterns with both straight and curved lines. This is a great example of what Maria Drujkova of Natural Math calls 'growing your math eyes.'  Once you've got 'em you see math everywhere!

If we go 'out looking' again, I'm going to pack two cameras, and some paper and crayons for making rubbings.