# #mathphoto16 and #symmetry Week 1

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I wondered a few weeks ago about the #mathphoto16 challenge.  It was fun last summer, looking for math around me.

Here are some things I noticed on my walk this morning.

The first picture I’ve noticed many times as I walk past my neighbor’s house.  The parabolic shape in the shadows is what first caught my eye.  What causes it to look like a parabolic curve?  Wondering… the symmetry of the parabolic shape I notice with the vertex on the line of symmetry.  But as I thought more, could I consider each shadow as a translation, then scale of the one before it?

The second picture of a black-eyed susie with some rotational symmetry.

I’m not sure I ever paid attention to the three types of leaves a Sassafras tree has until my daughter created a leaf collection as a 4H project recently.  Looking at the various leaves she picked along our road, I was reminded of the beautiful patterns we often overlook in nature.  I enjoyed listening to her compare the types of Maple leaves she found, looking at the leaf guides trying to decipher which tree each came from.

We learned some new terms as she searched for the names – was the arrangement opposite or alternate?  I see some reflection but also translational symmetry with those. Were the lobes pinnately or palmately arranged?  Again, translation / glide-reflection or a semi-rotational.  I see some good opportunities for rotational vs. point symmetry with pictures I’ve seen posted in #mathphoto16.

It was when she began inking the backs of the leaves to create prints that the true beauty became evident – so many details we never even saw before.

She has already begun looking at other trees – since next year, she will need to create a collection of 20 native trees different than the 10 submitted this year.