Angles "In Real Life": Gym Edition

Want to hear something interesting?  At least twice a week someone arrives at my blog via one of these search terms:

"right angle in real life"
"acute angle in real life"
"vertex in real life"
"[geometric shape] in real life"

A couple more just came in as I was starting this post!  I'm never sure exactly what folks are looking for when they use those search terms, but I am always hopeful that once they get here they find what they're looking for.  I was thinking about all this when I was at the gym the other day and, as I walked around the track, I started noticing angles everywhere I looked.  I had my phone/music/camera with me as I walked so I started snapping some pictures.

As I looked closer I realized -- you can't have angles without lines.  Every time I found an angle I also found a beautiful interaction of two or more lines, with the added enhancement of a sunny day and its inverse, shadow.

The track is curved in places but the walls are straight.  This leads to some interesting intersections.  Here is an obtuse angle where two walls meet. There is also a lovely bisecting line that creates two acute angles where the straight boards meet to 'turn a corner' as it were:

All sorts of lines here!  Red lane markings run parallel to each other.  The metal what-ever-it-is runs perpendicular, creating right angles.  The wall comes into the floor at a right angle, and the light shining from the basketball court around the corner creates a lovely acute angle:

And the basketball court itself!  There are a lot of right angles here, and some lines that intersect but don't really make angles.  Why is that?

A rectangle must have right angles...

But its shadow doesn't!  Look at this lovely rhombular patch of sunlight!  Two acute and two obtuse angles of winter sun.

I didn't need a bench to sit on (my workout was basically shot at this point and my heart rate was still barely above resting) but if you do, hopefully you'll find a nice sturdy one made with right angles.

Looking out into the day, the window is divided by perpendicular lines which make right angles.  How many right angles can you find in this picture (both inside the gym and outside it)?

Behind the basketball hoop are the wires that help keep it suspended in air.  I see three intersecting lines that create an asterisk 6-star as well as six acute angles:

And more lovely shadow angles!  This is the big curtain that divides the two sides of the basketball court.  Look at the lovely obtuse angle the light creates!  

Outside the gym a plethora a lines and angles on the way to the parking lot.  

Sun and shadow get the final word. 

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Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

Happy Christmas to...Me?!?

The doorbell rang.  The kid immediately jumped up from her lunch and launched herself at the front door, yelling "I'll get it!!  Maybe it's something for me!!!!"

Yes, lunch time is around when the mail is delivered at our house.

I called after the fleeting figure, "It's probably for me. It's my Christmas present."

Door opens, cute little square package on the doorstep.

"What do you mean, for you?" the girl asked, incredulous.

"Oh, you know, Grandma sent us money for presents.  I've already bought the presents she wanted you to have.  She gave me and Papa money too so we could buy presents for ourselves," I countered.

We opened the box  She looked curiously at the two little packages.

"One of them says Crystal the other says Flora, " I said. 

"Open Crystal!!" she said.

"Okay, let's see what they look like."  I opened up the Crystal pack and laid out each card one by one. 

"And, look!  There are two colors on each card, one on each side."  I took a few and started layering them.  "What if I put this one on top? And then turn it?"

"Oooohhhhh!" we both squealed.

Then I opened the Flora package.  The girl was ALL over it.  "Let me try!!!"

I purposefully did not buy Kaleidograph for my daughter.  I thought about it, but after many, many months of being called "math mommy" in an accusatory tone, I decided that these could be my special toy.  Given her enthusiastic response, though, I guess I'll let her keep using "my" present whenever she wants! 

I loved playing the Kaleidograph game online, but I wondered if the hand-held version would differ.  Both Kaleidograph sets are lovely to handle and look at, and might be fun to trace onto paper as well. I'm glad I went ahead and bought the physical version.  Even if it's not really mine anymore!!

A List, Some Links and a Thank You!

I've been doing a bit of virtual housecleaning lately.  The Math in Your Feet website is newly and thoroughly updated, and with a new look to boot!  While making the shift to the new website I was inspired to formalize an idea that's been brewing for the last year, something I'm calling Math by Design.

I've realized that all the math and making stuff I've done with my kid, and others kids as well, over the last year is really an extension of the approach I use when teaching Math in Your Feet.  Math by Design: Paper Patterns is a story of one activity I developed for my summer programs but it is also the best description and illustration of the Math in Your Feet approach being applied to a medium other than percussive dance. 

I've also put a new list of "Key Posts" up on the right hand column of this blog, but I thought I'd share them here as well.   I think my favorites are Marveling at Moving Patterns and The Elephant in the Room -- both describe, in different ways, a moment in my math journey when I realized just how connected math (structure, order, pattern) is to our daily lives. Here's the full list:

Dance & Math
Marveling at Moving Patterns
A Big Discovery (Attributes)
A Moving Classroom: "Find Your Center"
Chicken or the Egg? A Math Integration Tale
Teaching Below the Surface
What You Can Learn from a Square

Math & Making
Solids and an Observation on Scale
Beading Attributes
Scissor Stories: Tales of Transformation
Stars, Factoring & Patterns
Math by Design: Paper Patterns

The Beauty of Math
The Elephant in the Room

Finally, I just realized I missed my 2nd blogiversary (back in October) so I'll take this opportunity now to say thanks to all of you who read, subscribe, follow and/or comment in this blog!  And, perhaps the Math in Your Feet Facebook page would also be of interest to you as well?  It's a pretty fun place, if I do say so myself!

Friday Fractal Fun! (Video)

Watch the world's biggest people-made fractal being made! Time-lapse, 90-second video. Awesome!!

Mathematical Star Ornaments

I've finally succeeded in bringing my daughter (age 7.5) completely over to the mathematical stars camp thanks to this post at The Crafty Crow called "Woven Cookie Stars." 

My daughter is (in)famous for knowing her own mind and possessing very firm opinions about what interests her.  More power to her, I say, but it's required some flexibility on my part.  Over time I've been most successful in influencing her interests when I engage in my own colorful math related projects and 'just happen' to leave some scraps around for her to work with...if and when she so desires.

It was in this environment that I embarked upon our mathematical star inquiry this summer.  The details of this journey can be found in my Seeing Stars post, but I will quickly point to the picture below as evidence that although she often feigns disinterest in the 'math-y' things I do, her mind and heart are still permeable and receptive to the beauty and complexity of math, including stars.  Here's a picture from the child this summer showing her thinking about how stars are structured (explained by her in the post Plant the Star Seeds, Watch them Grow):



We really haven't done much with stars since late August.  I was stalled after a lackluster experiment with 'spinning' stars around nails; the whole thing was just too futzy.  But when I saw Crafty Crow's post I knew it was the answer I had been looking for.

I have lots of cardboard lying around.  I have scissors.  I have spice jar lids to trace.  I have embroidery floss.  My daughter saw my first efforts last night and immediately had to try it out herself.  She used up the only sparkly embroidery floss we had on hand, so today we went to the craft store and she chose her own thread -- sparkly gold and purple and some lovely shades of green. When I said I wanted to take a picture of her stars, this is how she arranged them, in all their glory:

Mathematically speaking, she's figured out a lot all on her own  Her stars are all variations of twelve-pointed stars (12 stars).  She started by wrapping thread around the circle, sort of randomly.  From there she very quickly figured out how to make her favorite star, the six pointed star she calls "the Jewish star" which is created using two overlapping equilateral triangles.  She made about twenty of those, and the last ten were completely uniform.  I encouraged her to see what would happen if she made two more triangles on top of the 6 star and lo!  There was a 12 star that echoed her work in the activity I developed for her, described in the post Stars, Factoring and Patterns.

I also encouraged her to try and make an asterisk star and wondered what it would look like if she used a combination of colors.  I really wish I had her aesthetic -- her stars are so gorgeous.

Here is what I was working on while she followed her bliss.  Initially I wanted to see how many 12 stars I could make which led me to play around with layering one color/version over another.  On the left are set of {12, 5} stars, one in each color.  The next column is a {12, 4} star combined with an 12 asterisk.  I think I like the one on top the best.  The final row (far right) is my least favorite but still pretty.  It's a {12, 3} star (see the squares?!) with a thick asterisk. (Here's more about notating stars.)

 
Every time I finished a new version or my daughter tried a new color to overlap the sparkly thread we ooooohed and ahhhhhhed.  It was a delightful morning, to say the least.  Just for fun, I experimented with a 16 star.  A little too busy for such a small space, but I do like the the one on the left.

And, although most of my time was spent trying to keep up with my daughter's demand for "more circles!" I still had time to experiment with a snowflake feel.  'Cause, you know half of twelve is six and six is a snowflake.  I want to come back to this soon.

So, by now, maybe you're itching to get started.  Remember, all the instructions are at The Crafty Crow.  And, remember, both my daughter and I got started by just playing around with the materials. Our first two or three tries each were quickly discarded but the process was incorporated into these darling beauties. Have fun!