Kaleidocycles and Tetrahedrons

February 19, 2017

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I looked up the definition of a tetrahedron today, I figured out how to spell kaleidocycle a few hours ago. Just saying.

kaleidocycle-colors-1 Paula Krieg

Pattern for one kind of Kaleidocycle

Sometimes an exploration pursues me. It’s always a gift to be preyed upon by ideas, but if my desk is already full and messy, and I think I can’t bear adding one more layer I pretend to kind of ignore the newcomer. No, this strategy doesn’t work.

I didn’t know that tetrahedrons were following me around. Like I said, just this morning I finally looked up the definition (a solid having four plane triangular faces; a triangular pyramid).

The image above is where this all started. This is not such a startling set of pictures until you know that the image shows the same, unchanged structure viewed from front and back. It’s on the facebook page of someone whose name is written in an alphabet I don’t understand. This is the link to the page on facebook https://www.facebook.com/artsmathematics/videos/718044448365422/ . Take a look if you can. It’s such an amazing bit of transformation, which I have yet to figure out how to do. What’s going on here is that this structure to made up of connected 3D shapes that rotate together to reveal different surfaces. It’s very tricky and fun to see the shapes turn, revealing new surfaces.

The next piece of this story is that a teacher just a bit south of me in Upstate NY posted some directions on how to build a certain  geometric shape, and he asked, via twitter, if anyone would be able to test drive his tutorial. It looked simple enough to me, so I thought I’d try it out the following Saturday morning. I thought it would take about 2o minutes. Ha ha.

Tetrahedron

Tetrahedron

Looking back, I think if this teacher, Mr.Kaercher, had done a tutorial on a simple tetrahedron it might have gone more quickly and I might have finished up knowing what a tetrahedron was. But, no, Mr. K provided directions for a tensegrity tetrahedron, and since I didn’t have much of a clue about the definition of either term, I didn’t really have much of an idea of what I was doing.

Tensegrity Tetrahedron

Tensegrity Tetrahedron

Even so, after a megillah of failures, I got it done and was quite pleased with myself.

In the meantime I was still thinking about those images from that facebook page.

I showed the FB clip to book artist Ed Hutchins. He told me that what I was looking at was a type of kaleidocycle.

Oh, and Ed just happened to have a hot-off-the-presses copy of what is probably the world’s most amazing example of a hexagonal kaleidocycle, designed by Simon Arizpe. (This is a fully funded Kickstarter Project, which you can view to see the book in motion.)

This structure tells a story as it rotates. Since these rotating sides can turn forwards or backwards, the sequence of the story is determined by the direction the viewer rotates the kaleidocycle. The way that I choose to turn it, it begins with a bear peeking out at a stream…

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…the bear opens his mouth, a salmon jumps out…

The Wild by Simone Arizpe

The Wild by Simone Arizpe

The Wild by Simon Arizpe

The Wild by Simon Arizpe

… and then the salmon jumps into the river. There’s one more frame, but I’m not going to be a spoiler and show it to you.

So what does this have to do with tetrahedrons? I’m getting there.

As it turns out, the last couple of times I’ve gone lurking at the Lawler family math page, they’ve been looking at, yes, tetrahedrons.

This shape that the Lawler’s were considering was beginning to look familiar to me. Part of the reason for this was that, ever since Ed had given me the gift of the term kaleidocycle I had been Googling around then assembling kaleidocycles.

Kaleidocycle, unhinged

Kaleidocycle, unhinged

Here’s one of my first attempts. Notice that I forgot to attach the ends together before I closed things up. This turned out to be a good thing, because, wait! these shapes appear to be repeated echoes of the shape that the Lawler family was exploring.

Just to pile it on, it certainly helped that just yesterday a package came in the mail, all the way from France, from Simon Gregg. In the package was, can you guess?… a tetrahedron.

Tetrahedron from Simon Gregg

Tetrahedron from Simon Gregg

That Saturday a few week ago that I tried, time after time, to create my tensegrity tetrahedron, I had been posting my failures publicly on twitter. I imagine that Simon thought that it might be merciful to send me some bamboo, as the straws that I was using would sometimes collapse. Included with the bamboo rods, Simon also gave me a collapsible tetrahedron, held together by stretchy cord.

With all of these pieces floating around me it,  I finally made the connection that units of kaleidocycles are series of tetrahedrons. 

Kaleidocycle/tetrahedrons

Kaleidocycle/tetrahedrons

So cool.

Now to reward you for making it all the way to the end of this post, here is a pattern for a kaleidocycle that you can make yourself.

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click the image to get the printable PDF

Just cut it out, use it alone or attach it to the one near the top of this post, but, in either case, do  make sure you attach ends to make it circular. Here’s a pleasant little video to show you how it’s put together.

I still intend to figure out how to make the kaleidocycle that I saw on FB. When I do sit down and try it out, at least, now, I feel like I’m starting with some helpful understandings.

I have no big attachment to figuring it out for myself, so if you are inspired to decipher it, please let me in on its secrets!

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That’s it for now. Thanks for staying with me through these meanderings.

playing-hockey

I’ve been going through last year’s  photos of projects that children created when I visited their classrooms. What a visual feast! I’ve added a whole bunch of these photos to my page on the sidebar here called  Gallery of Student Work.   If, like me, you  enjoy looking at student work, go take a look!

Re-Framing a Lesson

January 28, 2017

Bookmaking with First Graders

Bookmaking with First Graders

OMG Have I got a teaching tip for anyone who has ever pulled their hair out trying encourage students to make their drawings bigger, to fill up the page. It’s only taken me like 25 years of working with students to figure this out. This is big.

Filling up a page with a drawing

Filling up a page with a drawing

There’s this variations of a bookmaking project that I do with mostly first and second graders that includes a drawing. The bigger and bolder the drawing is, the better it looks in the book. Needless to say, it’s such a struggle for this age of student to make their drawings big enough.

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Usually I give the students the paper that their drawing goes on and do everything but beg them to draw bigger. Well, sometimes I beg. Then, yesterday  (Friday)  Carter, a 7 year-old in my first class of the day, suggested that, before they start their drawing, I  lay the paper inside the frame that will surround it. It had never occurred to me to do this, so I tried it out in my next class of the day.

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Unbelievable. In my next class, after sliding the paper behind the frame before the drawing began, every single student filled up the paper with large bold drawings to go along with their stories.

Never has this happened before.

Maybe it was just a fluke, maybe this class had been bribed enough times to fill up the page that they now did it instinctively. I had one more class to go.

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Next class, same thing happened. They filled up the space with big drawings.

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Some students lifted the frame away after the first part of the drawing was done so that they could make their drawings even bigger. OMG I was so happy. My conclusion: if you want students to make a drawing to fill up a space, FRAME THE SPACE with a dark frame! I don’t know why it works, but far be it from me to ever think I can fathom what goes on in the mind of a 7 year-old.

Now here’s the part that gives me chills…I have to ask myself, why did Carter put forth his suggestion? I give credit to this: recently I was impressed by reading Malke Rosenfeld’s book about engaging students in whole body learning. While I teach different subject matter than Malke, I am deeply impressed by how she gives her students permission to explore the learning space before she begins her lessons. I took this to heart, and this week, for the first time, within certain boundaries, I encouraged students to fold and unfold, then explore and examine the materials that we were using together. In some way I think this sense of engagement with the materials led Carter to making a suggestion that was based on what would have worked better for him. I already know that my best teaching tips come from the single digit crowd, I just don’t always know how to tap into them.

So thank you Malke, thank you Carter, and OMG I am so happy.

 

Women’s Work

January 26, 2017

Just when I needed a to be uplifted, Judy Kinzel wrote this blog post. Judy and I don’t know each other, but the fact that she had felt encouraged and empowered to make such awesome work after going through my posts, well, it means so much to me. Be sure to visit her site and look through her Chinese Thread Book gallery. I’ve been thoroughly inspired by her work!

Purple Tree Studio

Throughout the history of art, decoration and domestic handicrafts have been regarded as women’s work, and as such, not considered “high” or fine art. Quilting, embroidery, needlework, china painting, and sewing—none of these have been deemed worthy artistic equivalents to the grand mediums of painting and sculpture. The age-old aesthetic hierarchy that privileges certain forms of art over others based on gender associations has historically devalued “women’s work” specifically because it was associated with the domestic and the “feminine.”  (Elizabeth A. Sackler Center for Feminist Art)

In the 1970’s I had the good fortune to see Judy Chicago’s installation The Dinner Party when it was in Boston. The thirty-nine place settings celebrated a variety of incredible women – writers, scientists, activists, artists – and reflected the history and geography of each woman with media associated with women’s crafts. (Click her for more on The Dinner Party)  It…

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