Flexagons · folding

Video Tutorial for My Flexagon

About a month ago I zoom-taught a group of about 200 people how to make this very sweet fidgety flexagon that I had created. The Museum of Mathematics hosted the event.

As I want to show this to anyone who wants to learn it, I (finally) made a tutorial video of my flexagon.

Start with any square, or the cool graphic above, which is my work. I love this version with the MoMath logo on it.

Here’s the video:

A big shout out to MoMath, who, once again, were a pleasure to work with!

If you make one of these, send photos! Have fun.

Flexagons · geometry and paper

Flexagons and Me at MoMath

Some time ago I created this new kind of flexagon. I’ve kept the secret to myself long enough that I’m ready to share it. The Museum of Mathematics is hosting my reveal through their events program, via zoom, this coming Thursday, August 12 at 6::30. flexagon.momath.org. I want everyone to join me there.

There are many different kinds of flexagons. All of them can be folded into different configurations to reveal hidden sides and to show different patterning. I am enthralled by this genre of paper folding.

Some flexagons are quite tricky to fold. I think of this one that I’ve made as being elegant because it’s super easy to fold. It’s one of those things, that after you know it, you wonder why hadn’t you figured this out yourself.

I want everyone who likes my work to sign up for this event! It’s only $10 to join, and you can have your friends and family sitting with you with the same link. What’s even better is that proceeds will be benefiting the museum itself.

I’ve wanted to do this at MoMath because, throughout the lock-down, I’ve been so impressed by how MoMath kept up their programing via zoom, with programs for everyone from young children to senior citizens. The wide range of people they supported with their programs was truly impressive, and quite affordable including many free events, and lots of $5 sale events.

Oh, one more thing.

I’m making a graphic available for people to decorate. I designed this graphic specifically for my flexagon. I’m not sure if the museum will be distributing it (I think they will), but if not, I will make it available directly for people who sign up.

Gather together a couple of sheets of regular copy paper, glue stick, scissors, scrap paper, and four paper clips.

Be there or be square.

It would mean the world to me.

flexagon.momath.org.

Flexagons · geometry and paperfolding · summer art/math

Hexaflexagons in the Summertime

Molly’s

This past Wednesday was my third three-hour meeting with a group of teenagers I am doing projects with this summer. I’m getting to know these young people a bit more, which is the best part of what I do.

It means a lot to me to be able bring projects to them which they enjoy, that are dynamic, and that might teach them something new. I missed writing about last week’s project…oh well.

I’ve been planning three things per week. My thought is to start with with something really short but really cool. This week I started with this amazing puzzle I saw on a post by Mike Lawler :

What you’ll see if you watch this video is a square piece of paper that has a square cut out of the center which a CD must fit through. It looks impossible. It’s quite mind blowing. Take a look.

The main event the afternoon was making hexaflexagons, which I’ve written about numerous times. Basically, they are a tricky foldable structure that, as they flex, transforms the patterns that are applied on them.

For instance,

Jordan’s

these are two views of the same sides of the a flexagon. The way that the paper folds rotates the sides to create an illusion that you are looking at something entirely different.

 

It was great fun to watch these teens discover the different transformations of their designs.

These cats were a surprise. Mostly people were doing purely geometric designs. I had no idea how these cat motifs would work out. Just loved how they paired up!

The fellow that did this one, with the black square and the blue and red circles within, has surprised me during each class. He leaves me wondering if he’s going to participate at all and then I look over after awhile and see that he’s done something stunning.

 

Here;’s a PDF for 11″ x17″ paper. You need just one of these strips of 10 equilateral triangles to make a hexaflexagon

We made the flexagons using a template I created. What is needed is a paper strip which folds into 10 equilateral triangles, so this template I made can be used to make four separate hexagon-flexagons.

For some reason I kept messing up showing the group how to fold. One of the older teenagers, who’s position is counselor, really understood the folding well, so I took a video of her explaining how it goes:

If you still haven’t seen enough, well, I took just a couple more fun photos of the work of this talented group.

the drawing

the Transformation

So cool!

There was one last project we did during the last half hour together. It was doing some origami, but I had them each cut out a separate rectangular piece of paper. Each rectangle was a different size but proportionally the same. I have a thing about scaling: I want all kids to know how to do it.

Similar rectangles

After the paper was cut, I walked them through the steps of making an origami toy boat, not because I wanted a toy boat, but because I wanted to stack the different sizes and see what happened. Each person had a different size paper

This is what happened.

It stands on it’s own, and looks kind of like a ziggurat , or maybe it looks like a big hat.

I think we decided it looked like a hat.

After having spent most of the afternoon making flexagons with this group I came home and checked my twitter feed. Coincidentally, seems that my friends had been all atwitter about flexagons, starting with this from Vincent: https://twitter.com/panlepan/status/835988773875892224

Link to Dave’s PDF

Within the thread was a link to Dave Richeson’s template and instructions for what he calls a Cube Tri-Hexaflexagon, but it’s what I’ve been calling the hexaflexagon.  I made one of these immediately. It’s a great template.

 

Ok. It’s nearly time to start planning my next project with this group. Looking forward to it!

 

 

 

 

Arts in Education · Book Art · Flexagons · group project · Paper Toy

5th Graders’ Kaleidocycles of the Bill of Rights

Piling Kaleidocycles
Piling Kaleidocycles

They did it! This group of fifth grades did this hand-lettering kaleidocycle class project! I described the details of this project a few posts back so check out that post for more details. Here’s the general gist: After introducing the project, which is a 3D paper construction with rotating faces that will be graced with references to the Bill of Rights, students were given pages of letter fonts to choose from.

Tracing

Using the windows of the library as light boxes, students traced out letters to created one phrase each that described one of the first ten constitutional amendments, aka The Bill of Rights.

At the window

Every single student was highly engaged. Really.

Within two class sessions the students produced something that I could take home and scan into my computer . I won’t lie..scanning and cleaning up their work took time. Above you can compare what they gave me, on the left, to what I ended up with on the right. Some pages required much more work than others. The middle example above was so easy to work with that next time I will encourage students to just give me outlines. The most time-consuming letters to work with were those that were colored in and touching other letters. I moved things around a bit, like in the top example you can see I centered the word “OF.”

I brought home their work, scanned them into my graphics program, cleaned them up and laid them into a kaleidocylce template. Brought them back for students to cut around the perimeter and score.

Scoring the paper
Scoring the paper

Students made score lines so that the paper would fold easily and accurately. Scoring is generally done with bone folders but we used glitter pens to score the lines. They worked great, and kids were excited to be using the gel pens.

Assembling the Kaleidocylce

Then came the folding and gluing. I didn’t take many pictures of this process as I was, like, really really occupied helping move this process along.

One of four faces of the Kaleidocycle
One of four faces of the Kaleidocycle

This project turned out so well. Not everyone had a chance to finish up and decorate, but the wonderful school librarian will be able to help with the few than still need finishing.

Kaleidocycle yellow borders
Kaleidocycle yellow borders

Students enjoyed individualizing their own kaleidocycles.

Another side
Another side

I tried to get them to use completely different color schemes on each face, so that the differences between the four rotation of faces were dramatic. Students didn’t much listen to my suggestions.

Here’s one of their kaleidocycles in action:

I consider this project a great success. I got to talk to the students about design, about hand lettering, and they got to work with some cool geometry. I’d even go so far as to say that they are also much more familiar with the Bill of Rights , as they were constantly asking each other, which one do you have, which one is yours, and talking about their own.  I have to say that at first the students were confused about what I was asking them to do, after which the librarian told me that doing a group project was pretty much out of their experience, so the concept was hard to grasp at first.

One thing that made this possible was that this was a small class, just 12 students. I often work with 60 to 70 students in a grade level: I wouldn’t do this project with a big group. OH, but it was so delightful doing this with a small group.

Tower of Kaleidocycles
Tower of Kaleidocycles

Do I get to pick a favorite project of my teaching season? Yes? This is it.

For more about all this take a look at these posts:

https://bookzoompa.wordpress.com/2017/02/19/kaleidocycles-and-tetrahedrons/

and

https://bookzoompa.wordpress.com/2017/03/19/designing-a-seriously-fun-project/