At the National Museum of Mathematics

Math, Art and Puzzles in the City

Geez, had I known the math people have such a knack for playing around with materials to make exuberant visuals, I would have found my way back to math years before I did. I just recently got back from the Museum of Mathematics (MoMath) MOVES conference, celebrating recreational mathematics, which was finally scheduled after pandemic postponements. A few years ago I had been at another one of MoMath’s conferences, focused on paper folding, which was simply stellar. This one focused on puzzles and games, and, wow, what a visual feast.

Didn’t take many photos, as I was mostly taking it all in. But did get a few…

The amazing designs of David Plaxco on Rubik’s cubes

I got a close-up look at David Plaxco’s designs on Rubik’s Cubes. Mind boggling and stunning. I’ve been watching David’s work on Instagram, cubes_art but being able to hold some of his cubes and see all their sides was quite a thrill. I had spoken to him years ago after meeting him at previous conferences, and was intrigued with how he was thinking about seeing knots on cubes, but seeing where he’s taken this work was such so uplifting.

Chaim Goodman-Strauss with his hyperbolic creation

I also got to be in the room with Chaim Goodman-Strauss, who I’ve been hanging out with weekly this summer in MoMath sponsored Polyhedra Party sessions, where we’ve been building with paper. Here, though, what Chaim has done is used interlocking mats to create wildly big and beautiful hyperbolic surfaces. I love that his blackboard scrollings got into this photo, too.

Chaim with Suzanne and family

Chaim brought a huge amount of modified rubber mats to New York, and ,was heroically assisted by the museum’s director, Cindy Lawrence who (if am remembering this correctly) carted through the city, via cab, so they’d be ready for us to use to make these enormous waving surfaces.

There were so many fun details to enjoy. For instance, when I asked Lauren Seigel for her card, here’s the spread I got to choose from.

Image by Bob Hearn

The above photo is a print that Bob Hearn gave out after his talk called The Fractal Beauty of Compound Symmetry Groups, where he showed us one stunning image after the other, and how they evolved through orderly overlapping of shapes. His was the last talk of the last day, so I was pretty happy just to sit in the auditorium and watch the pretty pictures.

I had proposed a family workshop for the event, but this time around, probably because of the times we live in, there weren’t many families at this conference. Still, I had a small but mighty group come to do a tricky make-and-take project,

The mini-Jacob’s ladder made by Dave Richeson’

What we made is very much like what some people know as a magic wallet, though what I showed is able to be extended in the traditional toy, the Jacob’s Ladder, hence I call it Li’l Jacob.

To practice what I’d be doing at the conference, I made a video of the steps. Pretend you are in the room with me, and give it try!

As much I as I liked being at the conference, and enjoyed getting back to the city that was my home for nearly twenty years, the conference days happened on some of the hottest days of the summer. Outside, I fried.

Was happy to get home to green grass and flowers.

Drawings · Knots

Knot Obsessed

Celtic knot

I didn’t see this coming. A full month without posting. Here’s what happened.

Sometime after the pandemic isolations began, I slowly began noticing postings that were actively and enthusiastically bringing people together to fold, draw and build things together. For instance, Anne Perkins demonstrated a hundred days of projects on her blog and Clarissa Grande introduced monthly twitter hastags like #Maydala #GeometricJuly which were introduced with video tutorial support, and other little groups seem to pop-up here and there to work on something together, What’s happened with me is that I was swept away with learning new stuff from so many other people. Rather than creating content, I’ve been happily devouring it.

I think I will be writing at least a few posts, sharing some of the cool stuff I’ve been looking at, starting with knots.

Celtic Knot, Paula Krieg
Celtic Knot, Paula Krieg

No question about it, I like knots. Have been drawing them, on and off, for decades.

sketchbook page
Knots from 2012

I had seen Celtic Knots, but hadn’t paid much attention. Finally because of Annie Perkins post and which includes this video I decided to try one out. It wasn’t just her post that inspired me, it was also all the people who created and posted knots after they made them that caught my attention. I was still a bit slow : Annie posted in April but I didn’t get to this until August. Thought I spend one day with it.

I started getting carried away. What I realized was this: Even though starting with a standard grid makes total sense to me, I realized I could make knot that had, well, wonky grids. I loved discovering a way into creating my own grids. This means that if I have just a pencil and paper, I could amuse myself indefinitely making these knots. I can’t tell you how much this idea appeals to me.

Wonky Celtic, P Krieg

These wonky knots were really hard to do. I’d spend a great bit of time trying to figure out how to get them to work out just right. Sometimes I’d fail to get them to work out. The knot above has five separate strands.

Here it is, close up.

The next one is based on a larger number of crossings but is just one continuous strand.

I tried lots of ways to color this one in. I was happy with it once I was done, but wasn’t happy with any of the photos, except for this one:

These have been great fun for me. I feel like I am never going to be finished doing them, though I have slowed down a good bit.

It’s dawning on me that it might be a good thing to do a little video tutorial on how I go about making these odd knots. Besides enjoying making these myself, I think that making these would be great activity for kids as they could be as complex or as easy as is appropriate for each child. They are so much fun.

Ok. So fully intend to post a video. Here. Within a day or two.

Addendum: Here’s the video. Good luck with this!

Art and Math · Geometric Drawings · group project

Rotational Symmetry project with 5-9 year olds and Moms

I got to spend some time with a group of kids and moms this past Sunday. They had asked me to plan a math/art project for them. Last time we did this we played with shapes scaled according to the golden ratio. This time I wanted to help them make images that are made by rotating a graphic around a circle. We used a circle that was divided into twelve equal sections, and we got to talk about how rich the number 12 is, in that it comes up often in measurement of time (hours, months), quantities (dozen), distance (Inches) and so much more.

Images were made in two ways. One was to connect the dots around the circle according to a rule, such as connect the first dot to the fifth, connect the fifth dot to the tenth, connect the tenth dot to the dot that is plus+5 further around the circle, then continue until you are back where you started from. A star emerges!

Connecting the points around a circle

We started the afternoon by sitting in a circle of eight people, and doing the skip-counting activities that I described above. This was actually a thrill to me, as it’s something I’ve wanted to try out for a long time. As the star shape grew within the circle of people, who were the “points”, everyone was thrilled. They had no idea a star would emerged. I knew, but I was thrilled too.

I had PDF printout of circles and shapes.People cut out shapes that they wanted to rotate around the center, then colored them in if they wanted to.

I think the young man who did this image is about 8 or 9 years old.
I think the young man who did this image is about 8 or 9 years old.

The moms seemed to like this activity at least as much as the kids.

I never know how these projects will go. A couple of the boys didn’t want to be coloring any more after a while. One boy in particular really liked cutting paper, so I got him started with another kind of rotational symmetry: making snowflakes!

Snowflakes have rotational symmetry
Snowflakes have rotational symmetry

I hadn’t thought about snowflakes beforehand, but liked the way I was able to link to something that was already familiar to this group.

After awhile one of the girls was finished with coloring, I showed her how to make an origami pockets that were sized for the drawings to slip into.

Lot of pockets
Lot of pockets

She really liked making the pockets, and made them for everyone. This also let me segue into showing her how to make a square from a sheet of paper.

In the end, we had made lots of images, pockets, snowflakes and our work area was delightfully messy. Everyone helped with the cleanup, especially with the tiny pieces of paper on the floor.

At the end we put our tiles out on display.

Our tiles
Our tiles

A couple of hours later one of the mom’s texted me saying that, on the way home, her kids were asking to do more of these. YAY!