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.

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!


math sandbox

Last Minute Wrapping Paper

Lawler and Krieger
after Lawler and Krieger Click here for full sheet of printable paper

I am sure you still have a few presents to wrap.

I recently made some wrapping paper starting with images lifted from the twitter images of people that I follow. I liked the images so well that, well, if you need some last minute wrapping paper, you’re in luck, cuz I made more…

after Simon Gregg and Mark Chubb click here for printing

At it’s best, twitter is an interactive, conversational platform. As I was putting together these images I noticed that many of the images I was looking a had a collaborative component  before I lifted and fiddled with them.

after Dan Anderson's Moires
after Dan Anderson’s Moires Printing Page Click here

There are seven images here. After I started looking at through images of people that I follow, I felt like I could have stayed at the computer from now until Christmas, making these. But that would be silly because I wouldn’t get any presents wrapped.

after Malke Rosenfeld
after Malke Rosenfeld Click here for best printing 

If the originators of these images feel I have overstepped by taking their work, overlaying my own explorations on to them, and presenting them here, well, I hope they tell me and I will make polite adjustments.

made by me with Dan Anderson OP snowflakes
made by me with Dan Anderson OP snowflakes click here for printing

I had a hard time choosing from the really rich visual imagery that people are posting. Doing this gave me the excuse to scroll through peoples’ feeds, and I was surprised by how much I miss.

Martin Holtham-aug-29-1
Martin Holtham, modified Click here for printable page

I was quite sure that I was going to include something of John Golden’s, as he often dazzles me. But he recently posted an image of his daughter’s cookies, and, well, I couldn’t resist making wrapping paper from these delicious looking confections.

based on Isabella's, photo by John Golden
based on Ysabella’s cookies, photo by John Golden click here for printing

Now, just for the record, and in no particular order, here are the links to the tweets that I referenced, so, if you are interested, you can see how I meddled.

Addendum. 23 hours later…..I have never ever had a post that was viewed as often on its first day as this one. I guess lots of people have last minute wrapping to do. I suppose I will plan on doing a wrapping paper post every  December 24 from now on. Here are the presents I’ve wrapped with these papers: