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,

Thanks for the tutorial on making a (mini-)Jacob’s Ladder at MOVES @PaulaKrieg. I do already have glitter all over everything though… pic.twitter.com/j4STZ2UfGV

— Dave Richeson (@divbyzero) August 9, 2022

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!

https://youtu.be/ILGg5xtqq-Q

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.

Beautiful Papers

I’ve had my head into making beautiful papers for different projects I’ve been working on. Thought it would be nice to give a peek at the different ways I go about making these papers. This, sadly, is not a “how-to” post, as each technique has so many steps.

The one thing that these all have in common is that I create them using the computer.. While I have great affection for making decorative papers by hand, it’s been my experience that if I want to use the computer to print papers that it’s best to create them on the comupter.

The paper at the top of the post is created in Adobe Illustrator, using patterning I’ve learned from Islamic Geometry tutorials. These patterns are great to when I am teaching folding methods, as I can size the designs so that the designs line up nicely when the paper is folded precisely. This has made teaching certain things so much easier.

Here’s an origami box, folded with my papers. More boxes below. Same pattern, different colors.

I use Islamic Geometry a great deal on my papers, but not always.

Sometimes I just create from the tools that are unique to the programs I am using. Illustrator’s flare tool is very fun to use.

This one is made by overlaying, resizing and recoloring a rarely used tool in Adobe Illustrator, called the flare tool. It’s hidden at the bottom of the menu that contains the rectangle and circles tools. I love having an excuse to play around with flares. This one I used to build a shape in which I placed the design inside the shape so it only showed when the light inside of it was activated.

Another way a create designs is by starting with graphs of equations. Even if I don’t understand the graphs that I’m working with, I have figured out how to play around with equations then work with the resulting graph.

Playing around with graphs isn’t hard once you get the hang of it. You can do it right now. Click this link https://www.desmos.com/calculator/b9bjax0qjf and then click the little arrows to start and stop the animation. See what happens. When I get something I like, I copy get the lines in Illustrator, create tessellations, and add color.

The pattern with the orange in it comes from the desmos graph. The blue pattern uses another set of equations. I like that the colored and uncolored versions are showing here.

This flower-like image is made from trig functions. Gold and silver embellishments were added by hand. This one ended up being a thank you card.

Now might be a good moment to mention that I just put a set of beautiful notecards up for sale in my etsy shop. https://etsy.me/3EGgXY2

While Illustrator is my program of choice, I do dip my toes into photoshop once in awhile.

I’m pretty much a novice with Photoshop. Maybe that works to my advantage? (Wishful thinking.)

I’ve discovered I can lay down a gradient, use some filters and the gradient tool and sometimes make some really gorgeous papers. It’s quite a random activity. Soon as a design shows up I save it. There is no recreating these.

These Photoshop generated papers have become all sorts of shapes.

With the holiday season coming, I’ve been using my Photoshop papers to make these paper ornaments.

I could go on and on with the different ways I put designs on paper. Here’s just one more.

The design above started as black and white lines on Dave Richeson’s computer, which then made its way to twitter https://twitter.com/divbyzero/status/1415049185573879817?s=20 then made its way to my computer. I did the coloring with Sharpies, colored pencils, and other markers. I did try scanning this, but I knew, from past experience, I wouldn’t like the scan. Here’s what I do when I want to make copies of hand drawn designs: instead of scanning the images I simply lay them on the glass of my copy machine and make copies.

Ushexahexaflexagon

Using the copy machine retains the feel of the hand drawing, which can be really nice, as long as no one looks too close.

There, so I’ve shown you the Islamic Geometry designs, the design made from graphs, flare overlays, random Photoshop gradient washes, and using my copy machine.

Now I need to figure out how to package up some of these items that I’m making so I can justify all this ink that I’ve been using! So easy to just have fun, the business part is still in process.

Color My Math

Here’s a true story. I was attracted to patterns of curved lines. Then I started to learned how to make them, using math.

That story took about sixty years to be true, from beginning to end.

The woman who lived next door had a spirograph. I would go knock on her back door. She would set up the spirograph for me. I would sit and make curves while she ironed clothes.

My mother bought wrought iron headboards for the twin beds in my room. I would sit and stare at the spirals, run my fingers around the curves.

It wasn’t until my own children were in high school that I learned that spirograph curves could be described by mathematical equations. I wanted to know how to do this. I mean, I really wanted to know how to make curves using math. I learned how. I’m still learning.

Every piece of jewelry a person wears has a story attached to it. I enjoy asking about these items. In the same way, the curves I make have stories. I’ve written some of these down.

A number of years ago an extraordinary woman from down the road started a free summer program for the children in this area. Kids were served lunch, they played, and listened to stories. When it was clear that more and more children needed a place to eat, learn, and play, current and retired educators stepped up to create an exceptional program. Parents drop off their children, the children are fed, offered swimming lessons at a nearby lake, and have engaging educational experiences at the community center. Local teenagers are hired as counselors. Local teachers and artists are engaged to design and teach compelling learning blocks. Kids are treated to visits from people in the community who come by and share their own interests and skills with groups. With help from many sources, this generous program, which charges exactly nothing, is continually growing.

This year I’ve decided to sell something to support our Lunch, Learn & Play program.

I’ve made cards of curves to color. On the back of the folded card is my story of each curve. I’m also including a web link to a graph to so the curious mind can see how math makes these curves.

Are you curious? Hop over to the link below. There is a blue dot on the bottom row left. Move that dot an see what happens to the picture. You will be dazzled.

https://www.desmos.com/calculator/8w11q1vzrt

There are eight different black & white cards to color, and eight envelopes too.

The paper that these cards are printed on Springhill Digital Vellum Bristol White Cover, 67 lb, the perfect paper for crayons and Crayola colored pencils since these marking items work the best on paper that has a bit of roughness to it. Markers work really well on this paper, too, which is thick enough that there is very little soak-through.

These cards for coloring are going on my Etsy site, where, through the month of June, all proceeds from these cards will be donated to the local children’s program.

If you know a someone who would appreciate finding out something about the beautiful curves of math, and you would like to support a truly wonderful children’s program, follow this link: https://etsy.me/3uJkJuk

Lines and Circles Workshop

Linear Mod Design by Carly, tenth grade student

Last night 15 people showed up at the library for a couple of hours to make patterns based on lines and circles. I don’t think anyone knew quite what to expect but that didn’t keep them from showing up. A brave bunch. The participants were tweens, teens, and adults. There was at least a 50 year gap between the youngest and oldest: it was quite wonderful to have this group all in one room, as each generation brings their own aesthetic, energy, and reflective questions with them.

by Cordelll, a ninth grade student

I demonstrated two ways of making designs: using lines (which I wrote about in my previous post) and intersecting circles, which people have been exploring for many centuries. I had originally thought I would show just the circles geometry, but then considered that some people might be really uncomfortable using a compass.  A few people just worked with just the lines, a few people worked with just with circles, and the rest did both.

Michelle’s

Some people were curious about the math that went into the number patterns that I gave them, and I explained it to those who asked.

Lauren’s

At the next workshop I will bring in my laptop and show Dan Anderson’s linear mod open processing page, as well as the tables in desmos.com to people who want to know more.

Siri’s, in progress

There was a great mix of approaches to this way of working.

Jenna’s

I embarrassed myself by not having reviewed the process for making the circle patterns right before the class. I had made many samples of the “seed of life” circles patterns, but then I had done other designs, and when I started demonstrating I got quite confused. I had to go sequester myself for a bit to reconstruct the pattern.

Quinn’s designs

One young man didn’t have any interest in coloring anything in. Not only that, but he decided to try out his own pattern of lines. Actually, he tried out everything he could think of, with both the circles and the lines, and ended up with a pile of papers filled with all sorts of designs. It was delightful to see him working out his own templates and number sequences.

Quinn’s Crane and Siri’s Drawing

By the end of the workshop this young man had started doing some origami, which he graciously gifted to me. I photographed (above) his crane with the work of an adult, because I so enjoyed seeing having all these young people and adults in one room, all together making art.

Here are some links for anyone who is interested:

The PDF to use with the line designs

Dan Anderson’s Open Processing Linear Mod page to see what’s going on with the line designs

Dearing Wang’s Circle Drawings

Next Tuesday I will do doing another one of these workshops! I’m looking forward to it.