I absolutely love the #MathArtChallenge! Here are some reasons why:
- These challenges are incredibly accessible AND considerably complex. Annie has engaged a wide audience in recreational mathematical thinking. In a lot of ways, this is exactly what we try to accomplish with Play With Your Math.
- Annie’s warm and encouraging attitude sets the perfect tone. She is generous with positive feedback and appreciation. She models and preaches flexibility and self-forgiveness. I love how she occasionally abandons her plans when a new idea pops up and how she elevates her contributors and sources.
- Everyone knows that math can be useful, but rarely do we experience mathematics as a form of self-care. These challenges have helped me take my mind off things during difficult days and to feel accomplished when I feel stifled. I’ve asked my students to complete a challenge every week, and a few students have shared that it has helped take their mind off things too.
Below is my work with the #MathArtChallenge so far and a little reflection on each. I’ll try to update as I continue playing.
Day 1: Tons of triangles
I didn’t do this challenge right away because I didn’t anticipate why it would be interesting. When CiCi told me how much she enjoyed it, I finally realized why I was supposed to make SEVEN triangles. I love how this reminds me of hyperbolic geometry, which shows up a few other times here.
Day 2: Looping Colors
This was fun and easy. I’d seen something like this before, I think from James Tanton’s Without Words. I got the most student responses for this one.
Day 3: Isometric Cube Cutouts
This was hard for me, but I’m really happy with it! It took me a long time, and I felt a real sense of accomplishment.
Day 4: Hyperbolic Geometry
I love origami and hyperbolic geometry, so this was wonderful!
Day 5: Probability Designs!
This one was only okay for me. I didn’t know what to choose for the different dice rolls, and I wish they had a more cohesive image at the end, but it definitely took my mind off things.
Day 6: Circle Toruses!
I’ve been working through Samira Mian’s introductory Islamic Geometry course, so this was great practice with a compass.
Day 7: Cardioids!
These took a LONG time, but I find the shapes fascinating. I love the idea of curves made from lines.
Day 8: Apollonian Gaskets
I had to push through some perfectionism for this one – I wanted the circles to be perfect, but that would have taken forever!
Day 9: Comparing Origami Butterflies
I used one piece of origami paper for each color of butterflies. I wonder how I would make 3 …
Day 10: Arrays
I looked all around my apartment for arrays to capture and came up empty for a couple weeks. Then, I played codenames with some of my oldest friends and aha! FYI: I was on the blue team for this game.
Day 11: 8-Pointed Star
This was great practice for me. It feels really satisfying to see all the circles and lines that went into making these starts.
Day 12: DRAGONS
This was really hard. I couldn’t get my first method to work, so I tried another. In the end, I traced the previous imagine, rotated the paper, and traced the image again. I lots track of things a few times, so I started putting a little S to show which end I started with.
Day 14: Hitomezashi stitching (from Katherine Seaton)
I thought of so many questions while making this! Do the two colors cover the same area? Are the two colors broken into the same number of sections? How many single squares of each color are there? What is the biggest section of each color? Are the colors more/less evenly distributed than in other examples? My selection of 1’s and 0’s has some symmetry – where is that in the picture?
Day 15: Isometric Illusions
This was really hard for me, so I tried to do something relatively simple. It took me a while, but I’m really proud of the result.
Day 16: Mondrian Puzzles
I saw this as more of a puzzle than art. I’d love to go back, try it some more, and then make my answers pretty.
Day 17: PERMUTOHEDRONS
The Boston Math Teacher’s Circle played with permutohedrons on zoom and it was a blast. Each group had their own google slide and it was really interesting to see how they used that space.
Day 18: Celtic Knots
I have loved watching Annie make these – and I would love to play with these more – but this took me a long time and a lot of focus.
Day 19: Alternating Knots
I liked how low-tech and accessible this was. Usually knots are fairly intimidating, but this felt quick and easy. These challenges have stoked my curiosity about knots.
Day 20: Origami Icosahedron
I love modular origami! It’s my math art comfort zone. I hadn’t done this one before, and I really enjoyed it.
Day 21: Agra Fort Islamic Design
This was at the upper limit of what I feel capable of right now with Islamic geometry, but I am really satisfied with how it turned out. It looks simple but was actually really complicated to make.
Day 22: Extending Day 14 …
I feel like there are a lot of good questions that could come out of this … but also, my version felt kinda sloppy so I didn’t want to think about it much more.
Day 23: Brunnian Links
I wanted to try this right away, but I didn’t know what to use. I looked all around my apartment and realized I had lots of straws and could connect them like in the straws thingy. It worked great for 3 loops, but it was really hard with 4 because they don’t have a ton of flexibility. It was fun enough that I wanted to give it a full effort …
So I ordered some more yarn, reminded myself how to crochet, and sloppily figured out how to add snaps. Then I tried again. It made a world of difference to be able to twist and pull the loops around, and I realized I could transform the 4 loop version into the bottom image, which had a simpler structure. I extended that structure to a 5th loop and can easily keep going! I also realized that you could attach the ends together, making me curious about how many different ways there are to make these links … Overall, this is probably the challenge I have spent the most time on and gotten the most satisfaction from.
Day 24: Polygon Midpoints
The coolest aspects of this challenge were spoiled for me on Twitter, but that’s fine. I was surprised by how slowly the third one collapsed to the center.
Day 25: Tessellations
I’m fascinated by tessellations, but I always feel unartistic making them. I want to make some cool image but struggle and feel self-conscious. I decided to riff on Annie’s example and make a puzzle piece with different symmetry. The coloring took longer than I expected. Overall, I felt accomplished because I pushed through some discomfort.
Day 26: Golden Spiral
I’ve done this plenty of times, but it was satisfying to use a compass and add some color.
Day 27: Golden Icosahedron
I got halfway through the string part before I realized I had no plan for how to get to all the corners. I took it out and started over, but I still felt like I was taking a clunky route. I want to try this again some day and 1) decorate the cardboard and 2) find the best route for the string.
Day 28: Toilet Paper Edition (from Mark Kaercher)
This was quick and easy. I felt like I wasn’t being that creative, but then I let that feeling go.
Day 29: Paper Roll Polyhedra
This is so clever! It took me a little while to get a hang of the mechanic, but then I found a good rhythm and it came together nicely.
Day 31: MÖBIUS
This is cheating a bit because I didn’t do this during the pandemic. I like to have students play with Mobius strips on Valentine’s Day because I think these hearts are cute. I enjoy seeing students roll their eyes when they get the final product.
Day 38: Chirality
I first learned the word chirality from Vi Hart’s Hexaflexagon videos, and so that’s how I chose to represent it here. I wish the marker hadn’t bled so much, but oh well.
Day 39: Flowered Dodecahedron
I enjoyed the change of pace that came from cutting out the template for these. From there, this was pretty straightforward for me.
Day 40: Flexagons
I will always have a soft spot for flexagons. Vi Hart’s flexagons videos came out during my first year of teaching, and they were one of the first ways that I tried to engage students in recreational mathematics along with me. I had made tetraflexagons, trihexaflexagons, and hexahexaflexagons in the past, so I decided to try something new and made a dodecahexaflexagon using these directions. It’s a little fragile in places, but it works! Seven years later and they’re still engaging for me.
Day 42: Origami Octahedron
I’ve made this before, but it was years ago. I love the idea of using it for 3D coordinates and I want to try that someday.
Day 43: Sprouts!
In one of our first zoom calls, I introduced my students to the game brussel sprouts (a variant of sprouts). We played a couple games to get the hang of it, which was fun and got them trash talking and active. I asked them to try it with someone at home and this photo is one of their games at home.
Day 45: The Lotfallah Mosque Dome
I’ve seen this image on math twitter several times and always thought it was really pretty. It was gratifying to finally make it for myself. The only challenge was starting with a small enough circle to fit everything on the paper, and I had to start over once because I wanted three rings of squares.
Day 46: Origami Firework (from Yami Yamauchi)
I love modular origami and I am so glad that Annie posted this challenge! Making the final connections was pretty tricky, but the end result is fun to fidget with.
Day 47: Origami Cube with Windows
I made one of these years ago, and it was still on my bookshelf. These cubes are impressively stable. But I didn’t realize you could link them, so I went for it! It took me a few days to make 12, and the last connection was tricky. I decided that it looks like a wreath, and it’s now hanging on the closet door. Gravity turns it into a bit of an ellipse, and I’m not sure how long it’ll hold …
Day 50: Chair Fractals
I took a break from pencil and paper math art challenges for a couple weeks and this was my reentry. It took me a couple hours, but the focus required helped me relaxed and I was able to watch some TV at the same time. I made some mistakes along the way but was able to erase and move on without judging myself. I’m really happy with how it turned out. I think I originally wanted to go one step further but I did not have the patience to be careful with that many lines.
Day 55: Hyperboloid (from George Hart & Elisabeth Heathfield)
I’ve made these a few times before, so I decided to include it even though I didn’t make another one now. These photos are from 2014 when our fabulous math team would spent our Friday evenings doing fun math and – as Sara demonstrates in her snuggie – trying to stay awake until a respectable bed time. Fun times!
Day 56: Hyperbolic Crochet (from Danai Taimina)
I actually made this a couple weeks before Annie posted it because I wanted to remember how to crochet. Most of my experience with crochet is making these awesome hyperbolic surfaces. Shoutout to David Butler and Megan Parise Schmidt for teaching me how to make these at TMC.
Day 58: The Miura Fold
As I’ve said above, origami is my math art comfort zone, so this was calming and fun for me. It was hard to make creases with so many layers at some points. The final product is really satisfying to fold and unfold.
Day 63: Super Tic-Tac-Toe
I played Ultimate Tic-Tac-Toe with students on our first zoom class (we used this site). It helped break the ice. I asked them to play against someone or the computer as part of their first assignment. Above is one of their responses. Not sure if they were the winner or not, but it looks like it was close! (Note: The website blurs the game when it’s over.)